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BooksPart1 23 Jun 2006 - 14:00 CatherineJohnson






rma.jpg




0805829083.jpg

two fantastic books



Elaine McEwan's website





CalStateStudyIntro 23 Jun 2006 - 13:36 CarolynJohnston


Part 1 in a mini-series on a review of quality math ed research articles.

In 1998, the California State Board of Education contracted with a group of education researchers from the University of Oregon to conduct a review of high-quality mathematics education research papers. The resulting 100-page report is available here.

Their task was simply to search out all the mathematics education research that had been performed and published within a specified period, cull out the stuff that was of dubious quality (meaning it had unsound experimental underpinnings, or was performed in a setting that was not like a classroom, or had one of a number of other flaws), and see what the remaining studies had to say about mathematics achievement (that is, they avoided papers that did not measure study outcomes quantitatively, using tests of achievement; so studies measuring the impacts of changes in teaching methodology on students' confidence, for example, weren't included).

The results are surprising to me in places. There were studies on the use of manipulatives, studies on kids working with their peers, studies on the use of computers, calculators and technology, studies on motivational methods, and studies on the design of instruction. The researchers seem to have avoided bias, and to be genuinely searching out high quality research. I thought I would do a 'mini-series' describing and discussing their results, section by section. Stay tuned.



California study intro
California state study of group learning
California Board of Ed study part 2
education research - peer reviewed studies - chart





NewComments 07 Jul 2005 - 20:47 CatherineJohnson


SteveH has a new comment about Base 5 & fuzzy math in the CompareAndContrast thread.

update: More from Steve!

Thank you!

I love this, especially:

when my son was born, I told my mother that I wanted 3 things for him in life: 1. To care about other people. 2. To know the value of hard work. and 3. To be happy. Her response was that if he did numbers 1 and 2, then number 3 will take care of itself.

And this:

If Everyday Math (as an example), thinks that doing things in different ways is helpful, then why do they completely avoid the standard algorithms (the best ways)? While doing Singapore Math with my son at home, he ends up doing a number of things in different ways than his EM at school. This can be helpful, or it can be an overload of the brain.

I think SteveH is also the commenter who pointed out that ed school students are taught constructivist teaching methods via direct instruction.

I say that's not fair.

If our kids have to discover math, ed students should have to discover discovery.

Guess and check, guys!

Lots of sharp observations on math & practice, math & creativity, math & solving problems more than one way here: ILikeMath



AGoldenHello 28 Jul 2005 - 23:48 CatherineJohnson




If Parents Fret, Do SAT Tutors Cost $685/Hour? A) Yes (Update1)

Now that is a really golden hello.


via: Joannejacobs.com



FromAroundTheEdusphere 06 Sep 2005 - 04:32 CarolynJohnston


Here and there in the "edusphere" I've seen mention of Professor Plum. He's a fellow educational radical (as I've grown to think of people who favor actual instruction in the classroom), and today I checked out his website.

I learned, among other things, that Direct Instruction actually refers to a very specific method of instruction, and to a commercially available set of curricula. It's not just what happens when I Directly Instruct Ben on how to do a math problem, as I had thought. Professor Plum has a lot of material on it here, if you're curious.

But on a quick perusal, I wasn't attracted to Direct Instruction. I couldn't find what I thought was a sufficiently clear description of what Direct Instruction is about. I learned that it is scripted interaction between teachers and children, and that a great deal of teacher training is needed to implement it properly -- all of which statements I've also seen recently in the Connected Math context. I'd like to see more beef, up front and center.

One of Professor Plum's links also took me here, to a site for parents on how to develop contracts for children that help them achieve academic success. I really like this guy's ideas, which are built around a principle I've been using to good effect around here since Ben was a little toddler, namely bribery. It's not really bribery, of course; it's merely setting up a system of targeted incentives intentionally, rather than accidentally setting up the wrong ones haphazardly. There are lots of good suggestions and examples on this website; a lot of detail of the sort that makes you braver about actually implementing his suggestions.

I also did very much like a recent post of Professor Plum's, entitled Basic Features of Effective Instruction. This post is a gem; it summarizes the features of effective teaching very well, I think (I'd love to know whether KTM teachers agree with me on that!). While reading it, it struck me that I hadn't seen teaching methods of any sort described with such clarity since Ben was very young, and I was working with Applied Behavioral Analysts to implement the Lovaas curriculum, which is designed to treat young autism-spectrum children. There is no tougher customer to teach than a very young autistic child; they are extremely disinclined to pay the teacher any attention at all, and they are often not motivated by the things that motivate typical children (like praise and attention). A teacher can't mess around; her message has to be crystal clear, and her incentives have to be right on. Many of the principles he outlines here are typical-kid versions of those one uses in Applied Behavioral Analysis, to decrease confusion and ineffectiveness (and no surprise either, since he has worked with autism spectrum kids in his career). A terrific post.



WhatIsConstructivism 14 May 2006 - 17:18 CarolynJohnston


AndyJoy asked on this thread: Can someone explain extreme constructivism to me? Is the problem that proponents never want to introduce the standard algorithm for a problem or make children memorize facts?

The short answer is yes, but for the record, here is a fuller explanation. I think the best quick introduction to constructivism and its recent history in U.S. educational practice is Barry Garelick's An A-maze-ing Approach To Math, which appeared in Education Next this year. I'll excerpt a little piece of it to answer Andy's question, entirely without Barry's permission (but hopefully with his blessing).

Discovery learning has always been a powerful teaching tool. But constructivists take it a step beyond mere tool, believing that only knowledge that one discovers for oneself is truly learned. There is little argument that learning is ultimately a discovery. Traditionalists also believe that information transfer via direct instruction is necessary, so constructivism taken to extremes can result in students' not knowing what they have discovered, not knowing how to apply it, or, in the worst case, discovering (and taking ownership of) the wrong answer. Additionally, by working in groups and talking with other students (which is promoted by the educationists), one student may indeed discover something, while the others come along for the ride.

Texts that are based on NCTM's standards focus on concepts and problem solving, but provide a minimum of exercises to build the skills necessary to understand concepts or solve the problems. Thus students are presented with real-life problems in the belief that they will learn what is needed to solve them. While adherents believe that such an approach teaches "mathematical thinking" rather than dull routine skills, some mathematicians have likened it to teaching someone to play water polo without first teaching him to swim.

The Standards were revised in 2000, due in large part to the complaints and criticisms expressed about them. Mathematicians felt that the revised standards, called The Principles and Standards for School Mathematics (PSSM 2000), were an improvement over the 1989 version, but they had reservations. The revised standards still emphasize learning strategies over mathematical facts, for example, and discovery over drill and kill.

So how does this fine-sounding idea play out in the classroom? Kids tend to spend too much deriving everything from first principles. What gets sacrificed is time spent learning advanced skills, as Barry shows:

Concept still trumps memorization. Textbooks often make sure students understand what multiplication means rather than offering exercises for learning multiplication facts. Some texts ask students to write down the addition that a problem like 4 x 3 represents. Most students do not have a difficult time understanding what multiplication means. But the necessity of memorizing the facts is still there. Rather than drill the facts, the texts have the students drill the concepts, and the student misses out on the basics of what she must ultimately know in order to do the problems. I've seen 4th and 5th graders, when stumped by a multiplication fact such as 8 x 7, actually sum up 8, 7 times. Constructivists would likely point to a student's going back to first principles as an indication that the student truly understood the concept. Mathematicians tend to see that as a waste of time.

Another case in point was illustrated in an article that appeared last fall in the New York Times. It described a 4th-grade class in Ossining, New York, that used a constructivist approach to teaching math and spent one entire class period circling the even numbers on a sheet containing the numbers 1 to 100. When a boy who had transferred from a Catholic school told the teacher that he knew his multiplication tables, she quizzed him by asking him what 23 x 16 equaled. Using the old-fashioned method (one that is held in disdain because it uses rote memorization and is not discovered by the student) the boy delivered the correct answer. He knew how to multiply while the rest of the class was still discovering what multiples of 2 were.

Now, consider the constructivists' argument for allowing this lack of 'domain knowledge' to persist -- kids develop deeper understanding, 21st century skills, bla bla bla -- after having read KDeRosa's "Terminator essay" on math education.

That essay just puts this nonsense to death, don't you think?


p.s. from Catherine

I found the smart constructivism post.

Here are the 2 best passages.

Smart constructivism says:

A common misconception regarding 'constructivist' theories of knowing (that existing knowledge is used to build new knowledge) is that teachers should never tell students anything directly but, instead, should always allow them to construct knowledge for themselves. This perspective confuses a theory of pedagogy (teaching) with a theory of knowing. Constructivists assume that all knowledge is constructed from previous knowledge, irrespective of how one is taught (e.g., Cobb, 1940)--even listening to a lecture involves active attempts to construct new knowledge.**

Radical constructivism says:

It is possible for students to construct for themselves the mathematical practices that, historically, took several thousand years to evolve.





KenDeRosasDirectInstructionPage 17 Nov 2005 - 22:20 CatherineJohnson



Ken DeRosa has put together a page on Direct Instruction!


It's fantastic. Incredibly helpful. I've already sent pieces of it to Christopher's math teacher.


a reminder

To find out whether Ken has added new material to his page (or whether anyone else has added new material or new comments to the site) click on the What's New button on the sidebar to the left.

It looks like this:

whatsnew.jpg

(Siegfreid Engelman scripted that for me.)


update: scripted instruction in DI

Ken has added a terrific page on scripted instruction in DI, which I think is probably a major sticking point for people just encountering Direct Instruction.




ScriptingInDirectInstruction 21 Nov 2005 - 22:20 CatherineJohnson




Ken has just added a page on scripting in DI , which I think is one of the main sticking points for people unfamiliar with Direct Instruction. Just the sound of it—scripting—teachers slavishly reciting pre-programmed scripts....this is the image that springs to mind.

But the image is wrong.

Here's Ken:

Inevitably, whenever Direct Instruction (DI) is discussed the subject of “scripting” is raised. One frequent objection is that the scripts stifle teacher creativity. Nothing could be further from the truth.

Before we jump in, let’s first look at some sample scripts. Here’s a sample script on Writing Fractions. Here’s one on Subtraction. And, here’s another.

In DI, teachers use pre-designed scripts when teaching. The scripts are based on extensive research regarding student retention, and every aspect of every script is based upon results that were demonstrated through research. The great advantage of this approach is that every teacher using the script becomes the beneficiary of that research and will probably teach much more effectively than if left to her own devices.

DI designers test the programs carefully before publishing them and each DI program is extensively revised based on specific student error data from the field test. Scripting the lessons allows sharing of these “polished stones” across teachers. Also scripting helps reduce the amount of teacher talk. Children learn by working through the sequence of tasks with carefully timed comments from the teacher. Children learn little from straight teacher talk. Too much teacher talk decreases pupil-motivation, draws out the lesson length unnecessarily, and often causes confusion by changing the focus of the tasks, disrupting the development of the larger generalization, of which a teacher the first time through is usually unaware.

Also, without guidance, teachers may use language that students do not understand or that distracts students’ attention from examples. Scripts also allow aides, parents, and other paraprofessionals to assume teaching responsibilities, resulting in increased quality instructional time.

Moreover, even though the DI programs are carefully tested and scripted, successful use of them requires training in the special techniques of delivery. Teachers must make many decisions in response to the children's performance. Some of the most important decisions involve placing each child appropriately and moving the children through the lessons at a pace that maximizes their learning potential.

Lastly, the scripted presentations do not comprise the whole lesson, and the lessons do not comprise the whole school day. There are opportunities for group and independent work. A good DI teacher also creates additional activities that allow students to make use of their learning in various situations. So, there is a great deal of teacher creativity involved in the interpretation and presentation of the script, in attending to the needs and progress of all students and in designing expansion activities.

-- KDeRosa - 17 Nov 2005




Carol Gambill's method of teaching algebra
Direct Instruction professional development workshop
(online videotape of a workshop on direct instruction. excellent)
direct instruction & question-asking





EngelmannOnDistrictGuidelines 28 Nov 2005 - 02:29 CatherineJohnson



from Ken, here is Engelmann on District Guidelines (p. 18):


Specific Problems with District Guidelines

District guidelines have three characteristics that may create problems in implementing effective school reform models: Some function as a curriculum, some support laxity, and some tend to require work on material that is of only peripheral importance to accelerating student performance.

Guidelines as Curriculum. Guidelines function as a curriculum when they specify a pedagogical process rather than learning outcomes that are reasonable for a particular grade and subject. [ed.: this is the situation in NYC, where teachers are required to use constructivist techniques, & supervisors patrol the halls checking to see if the kids are sitting on the rug where they're supposed to be. We have reports of children covering up for teachers—something Ed tells me always happens.] A process is implied by every standard or guideline that requires schools to teach something before it would be taught in an effective program sequence. Such processes may override sensible instructional sequences. For instance, if the district (or state) guidelines call for teaching the fractions 1/2, 1/3, and 1/4 in kindergarten, the guidelines are not serving as standards but as a curriculum. The teachers are now required to follow this curriculum even though it does not represent a sensible way to introduce fractions or a sensible time to do so. The guidelines do not indicate an outcome that is important for going into Grade 1 or even Grade 2, yet they are very specific about what is to be taught. The guidelines fail to recognize not only that teaching fractions in kindergarten is unwise but also that this sequence of fractions will probably reinforce misconceptions about what fractions are and how they are related to the counting numbers.

There are many other examples of guidelines that function as curricula. For instance, if the guidelines require students to work on a particular type of word problem in fourth-grade math, even though it is doubtful that they have the math skills necessary to solve such problems, teachers must now somehow teach these skills. The idiom of “writing as a process” is reasonable in some ways, but the steps the district may require are certainly not the only set of steps that will lead to good writing. Furthermore, not all the writing the students do should be of the form that involves note-taking, first draft, revision, and publishing. Successful programs that emphasize students’ writing more and writing in a way that yields better first-draft material should not be forced into the Procrustean “writing process” mold.

Lax Standards. The second type of failure is created by guidelines that are too lax in that they do not require performance on a skill until long after it would have been taught in a reasonable instructional sequence. The curricular sequence is affected far less by lax specifications than by guidelines that act as a curriculum, but the credibility of the sequence is still challenged. Lax standards provide justification to teachers for not following the specifications of a validated sequence. For instance, districts may adopt the guideline, “Read by Grade 3.” NIFDI has consistently demonstrated that if a reading sequence is properly implemented in kindergarten, virtually all at-risk students with the exception of the profoundly retarded and the very frequently absent will read by the end of the year. No program that purports to be a model of reform should have a standard less demanding than “Read by Grade 1.”

Guidelines That Stress Peripheral Skills. Guidelines that stress peripheral skills create two problems. First, because they do not test key skills, they suggest that these skills are not important. Second, they test skills of questionable value, thereby implying that these skills are important. For instance, math tests—both standardized achievement tests and district- or state-created tests—tend not to test math skills that are absolute prerequisites for higher math and, instead, tend to test trivial skills and applications.

For example, one of the skills essential for higher math is facility at writing and rewriting equations. This skill is not included in many tests. Instead, tests typically present problem types that students have not learned how to express as equations. Much of what is tested is inconsequential from the standpoint of mathematics. Blueprints, graphs, and virtually anything that has numbers are treated as legitimate math items. Certainly, students should learn this material, but most of it is not really legitimate math content and should not replace legitimate math content. The main problem with guidelines that stress peripheral skills is that teachers become reluctant to follow an effective program because much of what is taught in the program is not tested. Understandably, the teachers are likely to see the program, not the guidelines, as problematic.


this sentence caught my eye

The guidelines fail to recognize not only that teaching fractions in kindergarten is unwise but also that this sequence of fractions [1/2, 1/3, and 1/4] will probably reinforce misconceptions about what fractions are and how they are related to the counting numbers.

Assuming I know what he means here, I wrote a post on this very subject not too long ago.

It seems to be the case that some fractions are 'innate,' meaning certain fractions, namely 1/2, 1/3, and 1/4, are naturally learned by children in the course of daily life without formal education.

Observing my own process of re-learning fractions, I felt that the very naturalness of a 'friendly fraction' like 1/2 was in fact an obstacle for me in dealing with the non-intuitive fractions such as, say, 1/42—or, even worse, 1 1/42 ÷ 3/5. The step from 'I have 1/2 and you have 1/2' to 1 1/42 ÷ 3/5 is not a small one. Nor is it just one step.

This led me to question whether it's always a good idea to start teaching 'where the child is [naturally]' or whether it's better in some cases to delay some content until you can peg it to 'unnatural' material the child has learned through formal education.

I think this is probably the same issue Carolyn raised back in the beginning of ktm concerning circle fractions.


California history/social science frameworks

I've mentioned Ed worked on the California history-social science frameworks, which are available online & to purchase, I believe. (Another item on my to-do list.)

Ed reveres Bill Honig, who is the villain of Engelmann's book......and yet still Peace and Harmony prevail in these parts!

I'll track down the Frameworks and get links posted.

I'd love to know the whole story on Honig, who almost singlehandedly imposed whole language on the country via the CA textbook adoption process—and then recanted after several successive years of children failing to learn to read. (Engelmann sued Honig in the CA courts and won.) I may have to order his book on reading if only to learn the story of how he came to see the light.

[pause]

A quick skim of the Amazon entry for Honig's book implies that Honig's story is what I suspected it might be; he didn't have a clue what the experts he hired were up to.

Honig's background, Ed thinks, was in business. Same with Michael Bloomberg's. Engelmann writes at some length about the problem of the business community's many attempts to reform education. Concerned Citizens involve themselves in education, and, as they do in the business world, hire experts to advise them.

What business people don't understand, Engelmann says, is that the field of education doesn't produce experts in the normal sense of the word. (I'll pull a passage on this later...)

In NYC, we now have enforced constructivism everywhere, We have enforced constructivism because Bloomberg turned to Columbia Teachers College for a plan.

Now the scores have gone up (I've heard this twice from our own Assistant Superintendent for Curriculum) so constructivism has been proved effective.

The fact that scores went up across the entire state doesn't enter in.

Welcome to Raw Dataville.




NewAirReportOnEducationalResearch 19 Dec 2005 - 01:30 CatherineJohnson



Ken just pointed me to a new AIR report on School Reform Models (pdf file) that I think should be a boost for DI (as for Success for All):

A new guide using strict scientific criteria to evaluate the quality and effectiveness of 22 widely adopted comprehensive elementary school reform models rates 15 as “limited” to “moderately strong” in demonstrating positive effects on student achievement.

Direct Instruction and Success for All are the only two 'reform models' withi moderately strong evidence of effectiveness.


from the full report:

Goals/Rationale

The Full Immersion Model of Direct Instruction has two foundational principles: all students are capable of learning if taught using proper techniques, and all teachers can be effective if provided with researchbased strategies and materials. Thus, the model seeks to accelerate learning for all students and provide teachers with appropriate strategies by targeting factors that are within a school’s control. These factors include assessment, instruction, grouping, scheduling, professional development, and resource allocation.

Notably, the model does not rely on parental involvement or technology; NIFDI believes that school leaders often cannot control these factors or use them efficiently.

The main component of the Full Immersion Model of Direct Instruction is Engelmann’s curricular program. Engelmann asserts that an implementation plan, such as DI, seeking to accelerate student achievement should include

  • A scientifically research-based instructional program;

  • Homogeneous and flexible grouping;

  • Appropriate student placement within the instructional sequence;

  • Daily practice and application of skills and strategies;

  • Scheduling that allows for cross-classroom grouping and provides sufficient daily instructional time;

  • Instructional activities that motivate, engage, and interest students; and

  • Ongoing data collection for instructional decision making.

Ken's taken the time to type up some passages from Engelmann's War Against the Schools' Academic Child Abuse, and I'll be copying more myself.

With Engelmann, the game is: did the students learn what you taught? Period. Constant formative assessment, the purpose of which is not to grade and categorize kids, but to find out what they've learned.

When they aren't learning, you don't ship them off to the school psychologist to assess learning failure.

You revise your curriculum and/or teaching methods.

I'm thinking......schools should have some writers on staff. (They've got everyone else! Why not writers!)

When you write for a living, you never, ever, get to send the folks who don't like and don't get your books to the school psychologist.

You get to go back to your computer and revise.


here's more:

Curriculum and Instruction

The DI approach is based on the belief that learning is affected by the sequential development of skills, instructional approaches, amount of skill practice and application, ongoing feedback given to students, and continuous monitoring of student progress. Four basic principles guide the DI curriculum and instruction:

  • The programs should develop specific skills through continuous practice and later combine these skills to form higher order thinking skills.

  • Lessons should emphasize reviewing and practicing already learned skills and integrate new skills as they are mastered.

  • Scripted and predictable lessons ensure daily assessment of student progress.

  • Field-tested instructional practices should be revised, adjusted, or maintained based on student progress and responses.

The central element of The Full Immersion Model of DI is the scripted curricular program. The curriculum materials include highly interactive yet fast-paced lessons. Each lesson builds on the previous lessons; therefore, the lessons gradually introduce new skills. The lessons require teachers to adopt specific instructional strategies such as directing choral responses and signaling. NIFDI suggests that schools phase in the implementation of the model typically by implementing the reading and language curricula during the 1st year, spelling and math during the 2nd year, and handwriting during the 3rd year.

Prior to implementing the model, NIFDI mandates that schools discontinue their use of other instructional programs that may compete for time and resources unless the programs are approved by NIFDI. For example, schools should not continue to implement programs that take students out of the classroom during instructional blocks.

Schools purchase the DI instructional materials from SRA (http://www.sraonline.com). Reading and language materials include Reading Mastery I–VI; Horizons A–D; Corrective Reading (Decoding and Comprehension); Language for Learning; Language for Thinking, Reasoning and Writing; and Expressive Writing. DI math and spelling materials include Distar Arithmetic 1, Connecting Math Concepts Levels A–F, Corrective Mathematics, and Spelling Mastery. These materials include scripted lesson plans, workbooks, and materials for assessing student performance. NIFDI provides teacher training for implementing these materials in the classroom.


I wonder if I can get hold of Expressive Writing.


I love this part:

The implementation manager places all students, including most students with special needs, in instructional groups; for this reason, the model does not generally accommodate pull-out programs.


DI doesn't allow a school to do pull-outs!

Class time in America is utterly fractured by constant, chronic, unceasing interruptions. Therapists coming in to pull-out kids; enrichment teachers 'pushing-in' to enrich kids; band teachers collecting kids for band; it goes on and on and on. And then there's the PA system.

A friend of mine has been helping out at the K-3 school. She said it feels like you don't get more than a few minutes' uninterrupted classtime there.


just keeps getting better

Technology

NIFDI feels that technology is peripheral to the mission of accelerating student achievement.

I'll say.


formative assessment

Monitoring Student Progress and Performance

During the initial stage of implementation, students take a placement test that determines their instructional grouping. Throughout implementation, teachers monitor student progress and grouping using daily assessment of student performance on lessons. Teachers are taught techniques to analyze and interpret data from these assessments; the techniques help with reflecting on their instructional practices, evaluating students’ responses to instruction, and identifying students who do not demonstrate mastery.

Each week teachers provide the school principal with a summary report of student performance, which notes any students that do not make adequate progress during that week. In return, the principal submits a summary report of student performance to NIFDI. During weekly conference calls, the school management team (principal, building coordinator, and peer coaches) discusses the progress of instructional groups and individual students with the implementation manager and project director.

If individual students do not make adequate progress for 3 consecutive weeks, the management team establishes a plan for remediation. The principal or building coordinator continues to monitor the students’ performance on a weekly basis. The model requires the management team to ensure that teachers receive feedback, coaching, and appropriate instructional materials to meet the needs of students requiring remediation.




If individual students do not make adequate progress for 3 consecutive weeks, the management team establishes a plan for remediation.

This is what I like about DI.

If a student isn't learning, they don't let years go by before anyone notices something's amiss.

Three weeks of no learning, and you're On The List.

Back when Christopher failed two unit tests in a row, amounting to a full 1/3 of his year's work in 4th grade math, I heard nothing from the school. I was working under intense deadline pressure, and I came close to missing what had happened.

Today he routinely says, "I didn't learn anything in 4th grade (math)," and I'm inclined to agree. But at the time, I had no idea. And the school didn't jump into a principal-managed remediation plan.

I did know that his dad was reteaching every concept at night, but I didn't know that wasn't good enough.

Christopher's partner in 4th grade math failure is still behind today. He's never closed the gap.


Executive Summary (pdf file)




JohnSaxonAndFrankWang 02 Dec 2005 - 21:04 CatherineJohnson



Incredible story of Frank Wang and John Saxon:

For Saxon president Frank Wang, getting good at mathematics was the answer to a personal crisis. In 1970, a doctor and school officials came to the conclusion that he had "neurological impairment" and could not be educated. This diagnosis was a great blow to his parents, recent Chinese immigrants to the US. Wang had his own solution: He noticed that what counted for intelligent in his school was an ability to do mathematics. This was the key to convincing school officials that he had a mind worth educating, he reasoned.

"I didn't want to live out this prophecy," he says. "I really wanted to prove to the doctors that I had intellectual capacity. And getting good in mathematics looked like the way to do it."

He began by studying past New York State Regents exams in mathematics - quietly, on his own time, one question at a time. It was tough at first, but he just continued working problems until he understood the principle, then moved on to another topic.

Finally, he told his eighth-grade algebra teacher that he already knew all the material in the course. The teacher sent him to the principal, who sat him down with an old Regent's exam (he'd already studied) to test the boast. Wang scored a 96.

"He asked me how I had learned all of this. I shrugged my shoulders and said, 'I don't know. It just came to me.' I outright lied, but it was such a delicious feeling. All of a sudden people's thoughts of me changed from a disabled child to someone with potential," he says.


The fact that experienced educators believed this child when he told them an entire year of eighth-grade algebra 'just came to him' is the most alarming part of this story.


Saxon

Wang met Saxon founder John Saxon after his family moved to Norman, Okla., where his father took up a position as professor of mathematics at the university. Saxon needed a research assistant, and 16-year-old Wang volunteered.

"He just struck me as a very eccentric fellow, but someone with a very strong and powerful sense of mission. He had very grandiose plans at that time. He thought that he had a better way of teaching mathematics, and the world should know about it," says Wang.

Saxon, once dubbed "the angry man of mathematics," was a retired Air Force pilot who flew 55 missions in Korea and later taught electrical engineering at the US Air Force Academy. Brash, outspoken, and never one to dodge a fight, he started his own publishing company to challenge the math orthodoxy of the day.

Smaller is better

Saxon's concern wasn't that math books were too full of pictures, chatter, and not enough problem-solving. (That came later.) In the early 1980s, Saxon argued that children should not be expected to learn math in big thematic chapters. He argued that math needed to be taught in smaller increments, with lots of practice and reviewing.

It turns out, that's exactly how Wang had taught himself mathematics. In the end, the youngster hired to punch papers and do errands contributed so much to the book that Saxon acknowledged him in the preface - and later invited him to take over his company.

"The Saxon pedagogy was incremental development: Teach in small pieces, continual review of those increments, and frequent cumulative testing. There would be no asking: Is this going to be on the test? Every Saxon test was cumulative, and every test gave kids a chance to redeem themselves," Wang says.




Saxon in Oklahoma

In 1992, Saxon offered to donate his program free to seven Oklahoma City elementary schools. A district follow-up found Saxon students outscored a control group of non-Saxon students in every math category on the Iowa Test of Basic Skills. Asked to cite weaknesses of the plan, some teachers said that lessons were too time-consuming.

Much of the evidence in support of the Saxon method is anecdotal, but compelling enough to have forged a strong following among some school administrators and parent groups.

Test scores at Falconer Elementary School in Chicago, for instance, went up so dramatically that the central office suspected its students were cheating. Students retook the test and scored at the same level. (76.9 percent of its third-, fourth-, and fifth-graders scored at or above national norms on the Iowa Test of Basic Skills. Prior to the use of Saxon only about a third scored at that level.) Another example: Saxon students at Riviera Elementary School in Kelseyville, Calif., one of the state's poorest districts, now outscore students in affluent Laguna Beach schools.



Someone needs to write a book about Saxon Math.


our hero

John Saxon was one of the first to oppose the recommendation of the National Council of Teachers of Mathematics to integrate calculators into math classes. The 1989 NCTM standards that urged students to "construct their own understanding" gave Saxon textbooks a new target.

"John Saxon used to say that understanding more often than not follows doing rather than precedes it," Wang says. "If I'm going to teach you how to drive, I don't lecture you on the theory of the internal-combustion engine. I get you behind the wheel of the car and drive around the block."

He adds: "We're not saying we're against critical thinking. But we feel that creativity comes from a well-prepared mind. What we want to give every child in America is the ability to work to develop a well-prepared mind."






IepsForEveryChild 19 May 2006 - 21:47 CatherineJohnson



Rereading Parent Pundit's post about her daughter's experience with Everyday Math and ALEKS, this passage caught my eye:

...they give a pretest and a posttest for the curriculum. In other words, they give the final at the beginning of the year and at the end of the year to track the learning. My daughter received a 25 at the beginning of her 5th grade year in math, but she only received a 69 at the end of the year....

Clearly, intervention was needed. In the summer at the end of 5th grade, I had her try the Aleks computer program in math, www.aleks.com. The Charter School in my town uses it, and I decided to try it for my own daughter. A tutor would have been expensive and less than optimal in this situation because my daughter does get concepts, she just needs more drill (how can most kids hone their number sense if they aren’t ever asked to multiply and divide numbers continuously), and she needs algorithms that have fewer steps so there is less possibility of error (everything that Everyday Math does not provide.)



I give Parent Pundit's school—and the authors of Everyday Math—credit for the pre- and post-testing.

My problem is: what comes next?

They give this child a pre-test and she scores 29; they give her a post-test and she scores 69.

And then......nothing.

"Clearly intervention was needed."

I'll say.

Why is intervention the parent's responsbility?

The school has failed to teach this child 5th grade math. When she takes the ALEKS test, the program tells her she knows only 21% of a typical 5th grade curriculum. (I'm wondering whether ALEKS allows people just to take the grade-level tests, and if so, how much they charge. I'll check.)

If this child were classified as having special needs, she would be entitled to be taught the content that is listed on her 'IEP,' which stands for Individualized Education Program.

Of course, in my experience the content on the IEPS doesn't get taught, either, but still.....it's there; the parent has a leg to stand on. (And in my own children's case, in fact it's extremely difficult to know what they are and are not able to learn, though I suspect Engelmann would make short work of some of the IEP meetings we've had.)

But with a typical child with normal intelligence, there's no mystery. She can learn 5th grade math in 5th grade. It's the school's job to teach it to her—and to reteach it if they failed the first time around. If that means providing tutoring or summer classes, so be it. It's the school's failure; the school needs to fix it.

This mother was in the same position I was in at the end of 4th grade. My child was failing; the problem was the school's, not his or mine. (In his case the problem was almost certainly the teacher, who I liked very much, but who apparently just could not teach math at that early stage of her career. The school didn't give her tenure, which was the right move. But children who lost a year of math in 4th grade weren't given any help or remediation. No one came to parents of these children and said: Your child failed to learn math this year, because his teacher was inexperienced and didn't manage to teach the subject to mastery. Here's what we're going to do to re-teach the material he missed.

American schools, by and large, teach for coverage.

Not for mastery.


free assessment at ALEKS?

It looks like ALEKS offers a free assessment. (I haven't tried to use it, because I'm not sure I can run the test twice on one computer, and I'm most interested to see where Christopher scores.)

If this assessment really is free, and is easy to use, it could be a useful tool in talking to teachers and administrators.

What we really need is our own simple-to-administer, at-home assessment, 'rolling' assessment tools.

I'd like to be able to send my school a report each month on where Christopher is in the curriculum.

Of course, that's another project.

report cards for the school




BlackAndWiliamRecommendationsForFormativeAssessment 07 Dec 2005 - 16:02 CatherineJohnson



Black and Wiliam (1998b) make the following recommendations:

  • Frequent short tests are better than infrequent long ones.

  • New learning should be tested within about a week of first exposure.

  • Be mindful of the quality of test items and work with other teachers and outside sources to collect good ones.

No more teaching for coverage.

No more punitive tests and shaming grades.

Teach to mastery.


key words: gapology
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
failing algebra in Los Angeles
formative assessment
formative assessment in a nutshell





PaulMillerAndRudbeckiaHirtaOnAssessment 19 May 2006 - 22:09 CatherineJohnson



I'm disheartened today. Watching Christopher fall apart is excruciating (all the more so given how much I know about fear and the brain), and.....

......and I've had it.

So when I got home this morning, after dealing with the THIRD car to be stuck in our driveway in two days (I'm starting to feel like Bill Murray in GROUNDHOG DAY), and found these comments from Paul Miller and Rudbeckia Hirta, I thought, There's hope. (I'll be a much more cheerful person tomorrow, or even.....later on this afternoon!)


from Paul:

One thing I've been putting a lot of thought into is how to teach to mastery in an environment where I'm on a strict schedule and have very limited time. I bet Black and Wiliam weren't thinking of people who have to jam what would be a whole year of algebra in high school into a semester.

Still, I have decided, there will be quizzes at least weekly next semester.



and from Rudbeckia:

This semester I gave twenty quizzes in calculus (the best 10 counted), and I'm thinking of giving quizzes every class next time I teach something from the algebra / precalc / calc sequence. Next time I'm going to make them VERY short, 3-5 minutes, and give them at the exact beginning of class. My bet is that the instructional face-time lost will trade well with increased studying.

Here's how I feel, reading these comments.

These comments, these actions, are a gift. A gift from two highly intelligent and educated people to the younger people they are trying to teach.

The way I'm feeling today, they're a gift to me, too.


where we are with English

Mrs. Roth can't teach our child. That battle we can handle, although the school will certainly refuse to move Christopher to another class. If I were a betting person I'd bet they end up moving him whether they want to or not, but we'll see.

Whether he goes or stays, he will never write another assignment for this woman.

Worksheets, fine; reading logs, check. But no written work. We're done.

What we need is for the principal to read Christopher's essay and tell him it's not a 'D.' His friends are making fun of him, telling him his parents are 'just saying' his essay is good, because we're his parents. All these boys insult each other all day long, Chris included. But on this issue his friends are drawing blood, which I'm sure they don't know. He's probably hurting them, too. The things they say to each other are appalling, and I have no idea what to do about it.

Advice?

Christopher's confidence is shot. He thinks he can't write, can't do math, can't do anything.

We saw this happen before, in 2001, after the attacks. He'd been an aggressive little soccer player, one of the best on the team. Then he lost his nerve. He just....stopped. On the field, he was diffident and slow. At school, he was bullied.

Ed was the soccer coach, so he was there; he watched it happen. He told me last night he's seeing the same thing all over again, only this time in academics, where it counts.

Maybe it's not like that; maybe he'll bounce back. We'll see.


question

So Mrs. Roth has to go, but the math teacher is another story.

She's very young; I think this is her first job. (back story for new readers stopping by: Her course last year was so brutal for the kids—unintentionally so—that the parents were in open revolt.)

She's a good egg. Last year must have been painful for her; the huge revisions they did to her course over the summer may have been distressing, too. Yes, it's important to have mentors and help, but having mentors and help in the context of parent fury is another story.

So....I need to push her for Christopher's sake, but I want to 'push' in a way that's positive, helpful, and likely to be listened to.

Here's what I think we need: If any of you have extra items to add, let me know


  • First item: I need to know, from the beginning of each chapter, what 'showing your work' means to Ms. Kahl.



Let me ask all of you: what is the work that would typically be shown for this question?

Compare using <, >, =

0.635 __ 0.365

To me, this is a simple comparison—but do teachers typically ask for work to be shown on this kind of question?

If so, does the student write a subtraction problem, or perhaps draw a number line?

I'll find out from Christopher's teacher, but I'm wondering about other peoples' experience.

I have no problem with the requirement that the kids show their work; I think it's probably good at this stage. But I've got to know from the get-go what 'showing your work' means for each given problem, so we can practice it from the get-go.

  • Second item, Christopher needs guided practice in class.


Christopher says that the norm is for Ms. Kahl to lecture and give an assignment. The kids do the procedure she's taught for the first time at home.

I'm sure his perception of the class and her perception of the class are going to be an imperfect match. she does have them do worksheets in class sometimes, or start their homework. I'm not sure whether either of those situations constitute 'true' guided practice, but they're probably in the realm.

Still, the fact is that he not infrequently comes home from school without a clue how to do the procedure she's demonstrated in class that day is significant. While she may be doing some guided practice, I need her to do more. Which means I'm crossing a line into the realm of telling a teacher how to teach.

  • Third, and most important, I need formative assessment to be happening in the class.


We have no teaching to mastery at all. Instead we have a classic 'accelerated' course, where the children are expected to be math brains, the teacher whizzes through the material, and only the strong survive. The weak fall behind, struggle to move their legs faster than they'll go, gulp down huge mouthfuls of air, pour sweat, and finally collapse in a heap. Only one grading period into the year so far, Christopher's nearing collapse. He earned a B on his first chapter test, a C on his 2nd, and, now, a D on his 3rd.

Yes, he could move down to the combined Phase 2/3 course.

He could move down and study place value. They've spent weeks on place value. I forget what they're doing now; I'll find out. It's not going to be anything he needs to spend an hour a day doing.

Here's my question: how do I broach these subjects?

These are large issues, not small. And this teacher is almost certainly in Paul's situation. She has to cover this material, and she has to cover it fast. What she's got to work with is nothing like a Singapore course where the curriculum has been painstakingly put together to allow the fastest possible progress for all children, math brains or no.

So she's up against it.

But we need these changes. We need the school and the individual teachers to assume responsibility for making sure the children have learned what they've been taught. All but the brainiest kids need this, and even the brainiest kids are going to need it somewhere along the line, too.


back to Rudbeckia & Paul

Actually, it suddenly occurs to me that I can cite Paul & Rudbeckia—especially, for my purposes, Rudbeckia's top-10-quizzes count approach.

That would be so much more humane for these kids, and so much more motivating.

Alright, that's a possibility.


what we told Christopher

The math situation is probably manageable.

Ed, this morning, read over Christopher's test and said that he's not having nearly the amount of homework he needs if he's to do the tests she's giving.

Math class lasts 50 minutes; the test had 24 questions, some with several parts. Christopher has two minutes at most to answer each question, and he has to show his work (and his handwriting is not only bad, but slow).

Now he's developed test anxiety, so he's not managing to read the questions. He must be freezing up, just not seeing the words.

The point is: if he's going to do 24-item tests in 45 minutes, he has to have more practice. Ms. Kahl sometimes sends home homework 'sets' with only 4 problems. Maybe the math brains can do 4 problems and ace a test (they probably can).

Christopher can't. If Christopher is going to do a 24-item test in 45 minutes he can't have done 4-problem homework sets. Wayne Wickelgren says children should do 30 problems a night. That's what Christopher needs to do. Thirty problems a night.

We were finally able to get through to him on this point last night—thanks to KUMON and to Saxon Math.

I said, "Do you ever flunk KUMON worksheets?"

Christopher said, "No."

I said, "Why don't you flunk KUMON worksheets?"

Christopher said, "Because I've practiced."

I said, "Because you've practiced a lot."

Then I said, "Did you ever flunk Saxon tests?"

"No."

Why?"

"Because I practiced."

"Because you practiced a lot."

Then both Ed and I said, You need to be able to do these problems as fast as you can write.

You need to be able to do them in your sleep.

You need to know them cold.

That's a simple message, and he understood it.

I hope it will finally start to sink in. Christopher thinks that if he can do a problem he knows it. It may take him 5 minutes to do one problem, but if he gets it right, he's done.

No one at the school has told him that isn't the way it works. He's had two months of "Study Skills" class and the only thing they seem to have told him about study and learning is 'Find a quiet place.'

I, of course, have been trying to get this message across for months, but, as Carolyn pointed out, we're hitting the end of parental influence.

Last night he heard us.

A couple of weeks ago I tracked down the Prentice Hall pre-algebra workbook that accompanies his text. We agreed that from now on he'll do ALL the problems on the work sheet, not every other problem, or, even worse, every fourth problem. (I'd put money on it Ms. Kahl has been told not to overload the kids with homework.)

Last night, that's what we did. Every single problem.

That proved to be a terrific object lesson.

He did one problem laboriously, taking far longer than he'd have on a test.

Then, because we were doing every problem, he did the next one— in half the time.

I said, "Look how much faster you got just from doing two problems instead of one."

He saw it.


cheeful thought

I'm going to get a grip now.

My neighbor, whose son struggled through this class last year, told me that the 7th grade book is mostly review. I think they start algebra in January, so I'm assuming they spend fall semester reviewing the gazillion procedures and concepts they learned in 6th grade pre-algebra, then make the move to formal algebra mid-year.

That's good.

I'm obviously back in re-teaching land; Christopher is losing another year of math instruction, just as he did in 4th grade.

But this time he's got KUMON, and KUMON speeds along. Yes, he's doing 3rd grade math now, but in two weeks he'll be doing 4th grade; 7 weeks after that he'll move to 5th. Slow but steady wins the race. Mr. Liu told us parents see major gains after one year of KUMON.

'You need to invest that time,' he said.

We're investing.

And this time I know I have to re-teach, and I'm starting now. I'll have the summer, too.

Then he'll have a fall semester of review with, I hope, the best teacher they've got.

So I think we can do this.




AGradeContractThatMakesSense 19 May 2006 - 21:14 CatherineJohnson



Ken's the first person I've ever met who could give me a run for my money on Googling skills. He's amazing.

Look what he came up with last night:


gradecontract.jpg



Here's the DI contract side-by-side with Irvington Middle School's contract:

gradecontracts.jpg



Think and Discuss


source:
Managing Classroom Behavior, p 149 (pdf file)



my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day
KIPP Academy contract





EngelmannOnRulesForInstallingCurricula 19 May 2006 - 21:55 CatherineJohnson



Ken's done more of the typing!

Thank you!


Here's Engelmann on rules School Boards should insist the school district follow when installing a new curriculum:


1. Don't install any practice or reform unless you have substantial reason to believe that it will result in improvement of student performance.

Test on small scale before wider implementation. Research validation. Field tested.

2. Don't install any approach without making projections about student learning.

The benefits of the approach must be measurable. Tests are needed to determine success. The tests should be "do it" tests, one that requires actual reading, answering questions, working math problems, etc (not multiple choice).

3. Don't install any practice without monitoring it and comparing performance in the classroom with projections.

formative assessment. Installed programs should be limited to a reasonable period of time such as no more than an hour aday for reading. The monitoring should deal with what the teachers do and how it relates to what the students have learned. Is the projected material being presented on schedule? Do the teacherfs need help? Is the program being followed faithfully? Are the kids mastering the material in the projected time.

4. Don't install an approach without having a back-up plan.

5. Don't maintain practices that are obviously not working as planned.

6. Don't blame parents, kids, or other extraneous factors if the plan fails.

The only factor that affects the plan is whether the kids and teacher are in attendance on a regular basis."If the teaching failed, it was because the teaching failed, not beacause the parents didn't get involved."



on manipulatives
The same problem exists with manipulatives. Kids play with rods that represent different values--based on the length of the rod. Kids can use these rods to perform a variety of "act-outs" that are consistent with complicated math notions, such as the idea that 10x2 equals 5X4, but the kids doing the acting-out are typically not learning the relationship. They're simply making one group of rods the same length as the other group. The great meanings that they're deriving are not in their minds but in the imagination of the educational observer.

Direct work with symbols and notations of math is a far safer method of teaching relationships because symbols are consistent with far fewer misinterpretations than noisy and often time-consuming act-outs. The [NCTM] Standards do not favor pencil-and-paper work, however, because such work implies skills, and the Standards are very ambivalent about skills.

War Against the Schools' Academic Child Abuse, p. 115



on the shelf life of learned material
Typically about 60 school days pass before any topic is revisited. Stated differently, the spiral curriculum is exposure, not teaching. You don't "teach" something and put it back on the shelf for 60 days. It doesn't have a shelf-life of more than a few days. It would be outrageous enough to do that with one topic-- let alone all of them.

...Don't they know that if something is just taught, it will atrophy the fast way if it is not reinforced, kindled, and used? Don't they know that the suggested "revisiting of topics" requires putting stuff that has been recently taught on the shelf where it will shrivel up? Don't they know that the constant "reteaching" and "relearning" of topics that have gone stale from three months of disuse is so inefficient and impratical that it will lead not to "teaching" but to mere exposure? And don't they know that when the "teaching" becomes mere exposure, kids will understandably figure out that they are not expected to learn and that they'll develop adaptive attitudes like, "We're doing this ugly geometry again, but don't worry. It'll soon go away and we won't see it for a long time"?

The Underachieving Curriculum judged the problem with the spiral curriculum is that is lacks both intensity and focus. "Perhaps the greatest irony is that a curricular construct conceived to prevent the postponing of teaching many important subjects on the grounds that they are too difficult has resulted in a treatment of mathematics that has postponed, often indefinitely, the attainment of much substantive content at all."

War Against the Schools' Academic Child Abuse, pp. 108-9




what people know and don't know

I was saying in a Comment on the Smartest Tractor thread that there are many aspects of DI & formative assessment everyone already knows. They just don't know they know...they probably haven't realized that what they know about DI & formative assessment amounts to an entire alternative educational philosophy, or would if they filled in the gaps.

But this 60-day figure is a statistic people really do not possess.

I had a funny experience with this at a PTSA meeting once. I was running the after-school program (this would be the program in which I hired myself to teach Singapore Math, btw). All of the program chairs were meeting to be filled in about forms, money, procedures, etc.

When the question of kids who couldn't afford the fees for the after-school program arose, the president said that the PTSA picks up the tab. The president said the teachers knew about the policy and would steer these children to us (something like that).

One of the volunteers said the teachers didn't know about it. She'd worked with a teacher the year before who had no idea this option existed. The president looked annoyed, and said, 'We sent them an email at the beginning of the year.'

That was a striking moment, because here we were, highly educated ourselves, devoted to our kids' schooling, and everyone in the room appeared to believe that if you've told someone something once they've learned it.

I think this is a common perception; I often have it myself. I'll think, 'I told him/her/them that already.'

I should know better.

It's true that in job situations—in any situation where you're responsible for hearing what people tell you, writing it down, and remembering and acting on it—people can say something once and expect it to stick.

But that's not the norm, especially when you're talking about one email sent to teachers at the beginning of the school year when they're swamped.

This is a factoid that needs to get out there.




CommentsToCome 15 Dec 2005 - 20:33 CatherineJohnson



I have a boatload of Comments to get pulled up front.....which means it's going to take awhile.

I thought I'd mention that the reason I pull Comments up front is that a) I don't want casual visitors to miss the super-meaty ones and b) once a Comment is on the front page it's part of the Category thread, so anyone reading that thread will be sure to see it. (All Comments stay connected to the original blooki posts, but a person reading through the KUMON category, say, isn't necessarily going to have the patience to click on each post individually so he/she can read each Comments thread individually.

So these things need to come up front.....

I've finally begun disciplining myself to KEEP A LIST, and here's what I've got at the moment:

  • Rudbeckia Hirta on finding stats on colleges "Random factoid (before I disappear into a cloud of office hours, reviews, calming of panic, and then grading): if you want a statistical profile of a college/university (like graduation rates, etc.) search their web page for the Office of Institutional Research and look for the Common Data Set."

  • Doug on 'the margins'

  • J.D. email

  • Verghis on KUMON honor roll



If there are things I've forgotten, let me know.


other

Since I'm posting a public to-do list, I also need to:

  • locate Ken's reading test & post links everywhere

  • post links to FERPA (thank you, Rudbeckia)

  • post links to the Rewards Reading Series, which both Dan and Smartest Tractor have mentioned (Smartest Tractor has purchased SOPRIS' writing program, IIRC)

  • post ALL links to reading/writing materials on the how-to-teach-writing page

  • collect the science-teaching links from.....was it today? (it's all a blur!)



I should probably go ahead and buy DON'T MAKE ME THINK....




AnneDwyerOnTutoring 16 Dec 2005 - 21:44 CatherineJohnson



What I've noticed with my tutoring students is this: if they don't understand something in math class, they try to find a procedure or "trick" that works everytime.

Since they don't really understand it, when they have to go back and do it on a test or later, they don't remember the "trick" exactly and their answers are consistent, but wrong.

For example, I was tutoring a student in basic math. He didn't really understand that a whole number has an implied decimal after the number (e.g. 3 is really 3. for a decimal problem)

When he first learned to divide decimals and he was following the teacher's examples, he was doing the problems right: So if he was dividing .045 into 15, he moved the decimal over three places for the .045 and three places for the 15. He even managed to get it right on the first test.

But he did them wrong on every test after that. When we were studying for the final, I was able to watch him do the problems.

Since he really didn't understand, he made up his own "trick". In the problem above, he would move the decimal over for the .045 correctly, but he put the decimal point in front of any number inside the divisor sign. So .045 into 15 became 45 into 150 instead of 15,000. And, because he had taught himself this trick, he ignored all decimal points inside the divisor sign. So even .045 into 1.5 became 45 into 150.

Needless to say, it took a while to find the problem and then to correct it.

IMO, with Christopher, because the class is going so fast and he doesn't always understand what he is doing, he will figure out his own rule and then apply it. You have to go back and see exactly what he is doing when he does the problems so you can identify the error he is making.




We are in fraction & decimal he** around here, which is annoying because I don't think we would be with Saxon or Primary Mathematics—and we weren't going into this course.

This is part of what I mean when I say Christopher is 'losing knowledge' he already had, or experiencing 'math regression,' or just......getting all jumbled up. I think he is becoming uncertain of procedures and knowledge he used to have fairly well nailed-down. (Though I don't know.)

Anyway, both of the ideas here strike me as excellent ideas.

First of all, I'm going to start writing whole numbers with a decimal point and some zeros to the right. I know that will help.

And second, I'm going to keep my eye open for 'invented shortcuts.'

One strategy I've begun, which I think is going to improve matters, is that I'm continually telling him that 'math shortcuts' come from the longer equations he's learned in the past. His teacher seems to be teaching only the shortcuts—either that, or he's only picking up the shortcuts, not the explanation for why they work. Either way, the result is the same: he's learning math tricks.

Last night, when I insisted on showing him why you could invert and multiply, he got his 'eureka' smile.

I'm sure he will have forgotten what I told him by today, but I'm going to keep hammering away at this.

I do think that the basic principle—that math shortcuts come from general principles he already knows—will stay with him, and will help.


reciprocal2.jpg



reciprocal_wreck.jpg



source:
reciprocals




ExpressiveWriting 21 Dec 2005 - 18:06 CatherineJohnson




0076020428.jpg



Ken tracked down this Direct Instruction writing curriculum from SRA. They have some interesting lessons posted online, and the Scope and Sequence categories are helpful.



He also rounded up two studies of the series:

Using the Expressive Writing Program to Improve the Writing Skills of High School Students with Learning Disabilities

Teaching Expressive Writing to Students with Learning Disabilities: A Research Synthesis



update: Smartest Tractor's pick

StepUp.jpg


Step up to Writing from SOPRIS WEST. Here's the Program Overview (pdf file)

Glancing through the Program Overview, I found the stoplight graphic I've posted below.

I like it.

I'm a fan of visual teaching in general; visuals stay with us in some way words don't seem to.

By way of support, I'll re-tell my sister-in-law anecdote.

My sister-in-law is a federal prosecutor in Philadelphia. One day we were talking about 'learning styles,' which I don't particularly believe in, but since everyone else does I don't automatically launch into a cognitive science lecture every time the subject comes up.

So we were talking about learning styles, and I said something about visual learning styles, and my sister-in-law said, "Everyone has a visual learning style."

"That's the first thing they tell you about presenting evidence to juries. If you want the jury to remember what you've said, you have to give them a visual."

I believe that.

Step Up To Writing gives kids a visual for writing that looks like it can probably be applied both to paragraphs and to entire essays. That makes sense; a paragraph can be thought of as a mini-essay.

I also very much like the stoplight metaphor. Writing should have rhythm; some parts should be fast, some slow, some in-between. That's a subtle concept to teach, and regardless of whether you try to teach rhythm explicitly, the stoplight image will be making the point.

My only problem, just on this cursory inspection, it that I find the final greenlight confusing.

I'm not used to thinking of a green light as meaning go back, and since the green light seems to take the writer to the essay's conclusion, I find 'green' for 'conclude' confusing.

However, that doesn't seem like an insurmountable problem. The conclusion in an action film is typically faster-paced than the rest of the film, and this can be true of an essay.....I think a student can probably survive the semi-breakdown of the analogy at this point.

I'll be looking forward to hearing how this program works for Smartest Tractor whose students are, IIRC, in 8th grade.


SteptoWriting.jpg



compare and contrast

graphicorganizeanonsm.jpg



'Graphic organizers' are huge these days, as far as I can tell. Everyone's using them.

If I were teaching a class of middle school kids how to write, I'd go with stoplights.




IrvingtonPtsaForum 19 May 2006 - 16:07 CatherineJohnson



IrvingtonPTSApulsesm.jpg



Anyone who cares to help me put together my 3-minute ideas, concerns and goals for the 2006-2007 budget, please chime in.

First and foremost, I don't want to buy more stuff.

I don't want to buy a K-5 Staff Developer, an Additional Media Specialist, an Elementary Math Enrichment Position, a new Textbook (unless it's Primary Mathematics in K-5 or Dolciani in 7th & 8th), or any more Technology.

I want Irvington to teach to mastery, not coverage, and I want a systematic program of formative assessment in all grades and classes that will let teachers, administrators, parents, and students know that mastery has occurred.

When mastery does not occur, I want immediate, effective remediation.

Oh, and I want a world class curriculum.

That's not too much to ask.

In 3 minutes.


"The mission of the Irvington School District is to create a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning."

That reminds me.

I don't want my child to attain his highest potential for academic achievement, critical thinking and life-long learning.

I want my child to attain a Singapore child's highest potential for academic achievement, critical thinking and life-long learning.




I'm going to have to spend some time studying Ken's road map.


Tell him what you are about to tell him. (the road map)

"A great curriculum has two major components: mastery teaching and formative assessment. DI is a great curriculum because it has both these things. It has mastery teaching because x; It has formative assessment because y." (You've just given the reader/listener a checklist that he can use to follow your argument to see if you've made your points)

Then tell him what you want to tell him. (the meat of the argument)

(Now you explain the x and y in detail.)

Then tell him what you just told him. (the conclusion/recap)

(Now you review the checklist.) "So you can plainly see that since DI has mastery learning because it has X and formative assessment becasue it has Y; DI is clearly a great curriculum becasue all great curricula include these things."



update

1 - 12 - 05
We went to the Forum last night. It was great.

I gather that this 'wish list' wasn't drawn up by the PTSA, but are items the School Board is considering.


see here, too


Irvington PTSA Forum
PTSA Forum Tonight
Ed's statement to the PTSA Forum
report: PTSA Forum
fact sheet for forum: Singapore Math & teaching to mastery & TIMSS gap





IfTheStudentHasntLearned 23 Dec 2005 - 22:16 CatherineJohnson





ktmTee3.png



revision

From Catherine:

Our new pretend-shirt specifically says "If the student hasn't learned, the school hasn't taught," not 'the teacher hasn't taught'.

No more thoughtless (and unintended) teacher-bashing.

Seriously. I'm the last person to want to make teachers feel blamed and bashed, seeing as how half my relatives have been or are currently teachers. I'm sure I'll be one again at some point, too.

The problem is that, when you talk about schools, it's the teachers who are visible. They're in the trenches, so they get the blame. (I realize I'm not telling teachers anything they don't know.) I know better than that, but I've been sounding like I don't.

Time for a course correction.

From Carolyn:

Hey, my entire family on my mother's side were also teachers, every man and woman Jack of them. I've been a teacher too; so has Catherine.

My observation is that policy flows downhill in a school, and the buck stops with the teachers. They get the responsibility, but not the authority; policy changes really have to start with upper management.

We're here to put the pressure on upper management, and support the teachers in doing what they know how to do.



FormativeAssessmentSummary 19 May 2006 - 22:01 CatherineJohnson



the OECD weighs in

The educational gains associated with formative assessment have been described as “among the largest ever reported for educational interventions.”
source:
Organisation for Economic Co-operation and Development


summary of Black & Wiliam

(full passage quoted below)

  • formative assessment: all activities schools, teachers, and students undertake to collect information that can be used diagnostically to alter curriculum, teaching, and learning

  • information gleaned from formative assessment allows teachers to make necessary instructional adjustments: reteaching, trying alternative instructional approaches, or offering students more opportunities for practice. Formative assessment allows schools to make necessary curricular adjustments.

  • Black and Wiliam literature review of 250 journal articles and book chapters: formative assessment produces significant learning gains, with effect sizes ranging between .4 and .7

  • students need specific comments about errors and specific suggestions for improvement; formative assessment is designed to provide this information

  • formative assessment allows teachers and students to identify gaps in students' skills and understanding and guides them through the process of remediating those gaps

  • formative assessment instills confidence in teachers, parents, and students that all students can 'learn to high levels'

  • formative assessment in the form of self-assessment and self-monitoring improves student learning when students understand the assessment criteria

  • specific feedback from formative assessment "emphasizes that students can improve as a result of effort rather than be doomed to low achievement due to some presumed lack of innate ability"

  • Black and Wiliam: low-achieving students, including students diagnosed with LD, improve most

source:
The Concept of Formative Assessment by Carol Boston


Purpose and Benefits of Formative Assessment

Black and Wiliam (1998b) define assessment broadly to include all activities that teachers and students undertake to get information that can be used diagnostically to alter teaching and learning. Under this definition, assessment encompasses teacher observation, classroom discussion, and analysis of student work, including homework and tests. Assessments become formative when the information is used to adapt teaching and learning to meet student needs.

When teachers know how students are progressing and where they are having trouble, they can use this information to make necessary instructional adjustments, such as reteaching, trying alternative instructional approaches, or offering more opportunities for practice. These activities can lead to improved student success.

Black and Wiliam (1998a) conducted an extensive research review of 250 journal articles and book chapters winnowed from a much larger pool to determine whether formative assessment raises academic standards in the classroom. They concluded that efforts to strengthen formative assessment produce significant learning gains as measured by comparing the average improvements in the test scores of the students involved in the innovation with the range of scores found for typical groups of students on the same tests. Effect sizes ranged between .4 and .7, with formative assessment apparently helping low-achieving students, including students with learning disabilities, even more than it helped other students (Black and Wiliam, 1998b).

Feedback given as part of formative assessment helps learners become aware of any gaps that exist between their desired goal and their current knowledge, understanding, or skill and guides them through actions necessary to obtain the goal (Ramaprasad, 1983; Sadler, 1989). The most helpful type of feedback on tests and homework provides specific comments about errors and specific suggestions for improvement and encourages students to focus their attention thoughtfully on the task rather than on simply getting the right answer (Bangert-Drowns, Kulick, & Morgan, 1991; Elawar & Corno, 1985). This type of feedback may be particularly helpful to lower achieving students because it emphasizes that students can improve as a result of effort rather than be doomed to low achievement due to some presumed lack of innate ability. Formative assessment helps support the expectation that all children can learn to high levels and counteracts the cycle in which students attribute poor performance to lack of ability and therefore become discouraged and unwilling to invest in further learning (Ames, 1992; Vispoel & Austin, 1995).

While feedback generally originates from a teacher, learners can also play an important role in formative assessment through self-evaluation. Two experimental research studies have shown that students who understand the learning objectives and assessment criteria and have opportunities to reflect on their work show greater improvement than those who do not (Fontana & Fernandes, 1994; Frederikson & White, 1997). Students with learning disabilities who are taught to use self-monitoring strategies related to their understanding of reading and writing tasks also show performance gains (McCurdy & Shapiro, 1992; Sawyer, Graham, & Harris, 1992).




key worsd: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
failing algebra in Los Angeles
formative assessment
formative assessment in a nutshell





TeachersStuckOnMastery 16 Sep 2006 - 20:08 CatherineJohnson


from Becky C, a smoking gun:

Investigationsmastery.jpg


Getting stuck in a unit because you are teaching to mastery is a bad thing.

TERC teachers aren't supposed to do it.

Because they'll be revisiting the concept later.

Note: visit.

Not teach.

Not learn.

Not study.

Not practice.

And not master.


This language doesn't happen by accident.



KIPP on the spiral

You know, talk about curriculum, if I put in front of you a fifth, sixth, seventh, and eighth grade textbook in math and opened up to page 200 and I jumbled them up, and said, “order them from fifth through eighth grade in order,” you'd have a very tough time because they all look the same. That's because, unfortunately, we have this national strategy of “we're not really going to teach to master, we're going to teach to exposure and over lots and lots of years of kids seeing page 200 in the math book, eventually somehow they're going to learn it. We're going to teach them how to reduce fractions in fifth grade, in sixth grade, in seventh grade, in eighth grade, in ninth grade and continue until finally somehow magically they're going to get it.”....[W]e have a different math strategy and a different math philosophy.


Maybe that's why KIPP Academy 8th graders pass Regents A at twice the rate Irvington students do.


key words: teach to mastery teach to coverage teach to exposure spiraling direct instruction




AnotherNotTeachingToMasteryStory 13 Jan 2006 - 19:48 CatherineJohnson


A KTM Guest left this story about her daughter, who is a junior in high school:

Her Honors Physics class has presented the most challenges. The kids are, for the most part, pretty highly motivated to succeed, and the teacher, no doubt, means well. Simply put, he doesn't teach to mastery, but tests them as if they have it. Then, he realizes that maybe they don't have it, and rewrites the test. However, he scolds them for not studying enough and tells them that next time, he may not have a retake option. Rather then have them take incremental steps, his questions require them to make big leaps, and they have just barely gotten comfortable with the basic concepts. There appears to be a significant gap between what is being taught and what is being tested.

Because our kid has high anxiety (which is a complicating factor and one that we deal with separately), and wants to do well, she spends a tremendous amount of time and effort trying to learn the material to mastery so that she can do well on the test the first time around. And typically, she gets the highest grade, even though it doesn't come easily to her. And, to be fair, the teacher does spend a lot of time after school helping the kids. However, keep in mind that these are high-performing kids!

Her biggest frustrtion, and therefore ours, is that he has assigned several "projects" as all-or-nothing. Either your project works, or it doesn't. The first time he did this, he made it worth 25 points, and it was the first assignment of the quarter. Several parents complained, and he stopped doing it. Then, he started again, but reduced the point value to 5 points.

Our daughter is a language whiz, but math and science concepts are harder for her to grasp. She loved Algebra but had to work very hard to get an A in Honors Geometry. She could do the proofs, but the conceptual part was a struggle. She received a very solid foundation in K-5 with basic math skills and this has helped her immensely.



That's exactly what my youngest sister was like, only she was wracked with anxiety in 5th grade in a farm town in central Illinois.

If she'd had to go to school today, I don't know how she would have made it, or what my parents would have done to get her through.

Here in Irvington, I'm going to be talking about Teaching To Mastery on every conceivable occasion and in all venues.

I can do it, too.




FactSheetPtsaForum 16 Sep 2006 - 20:20 CatherineJohnson



This is the Fact Sheet I distributed to parents & to the PTSA Executive Committee.

I don't think this is the most effective Fact Sheet possible; I would have preferred something much simpler.

I think a very effective Fact Sheet would be just one word problem printed in the middle of the page with this question:

Will your child be able to solve this problem at the end of 5th grade?

I would also want to get across the information that a perfectly average child in Singapore can solve this problem.

However, I really wanted to raise the issue of teaching to mastery and the spiral curriculum, so I filled up the sheet. Under the circumstances, I think that was OK.



Anyone who'd like to use this sheet for anyone reason — please do! And, of course, feel free to modify & improve it.

I would also appreciate feedback. I made this up very quickly, because I didn't get inspired until Ken left his post about teaching to mastery.

This is the best I could do in 15 minutes or so.

NOTE: all of this material fit on one side of one sheet of paper.





Sample problem from Singapore grade 6 placement test (end of grade 5)
The ratio of Zoe’s money to Yolanda’s is 3:7. Yolanda has $64 more than Zoe. If Yolanda gives ¼ of her money to Zoe, what will be the new ratio of Zoe’s money to Yolanda’s? http://www.singaporemath.com/EasyEditor/assets/pl_pm6atest.pdf (pdf file)


Can Irvington children pass Singapore tests?
Tests are available online at:
https://www.sonlight.com/singapore-placement-tests.html
http://www.singaporemath.com/Placement_s/12.htm



Mathematics achievement in the U.S.

  • Average eighth grade U.S. student is 3 years behind average student in Singapore, Japan & Korea source: Beaton et al, 1996 Mathematics Achievement in the Middle Grades
  • Nine percent of U.S. fourth-graders would be included in a talent pool made up of the top 10 percent of all students who took TIMSS [Trends in International Mathematics and Science Study – includes students from undeveloped countries].
  • Only 5 percent of U.S. eighth-graders would be included in this pool instead of the expected 10 percent.
  • The most advanced mathematics students in the United States (about 5 percent of the 12th grade cohort), performed similarly to 10 percent to 20 percent of that same cohort in other countries. Source: Lessons from the World: What TIMSS Tells Us about Mathematics Achievement, Curriculum and Instruction      source: American Federation of Teachers http://www.aft.org/pubs-reports/downloads/teachers/Policy10.pdf



The spiraling curriculum
“…if I put in front of you a fifth, sixth, seventh, and eighth grade textbook in math and opened up to page 200 and I jumbled them up, and said, “order them from fifth through eighth grade in order,” you'd have a very tough time because they all look the same. That's because, unfortunately, we have this national strategy of “we're not really going to teach to master, we're going to teach to exposure and over lots and lots of years of kids seeing page 200 in the math book, eventually somehow they're going to learn it. We're going to teach them how to reduce fractions in fifth grade, in sixth grade, in seventh grade, in eighth grade, in ninth grade and continue until finally somehow magically they're going to get it…..[at KIPP] we have a different math strategy and a different math philosophy.”
Source: Mike Feinberg, co-founder Knowledge is Power Program KIPP. 80% of KIPP 8th graders – disadvantaged children in the Bronx – pass Regents A at the end of 8th grade, as compared to approximately 30 to 40% of Irvington 8th graders, depending on the year http://www.pbs.org/makingschoolswork/sbs/kipp/feinberg.html



Time costs of teaching to exposure, not mastery
Summer regression under spiraling curriculum: 1 month at least
(source: Time for School: Its Duration and Allocation http://www.asu.edu/educ/epsl/EPRU/documents/EPRU%202002-101/Chapter%2004-Glass-Final.pdf)

Summer regression with mastery curriculum: 1 week at most
{source: Student-Program Alignment and Teaching to Mastery http://www.zigsite.com/PDFs/StuPro_Align.pdf spiralling curricula (pdf file, p 16)

American Children lose 3 weeks’ instructional time at a minimum each year that children in other countries do not lose. Some children lose more. While U.S. children are being re-taught skills they did not learn to mastery the year before, their peers in high-achieving countries are mastering new skills and concepts. Over the years, this lost instructional time adds up. 3 weeks lost in second grade means U.S. children are 6 weeks behind in 3rd grade, 9 weeks in 4th, 12 weeks in 5th and so on down the line. The gap widens each year.



Irvington PTSA Forum
PTSA Forum Tonight
Ed's statement to the PTSA Forum
report: PTSA Forum
fact sheet for forum: Singapore Math & teaching to mastery & TIMSS gap





ImCollectingStoriesAboutGaps 22 Jan 2006 - 16:02 CatherineJohnson



Engelmann's Student-Program Alignment and Teaching to Mastery is still rumbling through my Hebbian networks, toppling every domino in its path.

It's kind of fun. I'm experiencing my very own Paradigm Shift.

I don't know where I'll be when things calm down, but one thing I do know: I'm never going to see 'gaps' the same way.



killer Gaps

We're constantly hearing about Gaps, of course. Achievement gaps, learning gaps, teacher gaps — everywhere you turn, there's another Gap.

I've read so much about Gaps I never really stopped to think what a gap actually is, or might be.

I guess I've thought of gaps as static and predictable. All the gaps seem to grow wider over time, until they look like an ice cream cone lying on its side in a PowerPoint slide.

That was then.

Suddenly, gaps seem dynamic, dark, and entirely unpredictable — more properly a phenomenon belonging to Chaos Theory (does anyone talk about Chaos Theory any more?), not Excel charts.



Anne on diagnosing Gaps

What I've noticed with my tutoring students is this: if they don't understand something in math class, they try to find a procedure or "trick" that works everytime.

Since they don't really understand it, when they have to go back and do it on a test or later, they don't remember the "trick" exactly and their answers are consistent, but wrong.

For example, I was tutoring a student in basic math. He didn't really understand that a whole number has an implied decimal after the number (e.g. 3 is really 3. for a decimal problem)

When he first learned to divide decimals and he was following the teachers examples, he was doing the problems right: So if he was dividing .045 into 15, he moved the decimal over three places for the .045 and three places for the 15. He even managed to get it right on the first test.

But he did them wrong on every test after that. When we were studying for the final, I was able to watch him do the problems.

Since he really didn't understand, he made up his own "trick". In the problem above, he would move the decimal over for the .045 correctly, but he put the decimal point in front of any number inside the divisor sign. So .045 into 15 became 45 into 150 instead of 15,000. And, because he had taught himself this trick, he ignored all decimal points inside the divisor sign. So even .045 into 1.5 became 45 into 150.

Needless to say, it took a while to find the problem and then to correct it.





Susan J on diagnosing Gaps

I think it is very, very hard because it is so personal and unique to the student.

I'm 65 and a computational scientist and I still remember odd and embarrassing gaps that had huge negative effects even in graduate school. Even when you get to the point where you are in charge of your own learning, you can miss these things.

For the mathematicians on the site, I'll admit that it took me more time than it should have to understand that when one solves a differential equation, one is solving for an unknown function rather than a variable.

I still remember puzzling over a textbook diagram of a simple mercury barometer when I was a freshman in college. The difficulty (for me) was that the diagram was simplified and didn't show the support stand for the glass tube with its closed end up and its bottom end part-way submerged in a dish of mercury. So I could never figure out why the tube simply didn't fall over!





here's what I'm wondering

Although I believe that the gap between our kids and kids in high achieving countries starts in first grade or thereabouts, I do trust research showing that achievement slows in middle school. (This finding may not be confirmed, but at the moment I take it as probably true.)

Here's what I wonder.

When you don't teach to mastery — when you teach a spiraling curriculum — kids end up with gaps.

That much we know.

But kids probably don't all end up with the same gaps, except for the Universal American Fraction-Decimal-And-Percent gap.

So think what a middle- or high-school math teacher is up against. Ninety or more kids, each with different gaps affecting different areas of the new content they're supposed to be learning and/or spiraling.

It's Gap Anarchy.

At the moment, it seems logical that the further you go, and the more gaps you accumulate, the slower your learning curve is going to be, until finally you hit the wall.

I don't know whether that's true, but it seems logical.

More than logical.

It seems inevitable.



what do we know about learning gaps & how they work?

Here's Engelmann:

When students are not taught to mastery, they often mislearn the skills and concepts the teacher attempts to teach. For instance, they may learn to guess at words in sentences. Reteaching them requires many more trials and much more work than that required to teach them to mastery initially. Initial teaching may require only 10 or fewer trials on some skills. Reteaching the same skill after students have mislearned it and have practiced inappropriate strategies for years may require several hundred trials.


Here he's talking about the case of a student having learned the wrong thing, rather than merely having failed to learn the right thing. The news is bad.

What else do we know about gaps?

Or about reteaching?

And what have your own experiences been?

I'd love to hear.


key worsd: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
formative assessment and Richard Nixon
Terminator





-- CatherineJohnson - 17 Jan 2006



SteveOnWhyKitchenTableMath 16 Sep 2006 - 20:28 CatherineJohnson


The only kids who are prepared to take a proper college prep math (esp. honors or AP courses) track in high school are those kids who are very smart or get help outside of the school. The current crop of fuzzy, low expectation, no mastery, discovery, spiraling math curricula are HARMFUL to kids. In the old days, traditional math may have been taught very poorly or inconsistently, but I don't think that was on purpose (perhaps incompetence and neglect played a part). Nowadays, perhaps there are more controls and teachers are more consistent (with the program), but the math curricula do not get students from point A (counting numbers in Kindergarten) to point B (a full course in algebra in eighth or ninth grade). This IS on purpose.

The problem of education is not some myopic teacher-perspective view of the problem. It is not "if only". If only we had more money. If only we had smaller class sizes. If only we didn't have to meet (trivial) state standards. If only the administration would get off my back. If only parents would get off my back. If only we had a better school culture. It is much more fundamental than that and it's not just about the teachers.

KTM exists because schools are not doing their jobs. Parents have to do it at home at the kitchen table. KTM is not ranting. It contains specific help for parents that they cannot get from the teachers, administration, school committee, or parent/teacher groups. Most of the regulars here have spent a whole lot of time working within their systems. It doesn't work.




After Christopher failed 2 of 6 units in 4th grade math, I had the Bayesian perception that unless I learned math myself, he would be out of the running for any career involving math in any way.

That perception may have been wrong. I'll never know how things might have turned out if I hadn't plunged into re-teaching Christopher his math, plunged into re-learning math myself, and ultimately plunged into writing and, more importantly, reading Kitchen Table Math.

Looking back, I think it's right to say that I myself was locked out of any career involving math in any way.

In my own school days, I was taught to mastery. That teaching stood me in good stead. I had 'shopkeeper's arithmetic' down cold, and I was able to start over again learning math in mid-life, and make quick progress.

But it wasn't enough to let me take math in college. And at that age, in college, I didn't know what I didn't know. I didn't know whether I liked math or not, whether I might be reasonably good at math or not, whether I should be doing something related to math or not....I didn't know anything. if I thought about it at all, I just figured I wasn't a 'math person.'

As one of Carolyn's old professors says, the last person you want making life decisions is a 19-year old.

When we were in Los Angeles over vacation, I spent time with the now-grown children of friends.

These kids have had fantastic educations, every one of them in private schools, including Catholic schools.

None of them is headed toward a math-related field at the moment (these kids are high school seniors & college freshmen) but each one of them could choose a math-related field if he or she wanted to do so. The door is open.

That's what I want for Christopher (and for Andrew, obviously, if I can get him there). I want the door to be open.

We've chosen to live in a high-tax suburban town with good schools. This was our version of choosing a private school. Talk about not knowing what you don't know.

The Irvington math track, thus far, isn't going to put Christopher in position to choose a math-related career.

Everyone says the high school is fantastic, and given the principal there I'm sure it is.

But when I talk to parents whose kids have taken AP calculus at IHS — and those kids are the only American kids who are competitive with their peers in other countries — what I hear is this:

His dad is really good at math, so he helped him all the way through.

In other words: my son made it through AP calculus because his dad knows calculus.

I have also heard this:

My son couldn't find a calculus tutor anywhere. He had to get through it on his own.

The woman who told me this has an advanced degree in math herself.

Carolyn says she finds it hard to believe that there could be no calculus tutors in all of Westchester County, and I agree.

But — and here's the point — I can't take the chance.

Maybe there'll be calculus tutors in Westchester when Christopher gets to Irvington High School, and maybe there won't.

Maybe Christopher would have gotten back on track without my turning into Math Mom, and maybe he wouldn't have.

I don't know.

I couldn't take the chance.


-- CatherineJohnson - 26 Jan 2006



LearnersAreFragileRedux 16 Sep 2006 - 20:37 CatherineJohnson



learners are fragile

They are.

American middle schools teach to coverage, not to mastery.

When you teach to coverage — and you grade a child on his performance — it's sink or swim.

If the child has the organizational ability to manage, he swims.

More likely, she swims.

If the parents can carry a disorganized child bodily through the curriculum — fighting him (more likely him) all the way — he swims. Maybe.

Everyone else sinks.


-- CatherineJohnson - 26 Jan 2006



AccelerationNotRemediation 16 Sep 2006 - 20:38 CatherineJohnson



Carolyn's dead right about Saxon: the program moves students along at a brisk clip.*

I was thinking about it just last night, while I was doing my own Saxon lesson.

I'd put money on it I'm learning lots more than Christopher, whose book is, technically speaking, more advanced.

And I'd put money on it he'd end the year knowing more than he's going to know with Prentice-Hall if he were using Saxon, too.



slow and steady wins the race

The conventional wisdom about 'behavioral' programs like Saxon Math is that they're remedial; they're for slow learners.

Well, it's true.

If I were teaching a class of slow learners, I'd choose Saxon Math in a heartbeat.

But Saxon also moves fast learners through material at a fast clip. If you're a fast learner, you just work through the material more quickly. Back when Christopher and I were using Saxon 6/5, the 5th grade book, we were doing complete full lessons a day for a time.

Only recently have I realized that Teaching to Mastery means accelerating a student's rate of learning.

High achievers move faster with Direct Instruction:

Tarver and Jung reported that the Direct Instruction program was equally effective for lower and higher performing children who participated in the study. Other studies provide additional evidence that Direct Instruction programs accelerate the learning of high-performing students in language (Robinson & Hesse, 1981), reading (Schaefer, 1989; Sexton, 1989), and science (Vitale & Romance, 1992).
source:
Watkins & Slocum, The Components of Direct Instruction, JOURNAL OF DIRECT INSTRUCTION, summer 2003, p. 75-110




low achievers move faster, too

Direct Instruction is, expliticly, a teaching approach designed to produce 'maximum acceleration' for all students at all levels. (see: Student-Program Alignment and Teaching to Mastery by Siegfried Engelmann)

Not only can low achievers be accelerated, when they are accelerated their learning curves look like those of fast learners:


DIlearnercurves.jpg


I find this counterintuitive and almost bizarre.

When taught to mastery, low IQ students learn at the same clip as high IQ students?

Hard to believe.

On the other hand, I wouldn't be surprised. So many of our decades-old beliefs about students and learning are just pure ideology.

So I hope Engelmann's right.

Here's what he has to say:

Even students who would be predicted to have low levels of achievement benefit greatly from Direct Instruction. Gersten, Becker, Heiry, and White (1984) examined the yearly achievement test profiles of students in Direct Instruction classrooms to determine whether annual gains made by students with low IQ scores differed significantly from the gains made by students with average or superior IQ scores.

Figure 2.11 [above] shows the yearly gains made by students in reading as measured by the Wide Range Achievement Test. As shown in this figure, students with higher IQ test scores started at higher achievement levels and ended with higher levels than their peers with lower scores. However, the pattern of growth of students with low IQ scores is remarkably similar to that of other students. The group with the lowest scores (under 70) gained nearly as much each year in reading as students with much higher scores. By the end of third grade, those students with the lowest IQ scores were performing at the 70th percentile, or a grade equivalent of 4.3.

The results are even more pronounced in math as seen in Figure 2.12 [below]. This figure shows the students’ performance on the Metropolitan Achievement Test. The growth rate for all groups of students corresponds to one grade equivalent for each year in school.



DIslowlearnermath.jpg


These results provide evidence that Direct Instruction is appropriate for, and effective with, a wide variety of individuals including those with low IQ scores, those with IQ scores in the average range, and those with high IQ scores. In addition, because children in this study were taught in small homogeneous groups (having students with relatively the same skill levels), the gains of students with lower IQ scores were not made at the expense of other students nor the other way around.

Several reviews of research focusing on the use of Direct Instruction with special education populations have all converged on the finding that Direct Instruction is measurably effective with these students. White (1988) reviewed 25 such studies and found that all comparisons favored the Direct Instruction group. Forness, Kavale, Blum, and Lloyd (1997) conducted an analysis of various intervention programs for special education and determined Direct Instruction to be one of only seven interventions with strong evidence of effectiveness.

Perhaps because Direct Instruction programs have been so successful with students who have failed in other instructional programs, their use is commonly associated with children who are behind, who are failing, or who are at risk for failure. And some have questioned their appropriateness for general education. However, Figures 2.11 and 2.12 provide direct evidence of the effectiveness of Direct Instruction for students with IQ scores in the middle range and those in the upper range.

Engelmann and Carnine (1989) found that typical second graders who had received 2 years of Direct Instruction scored an average 4.6 grade equivalent in reading on a standardized achievement test. The children’s average scores in science and math were 4.0 and 3.4, respectively. Other researchers have arrived at similar findings. Tarver and Jung (1995) investigated the effects of a Direct Instruction math program (Connecting Math Concepts) and a discovery learning math program on the math achievement and attitudes of general education students in the primary grades. They found that, at the end of second grade, the children in the Direct Instruction program scored higher on measures of math computation and math concepts than children in the comparison group. In addition, children in the Direct Instruction program had significantly higher scores on a survey of attitudes about math. Finally, Tarver and Jung reported that the Direct Instruction program was equally effective for lower and higher performing children who participated in the study. Other studies provide additional evidence that Direct Instruction programs accelerate the learning of high-performing students in language (Robinson & Hesse, 1981), reading (Schaefer, 1989; Sexton, 1989), and science (Vitale & Romance, 1992).





acceleration for all students through Direct Instruction in a nutshell

  • The group with the lowest [IQ] scores (under 70) gained nearly as much each year in reading as students with much higher scores.

  • The results are even more pronounced in math as seen in....performance on the Metropolitan Achievement Test. The growth rate for all groups of students corresponds to one grade equivalent for each year in school.

  • because children in this study were taught in small homogeneous groups (having students with relatively the same skill levels), the gains of students with lower IQ scores were not made at the expense of other students nor the other way around

  • Perhaps because Direct Instruction programs have been so successful with students who have failed in other instructional programs, their use is commonly associated with children who are behind, who are failing, or who are at risk for failure.

  • Engelmann and Carnine (1989) found that typical second graders who had received 2 years of Direct Instruction scored an average 4.6 grade equivalent in reading on a standardized achievement test. The children’s average scores in science and math were 4.0 and 3.4, respectively. Other researchers have arrived at similar findings.

  • discovery versus Direct Instruction: Tarver and Jung (1995) investigated the effects of a Direct Instruction math program (Connecting Math Concepts) and a discovery learning math program on the math achievement and attitudes of general education students in the primary grades....at the end of second grade, the children in the Direct Instruction program scored higher on measures of math computation and math concepts than children in the comparison group. In addition, children in the Direct Instruction program had significantly higher scores on a survey of attitudes about math. Finally, Tarver and Jung reported that the Direct Instruction program was equally effective for lower and higher performing children

  • more on high achievers: Other studies provide additional evidence that Direct Instruction programs accelerate the learning of high-performing students in language (Robinson & Hesse, 1981), reading (Schaefer, 1989; Sexton, 1989), and science (Vitale & Romance, 1992).



KUMON is an acceleration program, too

Interestingly, KUMON adds the element of teaching children to become 'self-learners,' i.e. self-teachers:

Our aim should be to educate our students so well through the Kumon Method that they don't have to depend solely on classroom activities to be able to deeply understand the course content. Students who develop this capacity will have a good chance to enter leading universities. To make this possible, we must help students acquire the ability of self-study from an early age and accelerate their level of study beyond their school grade. (Emphasis added)


Here is the irony.

When Ed and I told our 'Team' that we want the school to be responsible for Christopher's learning, as opposed to Christopher being responsible for Christopher's learning, the principal objected. Christopher has to learn to be responsible, he said. He'll need it in high school.

It was another helicopter parent moment, though neither hostile nor critical.

The essential meme in middle schools everywhere seems to be that helicopter parents don't 'allow' their children to grow up and become responsible for themselves and their studies.

But KUMON says that a Teach-to-Mastery approach builds responsibility in children.

I don't understand quite how that happens.

But I believe that it does.

I think this is one of those Bayesian issues where parents have the right idea, without knowing why they have the right idea.

A parent sees his child floundering and failing, and knows this is a bad thing.

The parent knows the child will be far better off if the school continues to 'coddle' and 'protect' him while he learns the material his teachers are teaching.

But how do we know this?

What are we basing it on?

It's the same problem parents have 'knowing' fuzzy math is bad.

The minute I heard about fuzzy math, I knew it was bad.

But could I say why it was bad?

No.

Same thing with 'responsibility.'

Obviously, I want Christopher to grow up to be a responsible person.

And yet, somehow, I'm in the position of arguing 'against' Christopher being responsible.

I know — in the Bayes way of knowing — I'm right.

But I don't know why.

UPDATE 10-20-2006: Now that my child has spent one year in a math class in which full responsibility was placed upon parents for reteaching and students for learning, this issue is no longer a mystery.



* ed. update 4-21-2006: Dan has some reservations on this score. It's certainly true that the Saxon books have a tremendous amount of repetition from one book to the next.

Mike Feinberg of KIPP on spiral curricula
Steve and Susan J on spiral curricula
acceleration versus remediation
parents' stories about spiralling curricula


-- CatherineJohnson - 26 Jan 2006



DirectInstructionAndTheRigorConundrum 16 Sep 2006 - 20:39 CatherineJohnson



There's all kinds of good stuff in the various comments threads — in particular, Rick Ballard, who is amazing with statistics and polling, is trying to figure out what the 'Boy Problem' numbers actually mean.

I'm all over the place on the Boy Problem, obviously.

I don't like what I see as anti-boy bias in textbook development, and I think schools are too female-dominated. Those observations are pretty much incontrovertible.

I also think schools over-reward clerical and organizational skills, while over-punishing the lack thereof. These perceptions are more debatable (especially seeing as how I don't know what middle school girls are experiencing).

What I'm not at all sure of is whether there's a 'real' boy problem in districts like mine, where divorce is rare and dads are present.

Here's what Rick's found so far:

I'm still working on the data sets but I'm not finding any clear distinctions - other than that men are more highly rewarded than women after college for the same level of performance in college. IOW - there is no economic payoff for any edge awarded to women during school. I'm beginning to wonder if the higher rate of matriculation and graduation might not be attributable to innate differences in the importance that each sex attaches to organizational skills. The "leveling of the playing field" back in the seventies may have just revealed women's superiority in completing tasks within an ordered environment.


This is exactly what I've been wondering.

Is college just more of a 'girl thing'? (I say 'girl thing' neutrally in this case.) I was talking to Ed about this yesterday. He doesn't know what to think about the whole thing, either, but he pointed out that when you look at Continuing Ed, it's all women.

It's true. I've tried to take a couple of continuing ed. courses (I always end up dropping out) and the ratio is 10 to 1, if that. For every 10 middle-aged women taking a continuing ed. course, there'll be 1 guy.

Women like school!

So I don't know. I think Rick's still looking into it.....I'm going to be interested to read what he comes up with.



tp_rule.gif



There's lots of other good stuff, too, but I wanted to get this up front sooner rather than later.

Here's Ken, on acceleration of normal students through Direct Instruction:

Engelmann also claims that in a low mobility school with sufficient number of high performers, these high performers can be accelerated at 3-4 times the usual acceleration rate that DI achieves. To do this you'd need an affluent suburban school to become a DI immersion school and there's esentially zero probability of that happening in the absence of outright parental revolt.


At this point, I'd like to know exactly how fast a high-achieving child taught via Direct Instruction can move.

Toru Kumon, who wrote the KUMON worksheets and founded the company, had his own son doing calculus in 6th grade.

Even though I haven't taken calculus myself (yet), I'll go out on a limb and say I believe it. Now that I've worked with Singapore Math a bit, and spent so much time immersed in K-8 math, it makes sense.

Here in 6th grade, Christopher is being taught Algebra 1. That's what this course is. Algebra 1 and geometry (without the proofs). AND the kids have all started Algebra 1 without being anywhere near mastery of fractions, decimals, or percents.

He's having a heck of a time, but it's obvious to me, sitting and working with him, that if John Saxon or Siegfried Engelmann were running this course he'd be learning the material.

He'd be learning the material because it's not 'hard.' The fact that Christopher has apparently reached some kind of mastery on integers is evidence. He was utterly confused by integer operations at the beginning of the year; he's remained confused throughout the year (for 'the year' please substitute '3 months'); and now, all of a sudden, he can take a pop quiz on integer operations and score 20 out of 20 correct.

If integer operations were hard, he'd be scoring 0. Because he has sure as heck not been taught to mastery.

So how far and how fast can a high achiever go with Direct Instruction?

Do we know?



the rigor conundrum

For me, Direct Instruction and KUMON have solved the 'rigor conundrum.'

The rigor conundrum is this.

Many parents want their schools to provide a more rigorous curriculum.

At the same time, parents don't want their kids homeworked to death.

I'm not going to take the time now to pull all the evidence for this; you'll just have to trust me. There's plenty. Here's one: Tom Loveless, at Brookings, has some great stuff on the Homework Wars. All over the country you've got parents in open rebellion about how much homework their kids have to do — and when you look at it, it turns out nobody's doing any homework! We're doing less homework than other countries, and homework levels are the same as they always were. (This isn't strictly true; Loveless explains why parents believe homework demands have soared.)

So the question is: which is it?

Do parents want a more rigorous curriculum?

Or do they want a less rigorous, lower-work-loads curriculum?

Policy experts don't know; that's why you see Forums on the question of Will the American public support excellence in education & the like.

Meanwhile, I've had a paradigm shift.

More rigorous education versus Less homework is the wrong question.

'Rigor' doesn't mean '4 hours of homework' plus an Extended Response problem you have to know modular arithmetic to solve.

I think Ken's expression for this is fake rigor.

'Rigor' means material is taught to mastery so students can accelerate their progress through the curriculum.

and:

Material taught to mastery is far easier to learn than material taught through exposure.

What parents want is more rigor without more homework — without pointless, overwhelming, ditch-digging-in-San-Quentin levels of homework.

I'd put money on it that if parents saw their kids being assigned more homework that obviously increased their learning and mastery they'd support it.

But given what I've seen of KUMON, quantity shouldn't be the 'standard' in K-8 or perhaps even in K-12 (not sure about that).

KUMON's philosophy is slow and steady wins the race. Ten to twenty minutes a day, and don't over-do it.

They've shown that it works.



KUMON and 'responsibility'

KUMON talks about self-learning.

Kumon students study independently at both Kumon Centers and at home. The role of instructors within the Kumon Method is focused almost entirely on the development of a student's ability to learn on their own. Kumon refers to the ability to set goals and solve unfamiliar and challenging tasks independently as "self-learning" ability. Instructors foster this "self-learning" ability in students by using worksheets that allow students to learn at one's own pace, moving forward when they are ready. The students' enthusiasm for learning is aroused in this process, as the goals they set are their own goals. In addition, this process awakens a desire in the students to take on new challenges.

Instructors ensure that students can, without any hindrances, experience over and over a sense of accomplishment, thereby boosting confidence in their own abilities. Problem solving abilities are enhanced, and independent methods of solving problems are encouraged. Instructors must also observe the study behaviors of each student, get a sound idea of each student's particular learning situation and incorporate this into the method of instruction. Instructors routinely analyze the learning process. If problems become apparent, the instructors ask themselves pertinent questions about the problem before proceeding such as, "Is the student's pencil moving too slowly?" or "Is the student too lost in thought?" Through such careful observation of the student's learning, small obstacles are removed in a timely manner thus assisting the students in their self learning.

Consequently, it is a uniform approach, using the worksheets, the instruction method, the input and analyses of the instructors, and the abilities of the students, which make the method a great success.



That's a terrific description of KUMON, Ideal Type.

Around here, we're not experiencing KUMON, Ideal Type. Christopher isn't becoming a Self-learner via KUMON at this point; he'd quit today if I let him.

Nor are we having a lot of helpful analysis of pencil grip.

Doesn't matter. Christopher is practicing and learning every day.

KUMON draws a connection between correctly paced teaching to mastery and the child's eventual independence and self-motivation.

I believe it (and in fact I do see signs of it in Christopher at times).

Here's Ken again (yes, we're having an all-Ken-all-the-time day here at ktm):


The reason why DI and Kumon create more independent learners by the middle school years is because they start with a high degree of student support in the lower grades and gradually fade the support structure by the end of the program. Still, many low performers always need some level of support over the average student. With other kids, the support can be faded even faster.

Bear in mind that in any event the support is faded gradually and that the kids have been exposed to effective learning techniques over the course of many years off of which they can model their own learning. The rug just isn't pulled out from under them come sixth grade. There is no sink or swim, nor should there be at this age.



This is as good an explanation as I think I'm likely to see of how a 'passive,' 'spoon-feeding,' Directly-Instructing program like KUMON in fact leads to an active, independent, self-motivated and self-directed student over time.

I want my school to adopt an educational philosophy and practice of teaching to mastery.


dingbatWSJ2.jpg


extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal



-- CatherineJohnson - 27 Jan 2006



FormativeAssessmentAndRichardNixon 16 Sep 2006 - 21:05 CatherineJohnson



I was trying to pull together the various posts & comments on gaps and gapology when I discovered that one of the many benefits of formative assessment is that FA allows you to:

a) discover gaps

and

b) get rid of gaps

Feedback given as part of formative assessment helps learners become aware of any gaps that exist between their desired goal and their current knowledge, understanding, or skill and guides them through actions necessary to obtain the goal (Ramaprasad, 1983; Sadler, 1989)


The importance of this idea should have been obvious, yet I wasn't thinking about gaps when I first began looking into formative assessment.

So I was sitting here thinking about formative assessment and gaps when I flashed on the famous Howard Baker line about Richard Nixon:



What did the President know, and when did he know it?


That's formative assessment for gaps.




255px-Howard_baker_jr.jpg



key words: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
formative assessment in a nutshell
formative assessment and Richard Nixon
Terminator



-- CatherineJohnson - 31 Jan 2006



CarolynOnMasteryLearning 07 Feb 2006 - 19:54 CatherineJohnson



I was just doing some Librarian work on ktm (linking like posts with like, dropping 'back doors' into existing posts, posting links in the book-style index) — and I discovered that Carolyn wrote a post on mastery learning back in May!

How good is mastery learning? Two of the review studies looked at mastery learning by itself and with combinations of other curricula, and found that mastery learning by itself produces better results than what was termed 'conventional instruction'. However, mastery learning got its best results when used with other teaching techniques. One study got decent results for "mastery learning with corrective feedback" (meaning -- electric shock? The review didn't say), but got its best results from mastery learning with 'enhanced cues' -- extremely detailed instructions to the students on how to do problems.

Another study found that mastery learning and cooperative learning strongly enhanced each other (note: cooperative learning is structured working-together among students, as opposed to simply being stuck in groups to do your homework together: see part two of this series).

It's interesting, reading this post now, not least because I recognize one of the author's names: Doug Carnine.


Report to the California State Board of Education


-- CatherineJohnson - 06 Feb 2006



WholeSchoolReform 11 Feb 2006 - 01:38 CatherineJohnson



A series of links, starting with Carnival of Education, then moving to Jenny B & on to Foundations of Teaching and Learning brought me to a professor's notes taken on a lecture about bringing "research-based practices to scale in school."

I'm out of my depth here. I've begun reading books & articles on 'whole school reform'.....and that's about it.

Translating the findings of cognitive science on the nature & process of learning, which I do understand, into public policy and systemic institutional reform — I can't make that jump.

This lecture, and the study to which it refers, appear to come out at least moderately in favor of very early grades scripting, which I know sets a lot of people's teeth on edge —

As far as I can tell, it appears that scripting was effective in Kindergarten, but not in grade 3 (please correct me if I'm wrong).

I think I've mentioned that the Saxon books are scripted early on. I know the Kindergarten book is scripted, because I have it. I know the 1st grade book is scripted because my sister-in-law uses it in IL.

I don't know when Saxon stops scripting lessons, but I'll bet it's somewhere around 2nd or 3rd grade. (Again, if anyone knows for sure, chime in.)



leadership in schools

Although I don't understand public policy well, this passage doesn't surprise me:

ASP - focused on "cultural control" aimed at promoting "powerful learning" that schools needed to define themselves. Instruction is not specified in any centralized way.

AC - focused on "professional control" in which the emphasis is adhering to standards of teaching and learning. A key feature was a very aggressive leadership training program focusing on principals and coaches.

SFA - focused on "procedural control" in which instruction is highly scripted. What students should learn and how they should be taught are quite clear, particularly given the scripting. Coaches and leaders teach the design and monitor fidelity of implementation.

Teachers report that SFA and AC (compared with controls) have greater design specificity and consistency, and more interaction with leaders, but ASP has more support for teacher autonomy.

[snip]

Effects on achievement (using the TerraNova test).

SFA had a 1.5 month grown effect at K but not at grade 3.

AC had a positive effect of 2 months at grade 3, but not at K

ASP didn't have any significant effects.



As far as I can tell, for years researchers have been saying that strong principals are the key.

Until someone proves that to be wrong, I believe it. 'The person at the top sets the tone.'

It doesn't surprise me that a reform focusing only on 'culture' or on 'teacher autonomy' would produce no results. Schools need strong educational leadership.



question

Ken may know the answer to this.

What is the difference between Success for All & Engelmann's Direct Instruction?



update: Vlorbik on SFA

i'll take that one after barely glancing
at "success for all": engelmann is clearly
a human being with actual opinions of his own
but "s.f.a" is a committee of mushmouth obfuscators
with nothing in the world to say but feel-good cliches.




Vlorbik2.jpg



-- CatherineJohnson - 08 Feb 2006



RenaissanceLearningAndAcceleratedMath 13 Feb 2006 - 23:57 CatherineJohnson


ok, I am now officially too sick to carry on. (head cold; bad one)

I'll drop in these links, and come back later:

  • STAR Math 12-minute assessment program (part of Accelerated Math)




This sounds like a good idea, especially seeing as how a parent invented it. I almost always like teaching systems and ideas parents come up with.

Does anyone have experience with Accelerated Math?

The 'wiki' page is excellent — seems to be written by a teacher actually using the program.



can formative assessment be done by software?

Offhand, it strikes me that formative assessment is the area of math ed most compatible with software & programming...

A couple of teacher comments:

"I am thoroughly convinced that Accelerated Math can do things for students in math that are almost impossible to accomplish otherwise. The instant feedback and the emphasis on mastery ensure that students do not just coast through the program without truly learning the material. While the teacher (or someone) still has to do much of the teaching, students can be much more independent much of the time, and can cruise quickly through objectives that come easily to them. I have never made it through the end of the math book with any of my classes - I'm lucky to get past the halfway point with some of them. But with AM, motivated students can master EVERY SINGLE objective for the grade level library they work through, eliminating the gaps I see in the math skills of most of my students."

"The true power of AM is its ability to collect data about each student and to report that information to the teacher so he/she can act upon it. AM will notify a teacher whether a student is struggling in any given topic. It is then the teacher's job to act accordingly. The teacher may re-teach a lesson to the whole class, assign a peer-tutor to a struggling student, or to meet with the struggling student himself/herself. AM notifies the teacher of a struggling student much faster than the teacher ever could have figured it out if left to his/her own devices. I could continue singing the praises of this wonderful teaching tool, but I fear I've gone on long enough."


One last thing: Joanne Cobasko, of SOCMM, had a horrific experience with a software math-teaching program her school used with her son. I'll get her story posted at some point. The school wouldn't let her son advance, because the software, which was broken (IIRC, the headphones may have been defective...?) said he wasn't ready.

Apparently they put Hal in charge of math.



update: Joanne Cobasko on SuccessMaker:

Fairfax County, VA Evaluation of SuccessMaker Computer Curriculum Corporation (CCC) SuccessMaker Program Final Evaluation Report (pdf file)

From page 5 of the pdf file above under the heading Findings then sub heading of Student Achievement comes the following:

"For the most part, no significant differences were found between the performance of students at the CCC [SuccessMaker] program and comparison schools on the Stanford 9 mathematics tests. In all three years of the evaluation, students at both groups of schools demonstrated significant growth over the course of the year, and not many differences were found in terms of the rate of growth. Student gains from fall to spring on the Stanford 9 showed modest correlations with the gains made on SuccessMaker's own assessments, but did not show direct correlations with time spent on the system. In several instances....Students who spent under 20 hours on the program outperformed those who spent more than 20 hours on the program..." [bold emphasis is mine]

To put these findings in plain language there were only SMALL correlations with actual standardized test outcomes and the SuccessMaker reports teachers print out which show glowing results in student achievement. The students who spent the least amount of time on the SuccessMaker program scored better on standardized tests.

To further illustrate the lack of effectiveness of this program, Aspen Elementary has been using SuccessMaker since December of 2003 and their API scores have not shown ANY improvement. 2003 and 2004 API reports on the CA SBE web site (posted before 2004-2005 adjustments took place, show a 5 point drop from 879 down to 875, then a one point increase to 876) California Department of Education Academic Performance Index (API) Report

Why on earth is the administration requesting that the district finance this ineffective intervention? It is expensive and shows little in the way of results.

The IES has indicated there is NO VALID RESEARCH to show this program is effective: What Works Clearinghouse.

The district is further crippling CVUSD math education by using this program as it's sole intervention for students who are struggling with math.

If all students are required to spend 20min twice a week in the computer lab on this program you must add in the time necessary to line up and walk to and from the computer lab. There is probably 1.5 hours per week taken out of classroom instruction time to accommodate this intervention. THESE ISSUES MUST BE ADDRESSED BEFORE APPROVING GENERAL FUNDING FOR SUCCESSMAKER At the very least the district needs to perform a scientific evaluation of standardized test scores from the CVUSD schools that have been using SuccessMaker and the ones that have not. A teacher survey of their perception regarding outcomes will NOT be sufficient. The board members have a responsibility to protect taxpayers by insisting on a cost benefit analysis of this intervention.

Scarce funding would be better spent on tutors for after school Math and Reading programs staffed with human instructors, not computers.


-- CatherineJohnson - 11 Feb 2006



MiniProblems 15 Jul 2006 - 16:33 CatherineJohnson



I've been complaining for months about the lack of word problems in Christopher's math class.

The kids memorize one procedure/rule/formula a day, do a few calculations, and march on. As a direct result, IMO, their knowledge really is rote as opposed to procedural. At least, Christopher's is. And I've had enough math talks with other kids in the class to know some of them are in the same boat.

Today I had a eureka moment reading a Comment left by Kathy Iggy:


The old math books I found (the same ones I used in grade school) have lots of what they call "mini problems" used to illustrate how a recently taught concept would be presented in a word problem. Megan likes these because of their brevity and she doesn't have to struggle with comprehension that much.

For example:

20 yards of ribbon. 1/4 used for dress. How much ribbon used?



That's IT!

mini problems


That's the concept, and the phrase, I've been looking for.




mini problems:word problems :: basic skills:higher order skills .

That's from Ken, and he's exactly right.

[update 4/23/2006: no! he's not right! Actually, he's write about using mini problems to teach word problems; I'm talking about mini problems to teach math - to teach the fundamental concept in a lesson. Awhile back I realized that word problems are the 'real manipulatives.' Now I know what I mean by that.

All concepts should be taught — illustrated — with mini problems. All concepts, every last one.

PRIMARY MATHEMATICS does this; SAXON MATH does it; KUMON does it. I'll post examples.

I've come to feel that the first word problems illustrating a new concept should be so simple children can do them in their heads.

For example, the very first ratio word problem a child does should be something like this:


Christopher bought one pencil for one dollar.
How many pencils can he buy for two dollars?


The question should be written this way, too: on two separate lines, so the child sees instantly that the first sentence is the set-up, and the second sentence is the question. Richard Brown's revision of Mary Dolciani's BASIC ALGEBRA, a book I like very much, does this for many of its word problems. I'll post some of those, too, as I get to it.

mini problems are applications

The problem with word problems is that, in the U.S., they're always hard.

Word problems are so hard people have apparently come to think that if a word problem isn't hard it isn't really a word problem.

I'm wondering if we ought to ditch the phrase 'word problem' (ditto for 'story problem') and adopt the word 'application.'

A better idea: we should think about the point of word problems.

Some word problems are written and assigned to give students practice.

Many word problems are written and assigned to assess whether students have developed flexible knowledge.

I'm talking about a third purpose, which is instruction. I'm talking about word problems designed to teach.


instructional word problems


A word problem is an application. A super-simple, starter word problem explains and demonstrates a mathematical concept by showing students how the concept is applied.

As a matter of fact, an instructional word problem shouldn't even be a 'problem.' It should just be a question, and the answer should be obvious.

A simple, instructional mini-problem should not test the child, should not challenge the child, and certainly should not trick the child.

It should teach.


examples to come


be sure to see Google Master's comment



how do you teach your child word problems?
mini problems (important)
arithmetic to algebra & mini-problems



-- CatherineJohnson - 07 Mar 2006



DefensiveTeaching 13 Mar 2006 - 23:37 CatherineJohnson



Ms. K rarely assigns word problems.

What problems she has assigned have been, frequently, far above the kids' skill level. (examples here: scroll down for the entire list)

The parents do these problems at home, then the kids turn them in. This is an open secret. My favorite Extended Response moment happened last year, before Christopher had moved to Phase 4. One weekend parents all over the soccer grounds were grabbing each other & asking whether anyone knew how to do the latest Extended Response. These were all highly educated Westchester parents with important jobs requiring advanced training.

And they're running around the soccer games accosting people about the latest Challenge Problem their kids have to hand in.

This year there's one student in one of the Phase 4 classes who, last semester, was getting 60s & 70s on his tests and had straight '10s' — the highest score possible — on the Extended Response problems.





NOTE to IMS Math Department:

Look for a pattern!

Cs and Ds on tests, A+ on Extended Response problems — what does this suggest?





The Extended Response problems are assigned because, in the beginning, the Phase 4 students were supposed to be mathematically gifted, and Irvington's pedagogical philosophy where the mathematically gifted are concerned can be summed up in two words: Math Olympiads.



gifted and talented according to Math Olympiads

The MATH OLYMPIADS approach to educating the gifted and talented, as far as I can determine, is the following:

  • The mathematically gifted child needs, above all, to be challenged.

  • The best way to challenge the mathematically gifted child is to give him super-hard problems he's never been taught how to do & send him off to grapple with them on his own.


I have the Challenge Philosophy in writing. The Assistant Superintendent for Curriculum said, in a letter to me, that Phase 4 kids 'need to be challenged' — although he agreed that kids shouldn't be given problems so challenging their parents would have to do them.

He may be right about kids who really are GATE in math, although I can't imagine GATE kids don't need instruction.

And my leaning where GATE kids are concerned is towards acceleration over enrichment.

I may be wrong about GATE kids.

But I'm right about the high achievers.

Kids who do well in math because they're high-achieving don't need Math Olympiad problems.

In fact, I'll go for the Strong Form here:

Kids who do well in math because they're high-achieving are harmed when they spend time on Math Olympiad 'challenge problems' instead of word problems pitched to their level and embodying the concepts they are currently trying to master.

Ms. K assigns Challenge problems, not Instructional problems.

As a result, virtually all of the word problems Christopher has done this year fall under the heading of lost instructional time.

What Christopher needs are brilliant instructional word problems of the kind provided by Action Math.





has Math Olympiads become a national curriculum?

I always saw the Extended Response problems in the accelerated class as an 'add-on.' The mathematically talented kids were taught math like everyone else, only they had to do Extended Response problems, too.

Now I'm wondering whether in fact the 'challenge' approach is simply another manifestation of constructivist math.

Instead of being taught how to do word problems, kids are handed a problem and told to figure it out on their own.

Here's what I see in Christopher's class:

number one: The kids have been given virtually no 'normal' word problems — normal meaning do the odd problems for homework-type problems — all year.

number two: They've been given 9 Extended Response problems, only 1 or 2 of which they could plausibly solve on their own.

number three: To my knowledge, they've been given little-or-no direct instruction in the kinds of word problems that will appear on the state test.

number four: This week, when Ms. K. finally did assign a page of word problems for homework, she gave them no instruction whatsoever on how to do them.

number five: Having read all of the sample problems for the state test, I would be stunned if any problems like the ones Ms. K. assigned this week will appear on the state test next week.

number five: My guess is she didn't demonstrate how to do the problems in class the next day, either, unless the students asked her to. (I'll ask Christopher.) I don't see how she could have. There were 5 problems in all, each requiring a different approach the kids have not been taught, and they spent at least 10 minutes writing in their math journals. That doesn't leave a lot of time for demonstrating and explaining five different word problems in one class period.

update: As I suspected, Ms. K went over 'the problems kids had trouble with,' which means that it was up to the kids to a) know they needed help and b) say so in front of a class filled with peers who, at lunchtime, are going to be calling them 'fat,' 'gay,' and/or 'stupid.' The only problem Christopher remembers her going over in class was 'the runner problem.' (This is two days ago, we're talking.) He has no memory, none whatsoever, of what she actually said about how to do the runner problem.

I'm sure the runner problem came up because no one in the class could do it, so there was no shame in admitting defeat.

Almost certainly most of the kids solved problems 8, 11, & 12 through guess-and-check, and that was that. It's unlikely that any of the 11-year olds Christopher knows would say, "I got the right answer, but I'm wondering whether there's a more elegant and efficient way to go approach this problem."



I'm not privy to Ms. K's thinking, but I know exactly what the effect of her approach to word problems has been on Christopher (and I know he's not the only one):

a) properties, rules, and procedures are learned by rote

and

b) all word problems, including simple, beginning problems in algebra, become Challenge Problems


I'm guessing that this approach is the result of the constructivist pedagogy Ms. K, who is very young, would have been taught in ed school — whether she's aware of it or not.

She teaches the 'basics' in class, the kids memorize what she's put on the board, then the kids discover how to apply the basics to word problems on their own.

In fact, it's probably worse than that, since Ms. K. told a friend of mine that she teaches the concepts the day after the kids have done homework on those concepts. My friend said Ms. K told her this in a 'DUH!' tone, as if it should just be obvious a teacher wouldn't teach a new concept before assigning homework on the concept.

I'm wondering whether this is an ed school truism at this point.

Do ed schools teach future math teachers to have the students discover everything first, including rules, properties, and procedures, and then "go over it" later after the kids have discovered whatever they're going to discover?

I don't know.





this is where bar models come in

Here is 1 of the 5 problems Christopher's class was assigned for Wednesday night:


P-Hproblem9p283.jpg


None of the kids has been given any instruction whatsoever in how to set up such a problem algebraically.

Nor have they been given any instruction in the Official Prentice-Hall Problem Solving Strategies:


P-Hprobsolvechart.jpg


Wednesday afternoon I was working on these problems with Christopher and his friend M.

Needless to say, neither boy Looked for a Pattern, Guessed and Tested, Simplified the Problem, Made an Organized List, Worked Backwards, Accounted for All Possibilities, Made a Table, Wrote an Equation, Solved by Graphing, Drew a Diagram, Made a Model, Solved Another Way, or Simulated the Problem.

No.

Instead, both boys, working independently, subtracted 280 from 2870 and then stopped. They knew they weren't done, but they didn't know what to do next. They didn't know why they'd subtracted 280 from 2870, either.

I pointed out to M. that one runner went 280 m further than the other. Unfortunately I can't remember what he did with this information. I do know that he ended up with answers that were 280 m different, but added up to a whopping big batch of meters, far more than the original 2870. Then he started getting upset, and insisting his answer was right.

I decided it was bar model time.

In hindsight, this was the wrong decision where M. was concerned. Both of the kids do know how to translate English words into an equation, and M. might have been able to think the problem through using x to stand for one runner's distance.

He was flat-out unwilling even to look at a bar model. 'I don't understand anything about this problem,' he said, and that was that. He was done. My mistake.

Christopher was game. He knew he was getting nowhere doing what he was doing, and he'd had enough experience with bar models to take it on faith that a bar model would work.

Which reminds me: I must stress to Christopher that the point of the bar model isn't to solve the problem, but to show you which operations you need to do in what sequence. Bar models are a way of setting up the problem.

He didn't know exactly where to start, though he did know he should draw two bars, one for each runner.

When I started talking him through he caught on quickly and he was able to label everything correctly and quickly on his own, without prompting.

Here's what he drew (this is my version):


P-H9p283barmodelink2.jpg


Seeing the problem laid out this way, Christopher again subtracted the 280 from the 2870. Then he got stuck again, in the same place he'd been stuck before.

We've got work to do.

However, when I started walking him through it, asking what we had left now that we'd subtracted the 280, he was able to say that we had the two other segments left, and he was able to say, with prompting, that these two segments were equal.

The instant he said they were equal he realized he needed to divide the difference by 2.


2870 - 280 = 2590

2590 ÷ 2 = 1295


At that point I asked him where the 1295 belonged on the bar model, and he knew.

Then he knew that Runner 1's distance was 1295 + 280 meters while Runner 2's distance was 1295 meters.



So I'm thinking....

a) is this happening in other school districts? are math teachers taking a discovery approach to word problems?

and —

b) the best defense is a good offense


If I had little ones I'd be teaching them bar models just so they have a way to tackle all the discovery word problems they're not going to be taught how to do in the years to come.


My mom used to always tell us to Drive Defensively.

Same thing here.

Teach Defensively.





extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal



-- CatherineJohnson - 10 Mar 2006



FormativeAssessmentAndLearning 22 Mar 2006 - 01:05 CatherineJohnson



via joannejacobs, new research on formative assessment and learning validates what we've been saying here at ktm for months:


Scientists discover how to pass exams
By Alan Cane and Andrew Jack
Published: March 10 2006 02:00 | Last updated: March 10 2006 02:00
($, but you can access through joanne's site)
FINANCIAL TIMES

Psychologists have made an intriguing discovery that could have profound implications for our understanding of human learning mechanisms - and immediate significance for students revising for examinations.

...students understood and retained information more readily when subjected to frequent tests and quizzes while studying than students who simply read material over and over again.

"Our study indicates that testing can be used as a powerful means for improving learning, not just assessing it," said Prof Henry Roediger of the university's psychology department.

[snip]

...students who relied on repeated study alone frequently developed a false sense of confidence about their mastery of the materials even while their grasp of important detail was sliding away. By comparison, students who were either tested repeatedly or tested themselves while revising scored dramatically higher marks. A group of students who read a piece of text 14 times, for example, recalled less than a self-testing group who had read the piece only three or four times. The cause of the phenomenon remains uncovered: one theory is that we learn more efficiently in difficult situations.



So John Saxon, Seigfried Engelmann, and good teachers everywhere have known this for.....how long, would you say?

I'd say forever.

I'm sorry, this is not news.

Or rather, it shouldn't be news.

The comparison of 14 read-throughs to 3 or 4 is interesting, though.


keywords: formative assessment mathematics new study experiment


-- CatherineJohnson - 16 Mar 2006



SanFranciscoKippStudyFromKenDeRosa 29 Mar 2006 - 01:36 CatherineJohnson


SRI International has released a new study (pdf) of the new KIPP schools in San Francisco. It is close to 100 pages long but a good read. Not surprisingly, the KIPP kids are achieving better academic results although not yet stellar results since these schools are so new. In any event, the paper goes into detail as to what KIPP experience is like:


1. Long days (7:15 am to 5 pm)
2. Saturday classes
3. Mandatory summer sessions
4. Strict discipline
5. High academic expectations, usually using CA approved textbooks


I'd characterize the KIPP method as a brute force method of instruction that happens to work. However, I also happen to believe that similar results could be achieved with far less effort if:

1. KIPP started their program at K or 1 instead of grade 5 after these kids have had 5 years of failure in the public schools,

2. Used more praise, than punition (though the punition may be necessary for these kids at the stage they get them), and

3. Used a more efficient accelerated instructional Program. For example the DI programs achieve similar results using far less instructional time, even for low performers.


Nonetheless, KIPP shows what can be achieved with low performers with a little hard work and effective class room management, neither of which they get in the traditional classroom.



Catherine here. Every so often it crosses my mind that Ken and I may have been separated at birth; "brute force" is the exact term I've often used, in my own mind, to characterize KIPP's approach — and I say 'brute force' with a smile. I'm an enormous fan of the KIPP Academy, to the point where I've actually broached the possibility, with Christopher, of sending him there as an exchange student. (He says no.)

The KIPP people know what they're doing, and I'm not going to pick nits. But I do ask myself whether they absolutely need 6 days a week, schooldays lasting 'til 5, plus some of the summer to do what they're doing.

On the other hand, Christopher and I often put in some time on both weekend days as well as quite a few vacation days.....so I'm raising this question just to raise it, because I'm interested, and curious.

Rafe Asquith says, "There are no shortcuts."

But efficiencies and productivity gains are possible in most other realms (unless I'm overstating the case?)....why shouldn't there be efficiencies possible even in the realm of remediation and closing-of-gaps?

Or is more always more?



KIPP for all

from the U.S. News interview with Feinberg & Levin:

Finding qualified teachers to sign on to this cruise, however--even with the higher salaries KIPP pays--is a growing challenge, one that Feinberg and Levin say they can't solve without taking control of the training and certification process themselves. Already, KIPP runs a training program for principals at the Haas School of Business at the University of California-Berkeley. Extending that to teachers is an ambitious goal, one that would very likely require new legislation in individual states. But Levin, nothing if not persistent, insists that anything less is just tinkering around the edges. "Teaching has to become one of our society's most critical professions, rewarded and respected," he says. "And the cartels that control entry--the unions, the education schools--need to be addressed."


I'm in.


-- CatherineJohnson - 23 Mar 2006



EngelmannOnComputersInTheClassroom 25 Mar 2006 - 02:32 CatherineJohnson



Ken strikes again —

All these attractive capacities [of the DI videodisc program] give the medium great potential, but without good, carefully designed instruction, all the flashy video and the clever features of the program will flop. The medium is not magic, a lesson that should have been learned from the school's abortive and costly love affair with computers.

Many districts committed heavily to the promise of CAI (computer assisted instruction). The problem was that most of the software was just this side of pathetic, relying largely on bleeps, gimmicks, and other funsy-cutesy devices to make the machines "user friendly." They weren't friendly. Except in ermarkably few software packages, the instructional sequence was sophomoric.

In over 90 percent of the cases, the software packages were in complete disuse -- gathering dust -- within four months of their purchase date. And the computers all but ceased to be used for CAI. Instead, the computers became "word processors" and "spreadsheet designers."

Whether the medium is a text or a computer, the design of the instruction overrides all other factors, including individual differences in kids.

source: War Against the Schools' Academic Child Abuse
page 85



My mom was telling me about all kinds of funding scams in Chicago, and how there are whole warehouses filled with brand-new computers no one's ever even taken out of the box.

I told her it was probably just as well.


-- CatherineJohnson - 23 Mar 2006



ItsVeryDifficultToSynthesizeGibberish 30 Mar 2006 - 05:37 CatherineJohnson



I had to do it:

Another issue is the "sequencing" of what kids learn in high school and some of the current abuses. For instance, there's debate among high-school biology teachers about how much time, if any, should be spend on teaching facts of basic chemistry before launching into cell biology. Consider that most high-school biology students have not studied any chemistry, and may not know what a chemical reaction is; however, they study biology, much of which is nothing but chemistry, and very complicated chemistry. The sonsensus seems to be to assign the kids a chapter that presents some information on chemistry, launch into biology, and when the kids get helplessly stuck over trying to understand what is happening during cell respiration, present more information "as needed." Teachers who support this consensus believe that because the students will study chemistry the following year, they'll be able to synthesize what they learned in biology with the facts about chemistry. Of course, this plan is insane. It's very difficult to synthesize gibberish.

        guess who?

0894202871.01._AA240_SCLZZZZZZZ_.jpg

        via Ken —


-- CatherineJohnson - 29 Mar 2006



ParentBillOfRights 02 Apr 2006 - 01:11 CatherineJohnson



I've been reading articles about George Mason, who refused to sign the Constitution because it lacked a Bill of Rights:

Mason was among those who opposed adopting the draft constitution because it had no language to protect individual rights. They failed at first. But the Declaration of Rights Mason had written into Virginia's constitution 11 years earlier became the model for the Bill of Rights that was adopted in 1791 as the first 10 amendments to the Constitution. It became Americans' guarantee of free speech, free association, religious liberty and all our other fundamental freedoms.

source:
Final Four's Founding Father
USA Today


Naturally, that got me to thinking...maybe parents and students at Irvington Middle School need a bill of rights.

That seemed like such a good idea that I figured somebody else must have beat me to it.

So I started Googling things like "student bill of rights"; "student bill of rights" "middle school"; "parent bill of rights"; "parent bill of rights" "middle school"....

One thing led to another, and I landed on this document: Bill of Parent Rights and Responsibilities, New York City Department of Education, January 2005 (pdf file). (It's posted on this webpage as well.)

This document has been prepared by:

Jemina Bernard, Executive Director
Office of Parent Engagement
New York City Department of Education

Office of Parent Engagement, I thought!

How does New York City get an Office of Parent Engagement and we don't?

Not that I want to pay for a whole new Office of Parent Engagement (although Ed has decided the Irvington School District needs an ombudsman).

I started flipping through pages.....and I realized that some of this sounds like the rights my disabled children actually do have.

Then it occurred to me: I need to be looking at the specific language used in special education.

Meanwhile, this isn't a bad place to start:



THE RIGHT TO BE ACTIVELY INVOLVED IN THE EDUCATION OF THEIR CHILDREN

Parents have the right to be given every available opportunity for meaningful participation in their child’s education.

Parents have the right to:

1. be treated with courtesy and respect by all school personnel, and to be accorded all rights without regard to race, color, creed, religion, national origin, sex, gender, age, ethnicity, alienage, citizenship status, marital status, sexual orientation, gender identity, disability or economic status.

2. participate in communication with teachers and other school staff and share concerns regarding their child’s academic, social and behavioral progress.

3. visit their child’s school to meet with his or her teacher and principal at mutually agreeable times.

4. participate in meaningful parent-teacher conferences to discuss their child’s progress in school.

5. be informed of their child’s academic and behavioral progress in school.

6. be encouraged to participate and receive assistance in participating effectively in governance and educational decision-making through the School Leadership Team at their child’s school.

7. be accompanied by a friend, advisor, or interpreter at hearings, conferences, interviews and other meetings concerning their child, in accordance with established procedures.

8. be provided, if they are hearing impaired, with an interpreter at any meeting or activity which they attend which is specific to the academic and or disciplinary aspects of their child’s educational program, provided a written request is made prior to the meeting or activity; if an interpreter is unavailable, other reasonable accommodations shall be made.

9. have school staff make every reasonable attempt to ensure that parents receive important notices from the school, such as notices concerning parent-teacher conferences, open school week, parent association notices, etc.

10. be a member of the parent or parent-teacher association of his or her child's school without regard to the payment of dues.

etc.

THE RIGHT TO FILE COMPLAINTS AND APPEALS

Parents have the right to follow appropriate procedures to pursue complaints or appeal decisions affecting their child.

Parents have the right to:

1. appeal any entry in their child’s records on the grounds that it is inaccurate, misleading, or in violation of their child’s privacy rights and request that such records be amended, in accordance with Chancellor’s Regulation A-820.

2. follow applicable procedures for filing complaints or appealing decisions which they believe violate their own or their child’s rights.



What I don't see here is the right to have one's complaint and appeals resolved within a specified period of time, or ever.



parent rights in 1970

I'm just starting to look into this area.

Here's a page that mentions a Parent Bill of Rights in Philadelphia in 1974.

As well, the state of Texas has a law governing parent rights. Haven't read yet, but I like this section:

Access to Teaching Materials

(a) A parent is entitled to:

(1) review all teaching materials, textbooks, and other teaching aids used in the classroom of the parent's child; and

(2) review each test administered to the parent's child after the test is administered.

(b) A school district shall make teaching materials and tests readily available for review by parents. The district may specify reasonable hours for review.

(c) A student's parent is entitled to request that the school district or open-enrollment charter school the student attends allow the student to take home any textbook used by the student. Subject to the availability of a textbook, the district or school shall honor the request. A student who takes home a textbook must return the textbook to school at the beginning of the next school day if requested to do so by the student's teacher. In this subsection, "textbook" has the meaning assigned by Section 31.002.



You have to love the fact that somebody actually had to write a law requiring the school to let kids take the textbooks home.

oh - wait!

They didn't even get that far.

The school has to let students take textbooks home subject to availability.

yeah, well, I can see that.

Our 7th grade Spanish class doesn't have enough books to go around.

So if everyone wanted to take a textbook home to study, they'd be in trouble.


-- CatherineJohnson - 02 Apr 2006



AllKenAllTheTime 10 Apr 2006 - 23:07 CatherineJohnson



Ken's been practicing again. [update: original post is here ]

I have to put up some posts from a book I found....in Cambridge, I think. It's about what great teachers do differently. One of the main things they do differently is have high expectations for themselves.

Also, I MUST interview my sister finally. She was a teacher before she had kids; she is the exact opposite of the teachers on Ken's thread.

When we talked about her experiences teaching, she said things like, 'I always felt like if a child got a bad grade, that was a grade on me.'

Japanese teachers say the same thing, IIRC. (I think Stigler & Stevenson report this, but I'M NOT GOING TO LOOK IT UP NOW!)


-- CatherineJohnson - 08 Apr 2006



InputsOutputs 11 Apr 2006 - 19:19 CatherineJohnson



Clowes: So Project Follow Through confirmed what you had already found about the ineffectiveness of those other programs. Yet those programs still are being promoted in teacher colleges and they still are widely used, while Direct Instruction is not. Why?

Engelmann: The answer is really simple, but it's very difficult for most people to accept: Outcomes have never been a priority in public education, from its inception. That's the way the public education system is. The system is more concerned with the experience of the child: "Let the child explore," "Let the child be his or her self," "Don't interfere with the natural learning process," and so on.

source: "If Children Aren't Learning, We're Not Teaching" interview




Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics

The paper is here. (pdf file)


key words: blame the student school psychologist
Pamela Darr Wright summary of Galen Alessi study
Evolving Functions for the School Psychologist
Whose Fault Is It?
educational rights of special need children versus typical children
Engelmann on Galen Alessi study
Pamela Darr Wright posted to ktm
"public school has never been about outputs..."



-- CatherineJohnson - 11 Apr 2006



DeadReckoning 11 Apr 2006 - 19:55 CatherineJohnson



right here


-- CatherineJohnson - 11 Apr 2006



KippGoesToKindergarten 04 Oct 2006 - 16:11 CatherineJohnson



Trying to track down a Jay Matthews column on St. Anne's school in Brooklyn, I came across this column saying KIPP has started an elementary school in Houston.

That's good news.

And check this out.

They're combining Saxon Math with Everyday Math:

At SHINE, Brenner says, he is blending the more modern Everyday Math with the more traditional Saxon Math for first-graders. The proponents of those two teaching programs have been at war for 20 years; can combining them really work? I'd predict that joining such radically different elements would cause an explosion, like when I used to toss manganese shavings into the surf to illuminate beach parties.

Brenner seemed unfazed by my doubts. "Our kids are off the charts in math," he says. I haven't surrendered my skepticism, but I will visit his school, and then watch what happens when Laura Bowen brings all this here, where Washington can get a really good look at it.


I'm not surprised.

My friend with the kids in the fantastic private school told me her school combines Everyday Math with traditional math. They seem to do nothing but EM for the first couple of years; then they shift.

I was shocked when she told me this, and assumed that her kids were getting shortchanged.

Then she faxed me her son's math homework.

WAY past anything kids are doing in public schools. This boy was doing long division with a gazillion digits; no forgiving division anywhere in sight. The word problems were serious and challenging - challenging at his level. My friend was shocked that we have to reteach math at night. She and her husband never reteach any subjects at all. The kids in her school are way up at the top of U.S. kids, and they're learning everything they know at school.

Barry has mentioned before that James Milgrim thinks Everyday Math would be a good supplemental program when used with a traditional math curriculum.

Looks like he's right.


-- CatherineJohnson - 12 Apr 2006



EducationJournalism 19 Apr 2006 - 17:54 CatherineJohnson



at D-Ed Reckoning

...the kids who need the most parental support are least likely to have parents who are able to provide effective support. That's why we send these kids to school in the first place, isn't it? Because their parents do not have the ability and/or are unwilling to teach them. The assumption going in should be that no parental support will be forthcoming. The instructional design should be premised on that.

Ed just wrapped up the college interview season (he interviews for Princeton).

His impression, interviewing a number of very high achieving kids, is that the kids who take & succeed in AP calculus all have 'Math Brain' parents. Most of them have parents who weren't just 'good at math' in college, but are actually working in math-related fields today. Some of these kids have two parents working in math-related fields.

That jibes with what I've heard from the few parents of high schoolers with whom I've discussed the issue so far.

Kids who 'go the distance' in high school math have parents who can reteach and/or tutor algebra, trig, and calculus at home. I'm developing an image of a hereditary 'Math Elite' here in America, a Special Caste. If your folks didn't take calculus, you're not taking it either! *

I just have to hope I can get to calculus and come close to mastering it before Christopher does....

....which brings me to —

dingbatWSJ2.jpg


graduation day

I've just this moment finished Saxon 8/7!

Investigation 11 is behind me!

The one thing I did wrong, in case any of you are interested, was that I didn't do the 'Fast Facts' sheets students are supposed to complete at the beginning of each lesson.

That was a mistake. Towards the end of the book I realized I need a fair amount of simple memorization of things like metric conversions, area & volume formulas, terminology & the like.

So I'll be doing a Fast Fast sheet every day for awhile.

But I start Algebra 1 tomorrow! Yay!

I'm using Saxon Algebra and Dolciani together (Solution Key), with Foerster (THANK YOU, BOOK FAIRY!) on the side.

Can't wait.


dingbatWSJ2.jpg


Foerster algebra

wow

Check out this review of Foerster from Mathematically Correct.

The book provides an outstanding opportunity for student learning. Even achievement at the highest levels is supported, although sometimes only at good levels rather than outstanding levels.

Perhaps the greatest strength of this program lies in the abundance and quality of student exercises, especially application word problems. But, virtually all ratings of this program are outstanding. Simply put, it does a good job of the topic of introductory algebra.


I may have to re-think (as well as track down the supporting teacher materials for Foerster...)

Maybe I'll do all 3!


* The kids I know who went to private and/or Catholic School took calculus and succeeded in it regardless of their parents' careers or number of math courses taken when they were young, but this hasn't been true of the kids I know in public schools. I'll keep asking. My sense is that even very good public schools rely on parents to get their kids through math.

Greta recommends Foerster
more from Greta



-- CatherineJohnson - 14 Apr 2006



FourSevens 20 Apr 2006 - 02:11 CatherineJohnson



via D-Ed Reckoning, an example of traditional math versus reform math in Seattle schools:


TRADITIONAL MATH

Simplify each expression.

1. 25 — 10 ÷ 5
2. 14 + 7 x 6
3. 50 ÷ 5 — 2
4. 32 ÷ 8÷ 4
5. (32 ÷ 8) ÷ 4
6. 32 ÷ (8 ÷ 4)

REFORM MATH

Write an expression for each number using exactly four 7's and no other digits. You may use the following symbols as often as you wish:
+ - ( ) X ÷

1. ______________________ = 1

2. ______________________ = 3

3. ______________________ = 9

4. ______________________ = 10

5. ______________________ = 28

6. ______________________ = 35




Offhand, I don't know how to solve some of these. 77 ÷ 77 works for number 1; 7 + 7 + 7 + 7 is the answer to five; 7 + 7 + 7 ÷ 7 is the answer to number 3.

And after that, I would have to sit and stare at my paper for awhile.

Which presents an opportunity cost.

Figure out how to express the number 9 using four 7s and no other digits?

Or do two lessons in Saxon Algebra?

I know!

I'll get all of you Math Brains to tell me the answers, while I go (re)learn some algebra.


-- CatherineJohnson - 19 Apr 2006



FlexibleAbilityGrouping 07 May 2006 - 15:02 CatherineJohnson




from Dan (bulleted version below):

I happened to have a meeting with my daughter’s teacher yesterday about the kind of differentiated instruction that I like. It’s not enrichment or pull-out from the heterogeneous group. It’s actual homogeneous ability grouping.

My daughter is in first grade in a K-5 public school. I don’t know if the school previously had some homogenous ability grouping for reading at the upper levels before or not. I do know that this is the first year that they’ve taken the grouping all the way down to the first grade level. So, four days a week, my six-year-old leaves her homeroom class and goes down the hall to a different first grade teacher for her “reading block.” There are four first grade classes in this school, so they have four levels of reading groups. Let’s call them A, B, C, and D, where the D group has the most proficient readers, and the A group kids were still shaky on the alphabet back at the beginning of the school year. They call it a reading block, but it also includes spelling and other activities.

I can’t speak with certainty, because I haven’t done any thorough analysis. Still, I think that the results of this grouping have surprised the teachers. My daughter is in the D group (highest ability). Every week, these kids are learning spelling words that rival the difficulty of the words used in my other daughter’s fourth grade class. Here are a few of the words she brought home this week: Wednesday, beautifully, anniversary, rectangle. The reading teacher has also borrowed materials from a third grade teacher to have the kids do an invention convention, where they each designed some new invention, described it, prototyped it, and created a script for an advertisement for it. They also worked with their parents to research an existing invention and its inventor. Then, the child had to write a report on it. For all of these writing steps, the teacher had them turn in drafts, which she then corrected for them to rewrite. I think it turned out very well. They’ve also read and reported on biographies. They’ve learned alphabetization and dictionary skills. Any of these things, taken by itself, is perhaps not so amazing. I can’t imagine, though, that so many topics could really be covered—and understood—with this level of quality if pursued in the context of a heterogeneous ability class.

My understanding is that the grouping is also quite successful for the lower groups. We were talking to my daughter’s homeroom teacher. She has the A group (lowest proficiency). I might be misremembering my numbers, but I think she said she began the year with 23 kids in her group. Several have moved up to other groups; she has 16 now. When the rest of the class is not leaving them behind, even the lowest performers can make real progress. I think it’s great that she has the fewest students at this point, because they probably need the most attention. The teacher also told us about a girl that had recently moved up from the C group to the D group. Nobody is locked in and held back.

The reason we were meeting was to ask about next year. Given that our kid has done a project usually pursued in third grade and is handling spelling words that match those in fourth grade, how are they going to deal with her in second grade? The answer is that nobody is quite sure. This is also the first year that they’ve done ability-based reading groups in second grade. Next year, though, will be the first time they will be confronted with students coming out of ability-grouped first grade reading. I expect the second grade teachers to be blown away.

We also face some uncertainty about math instruction in second grade. The first graders have not been regrouping for math. Instead, this is where some pull-out acceleration has been applied. My daughter is not yet automatic with her multiplication facts, but her teacher has started giving her some division problems. There’s no way they can start next year by asking her to plod along with Saxon second grade.

It will be interesting, but I am very optimistic. To me, this is pretty close to the right way to do differentiated instruction.



I am firmly convinced, at this point, that flexible ability grouping - Susan's term - is tremendously helpful for average and slow learners.

Here is Tom Loveless's description of tracking in a Catholic High School:

Reba Page’s 1991 study, Lower Track Classrooms, painstakingly reports on the daily activities of eight low track classes, documenting how they often function as caricatures of high tracks, how teachers and students in low tracks make deals to not push each other too hard so that they can cope with their environment. Low tracks may be used as holding tanks for a school’s most severe behavior problems.

[snip]

Intellectually stimulating low track classrooms do exist, however, and researchers have found the most productive of them in Catholic schools. Margaret Camarena and Adam Gamoran have described low track classrooms where good teaching, lively discussions, and ample learning take place. In 1990, Linda Valli published her study of a heavily tracked Catholic high school in an urban community. The school’s course designations publicly proclaimed each student’s track level. Textbooks and instruction were adapted for each track. Yet Valli discovered that "a curriculum of effort" permeated the entire school, even the lowest tracks. The school culture centered around academic progress, and the tracking system was but another facet of the school that served this aim. Students of all abilities were aggressively pushed to learn as much as they could. Every year, low track students were boosted up a level. By the senior year, the lowest track no longer existed. A judicious tracking system teaches low track students what they need to know and moves them out of the low track as quickly as possible.



dingbatWSJ2.jpg


in a nutshell:

  • daughter is in first grade in a K-5 public school

  • school is doing homogenous ability grouping for reading

  • students in highest level group (D) are learning spelling words that rival the difficulty of the words used in fourth grade class, e.g.: Wednesday, beautifully, anniversary, rectangle

  • each student in D group designed a new invention, described it, prototyped it, and created a script for an advertisement for it

  • each student in D group worked with their parents to research an existing invention and its inventor, then wrote a report using drafts and revisions

  • children in the lowest proficiency group, the A group, can and do move up; teacher began year with 23 children and is ending year with 16 (figures from memory)

  • Nobody is locked in and held back.



dingbatWSJ2.jpg


sources cited by Loveless:

Linda Valli, "A Curriculum of Effort: Tracking Students in a Catholic High School," in eds. Reba Page and Linda Valli, Curriculum Differentiation: Interpretive Studies in U.S. Secondary Schools (Albany: SUNY Press, 1990), pp. 45-65.

Margaret Camarena, "Following the Right Track: A Comparison of Tracking Practices in Public and Catholic Schools," in eds. Reba Page and Linda Valli, Curriculum Differentiation: Interpretive Studies in U.S. Secondary Schools (Albany: SUNY Press, 1990), pp. 159-182.

Adam Gamoran, "Alternative Uses of Ability Grouping in Secondary Schools: Can We Bring High-Quality Instruction to Low-Ability Classrooms?"


dingbatWSJ2.jpg


strategic plan for differentiated instruction
is there a research base for differentiated instruction?
timeline for implementing direction instruction & the administrator's career path
teacher's role in differentiated instruction
differentiated instruction in middle school
tiered instruction
differentiated instruction & the pre-test
differentiated instruction in Steve's town
follow-up on DI in his town from Steve
pre-tests & post-tests w/o formative assessment
differentiated instruction & executive function

flexible achievement grouping & accelerating average children
acceleration for average & slow learners
Tom Loveless on tracking research
flexible achievement grouping in Dan's school

Wayne Wickelgren on math talent & when to supplement
Wickelgren on math talent



-- CatherineJohnson - 21 Apr 2006



AdjustableReservoirForIndoorPlants 22 Apr 2006 - 21:47 CatherineJohnson



I've been wanting something like this ever since my mom bought us an EarthBox two years ago. A few months back I found an expensive variant of this "adjustable reservoir" indoor pot, made in a Scandinavian company, in an online catalogue whose URL I seem not to have recorded. But that pot was designed mostly to be lovely to look at.

This is the real thing:


33-456.jpg


source:
Gardeners.com
gardeners.com has lots of EarthBox-type outdoor planters as well


I managed to kill one of my few house plants this winter, through inattention, general spaciness, and way too much multi-tasking. I've been feeling bad about it ever since, and naturally, being an American, I've been thinking Technology Can Solve My Problem.

Speaking of technology solving my problems, I also missed a doctor's appointment this week, and will solve that problem by finally purchasing a PDA that links to my Mac, which my old PDA does not, or not smoothly enough at any rate for me to be willing to troubleshoot the software every time I need to synch.

I don't know whether the adjustable reservoir will work as well for indoor plants as the EarthBox does for outdoor plants.

However, I expect it will, assuming the reservoir holds enough water to tide my plants over on the days I forget they exist. I'm guessing that the reason the EarthBox works so well is the same reason producing your own insulin is vastly preferable to injecting yourself with insulin on a schedule. The plant gets the water it needs when it needs it, and it never gets too much or too little.

It's a form of biological 'efficiency,' I guess.


dingbatWSJ2.jpg


efficiency in learning?

It's the same kind of efficiency I want to see in education, including self-teaching.....what is the most efficient, most thorough and rapid way to learn a subject or a skill? And by 'efficient, thorough, and rapid' I don't mean the kind of brute-force Death March to Harvard schedules imposed on kids by elite private schools, which around these parts assign 9th graders 6 hours of homework a night.

I think Seigfried Engelmann may be one of the few people on the planet with real insight into this question, and nobody listens to him. Well, Seigfried and Toru Kumon.

I say 'I think,' because I haven't dug into this. It's entirely possible cognitive science has something to say about learning efficiency. Another item on my to-do list.


about-torukumon.jpg



EarthBox investigation with Christopher
adjustable reservoir for indoor plants
EarthBox reminder
self-watering pots and planters from Denmark



-- CatherineJohnson - 22 Apr 2006



ThankYouWholeLanguage 03 May 2006 - 16:57 CatherineJohnson



Lesley pointed me to this essay posted at Illinois Loop. I'd never seen it before —

Thank you Whole Language. Thank you for your many pearls of wisdom. Thank you for Context Clues. Thank you for Prior Knowledge. Thank you for the Initial Consonant. Thank you for Picture Clues. Thank you for Miscues.

But most of all, thank you for my wife. The other day she and I were riding along the highway and saw a sign for a town called Verona, so my wife read "Veronica". It's very simple, you see. First she applied Context Clues (she knew we were looking for a name). Then she applied the Initial Consonant ("V"). Then she applied Prior Knowledge (she already knew of a name "Veronica"). She put these Whole Language strategies together and ... success! At least, as much success as we can expect, I suppose.



Like the man said, Read the whole thing.


stupid mayor trick
Thank you, whole language
guess and check reading
stupid mayor trick part 3: the good news

National Reading Panel (official website)
The Partnership for Reading
(govt website: "bringing scientific evidence to learning")
National Reading Panel report full text (pdf file)

who is Lucy Calkins
having a Lucy Calkins day
Cargo Cult Lucy from Becky


keywords: nationalreadingpanel


-- CatherineJohnson - 30 Apr 2006



KenDeRosaBlog 01 May 2006 - 17:09 CatherineJohnson



D-Ed Reckoning

It's fantastic.

He's already out-writing Carolyn and me; he's managed to get several posts up on the NEW YORK MAGAZINE "reading wars" article before I checked back in today!

One thing I've noticed: Ken's got title-writing down. I've never been able to write titles. I don't know why.

Title-writing is an actual job in Hollywood, fyi. A novelist friend of mine was once hired to come up with dozens of titles for a film that was in production. Ken could probably nail that job, although, on second thought, few Hollywood movies are likely to be titled, When Losers Don't Surrender.


dingbatWSJ2.jpg


the emporer has no clothes

Ken posted this wonderful passage from War Against the Schools' Academic Child Abuse that I'd forgotten:

While some kids may learn to read from this approach (nothing is preventing them from learning what they're supposed to learn), some higher performers may totally misinterpret the game, and lots of lower performers fail to catch on to what reading is.

We once did a nice demonstration that showed how confusing the approach may be to naive kids. We went into a first grade classroom where a teacher had worked on four different selections. Each had an illustration and the text. The kids could "read" all selections perfectly. We then switched the illustrations and the text (paired them with different texts) and tested the kids. About half of the kids pointed to the words one at a time and, with great fidelity, recited the passage that was appropriate for the picture. In other words, half the kids didn't have the faintest idea what reading was all about.


Devastating.


-- CatherineJohnson - 01 May 2006



LoneRangerTutorsReading 06 May 2006 - 01:00 CatherineJohnson



I think whole language causes many children to become utterly confused about reading and appear to have a disability. Then the problem compounds itself as the child begins to feel stupid and then stops trying. I think many children are suffering from poor instruction not dyslexia. I believe that becuase once these students experience systematic explicit instruction they are cured. The young teachers here also were taught as children with whole language and do not have any background with phonics. Colleges of Education also favor balanced literacy. These teachers are mystified when a child cannot learn to read using balanced literacy and speak with reverence of the savior, "Linda Mood-Bell" This phonetic approach is saved for Special Ed kids in 4th or 5th grade, when all else has failed. "All else" includes Reading recovery which is whole language applied one-to-one. It's infuriating to me because I believe it is educational malpractice and waiting until 4th or 5th grade is too long as the damage has been done. I had another little guy in 3rd grade and his Mom came to me in tears. She reported that the school said her son would never learn to read. I realized immediately that the little boy was brilliant. He knew many things about the world and his vocabulary was incredible. He couldn't read at all. We started with Phonics Pathways, a white board and my magnetic letters and worked on consonants combined with short vowels.. sa, se, si, so ,su etc. In 3 half hour lessons he was starting to read the BOB books. This was due to the explicit program I used, not me. It is not rocket science to teach someone to read, but it sure is rewarding. Too bad our school system can't seem to get it right.

Thomas Zeffiro, of Georgetown, told me a few years back that the Linda Mood-Bell folks are fantastic.

He said (paraphrasing), "If you wanted your child to become a superb basketball player you'd get the best coach you could find. The Linda Mood-Bell people are the best reading coaches out there. They're light on their feet."

I loved the image of reading tutors being light on their feet.

He meant that they were completely focused on the student and on what the student was learning.

If what they were doing wasn't working, they shifted at once.

Which brings me back to my Columbia U. story....a friend of ours told us that there was a legendary professor at Columbia Medical School who taught all the Big Medical Brains in the city.

His motto, which he drilled into his students, was: If what you're doing isn't working, try something else.


dingbatWSJ2.jpg


Zeffiro's study

I'm sure this is the one he was telling me about way back when:

In this study, Eden, Zeffiro and their colleagues studied 20 adults with a lifelong history of dyslexia. They divided the adults into two groups of 10 and conducted baseline brain scans on both groups. One group then participated in an intensive eight-week interventional program designed to improve reading skills, while the other group received no intervention at all. At the end of the eight-week period, brain scans showed that the group that had taken part in the reading program showed measurable improvements in reading and related changes in neural activity. The brain scans of the control group showed no differences.

"It was quite exciting to be able to see such clear confirmation of our hypothesis in the fMRI scans," Eden said. "This is a great step towards better understanding the neural mechanisms involved in reading and learning."


I'm just about positive the program he's talking about here is Linda Mood-Bell. IIRC - and I do - he said the improvements were staggering. These were lifetime dyslexics. I have a memory of him saying some of these folks were almost illiterate (that could be wrong).

I spent a long time talking to him, because I was desperate to teach Jimmy and Andrew to read. He was serving on NAAR's Scientific Advisory Board that year. Fantastic guy.


dingbatWSJ2.jpg


visual processing & dyslexia

Zeffiro also told me, when I repeated the standard line about dyslexica being a problem with phonological processing, that this wasn't as true as people thought. There are visual components, too:

Addressing a long-standing controversy concerning the causes of reading disability, a series of research studies done by a team at the Georgetown Center for the Study of Learning indicate that the areas of the brain used for reading are the same areas used for other visual tasks, and that these areas may not work properly in the brains of people with dyslexia. However, the researchers also found that an intensive, phonologically based reading intervention program could not only improve reading skills in dyslexics, but could also effect changes in brain activity that can be measured using functional magnetic resonance imaging (fMRI) technology.


dingbatWSJ2.jpg


more from Lone Ranger

I know two teachers who have jumped off the balanced literacy bandwagon.

Teacher 1 : For the first seven years of her teaching career, she taught k-2 grades. She preached balanced literacy. We would get into heated debates over this topic. She went on to get her master's and is now a Reading Specialist. She has ditched balanced literacy for phonics instruction. She has used the same workbooks (Explode the Code), borrowed many from my homeschooling library (including Phonics Pathways) to remediate the kids that are in the "pull out" programs at her school.

Teacher 2: Taught 1-3 grades for many years. She too bought into the balanced literacy approach. She decided to homeschool her own three children when they were in 2,3 and 4 grades for health reasons. She realized that her oldest (4th grade) hated to read and was struggling. Retaught her oldest to read using phonics. She has said that she could never go back to teaching using "balanced literacy" as she has seen first hand the results. If she returns to teaching, it will most likely be as a reading specialist where she can use phonics.


The whole thing is horrifying to me.

The whole language versus phonics "debate" was resolved years ago, when the NICHD came out with its findings.

Now it's been unresolved.

Now Reid Lyon is an affiliate of George Bush and the White House push to require schools to use research-based curricula is "improper" and "scandalous."

A National Institutes of Health–created commission of Ph.D.’s came down squarely on the side of phonics in a 2000 report, influencing the Bush administration to crack down—some say improperly, perhaps even scandalously—on non-phonics programs.

This really is something.

The NIH says phonics is supported by research & whole language is not, and NEW YORK MAGAZINE translates this into a possibly improper and even scandalous "crack down" on schools.

These are people who make their living writing stuff for other people to read.


-- CatherineJohnson - 05 May 2006



QuizSite 06 May 2006 - 19:15 CatherineJohnson




terrific quizz site - includes a link to Selected Answers to Questions at Math Forum



-- CatherineJohnson - 06 May 2006



EmailToTheMathChair 15 May 2006 - 19:31 CatherineJohnson





a Mother's Day Special —



Hi Karen—

We’d like to request that you place a note in Christopher’s file to accompany Ms. Kahl’s midterm report, dated 5-10-2006, which Ed and I have returned to her with our signature. We’ve kept a scanned copy for our files.

We’ve signed the report only because Ms. Kahl will lower Christopher’s grade if we do not. Our signature should not be taken to imply approval, acceptance, or “resolution” of grading disputes with Ms. Kahl, all of which we consider to be open and ongoing. We would appreciate your making a note of this in Christopher’s file, as well as in any and all administrative files concerning Ms. Kahl’s performance and effectiveness as a teacher and her ability to work cooperatively with parents.

From her latest report, we gather that Ms. Kahl has given Christopher grades of 50% on several assignments due to missing labels on charts and graphs. Her grading has grown even more punitive than was the case with her previous 20-point deduction from Christopher’s scale model drawing, a 4-hour assignment, for failing to show his work in the manner she desired.

As an aside, we understand that IMS considers the latter grading dispute to be “resolved.” We do not. To this day we do not know what Ms. Kahl considers “show your work” to mean on that assignment as on many others. We allowed Christopher to hand in his drawing without further effort because we believed that he had shown his work. Obviously we were wrong, but Ms. Kahl has neither answered our questions concerning the “right” way to show work, nor provided us with a Solution Key. We remain in the dark.

Now matters appear to have deteriorated even further. Ms. Kahl reduced Christopher’s grade on the drawing from an A+ to a B-; currently she is making deductions of 50% for a failure to label.

Punishment is poor pedagogy. If Ms. Kahl wishes Christopher to learn—and to remember—to label charts and graphs, she needs to provide him with distributed practice. That is what we will do this summer when we re-teach pre-algebra at home.

Distributed practice is particularly important in light of the fact that Ms. Kahl is deducting points not for accuracy and comprehension, but for issues of organization and memory. Like many 11-year old boys, Christopher has trouble with organization; keeping directions and instructions straight is a challenge. That is to be expected. Frontal lobe development in boys lags two years behind that in girls.

Ms. Kahl cannot alter the speed or timing of her students’ brain development through punitive grading practices, a fact her latest report amply demonstrates. She has been docking points all year long, yet Christopher remains disorganized and forgetful. The only way to teach an 11-year old consistently to label charts and graphs is to provide him with enough practice that the procedure reaches automaticity.

Finally, a word about Scott Fried’s recent statement to the community concerning the distinction between punishment and discipline. We gather that Principal Fried regards the practice of lowering a student’s grades for issues of forgetfulness and disorganization as a form of discipline, which is “educational,” not punishment, which is not. Parents punish; principals discipline.

We disagree.

Behavioral psychologists define “punishment” as: “[providing] a consequence that makes a particular behavior less likely to occur in the future.” Ms. Kahl’s grading practices are clearly intended to decrease the behavior of turning in work she considers sloppy or incomplete. A consequence intended to decrease the behavior it follows is a punishment.

Throughout this year Ms. Kahl has repeatedly punished Christopher for failing to remember, failing to understand, failing to know what is required of him. The choices she has made have had predictable results. Christopher entered Irvington Middle School telling us that he liked math. Today he may dislike the subject as much as he did at the end of his 4th grade year, the last time he had a teacher who was sub-par.

We would very much appreciate your appending this response to the appropriate documents, and entering in the appropriate files. Thanks so much.

Catherine Johnson
Ed Berenson


dingbatWSJ2.jpg


email from the math chair



-- CatherineJohnson - 15 May 2006



MasteryLearningInSports 16 May 2006 - 11:08 CatherineJohnson



Mastery learning is an instructional strategy that embraces the philosophy that almost anyone can learn what is being taught given sufficient time and help. Mastery students receive knowledge about the results of their performance, along with a prescription of corrective or enrichment activities, each time an assessment is made. This study attempted to instruct three basketball skills to seventh-grade boys.

A control and non-mastery instructional group were compared. Students in the mastery group were not taught new skills until 80% had mastered the skills instructed. The other two groups did not change in individual skill performance. The mastery group performed significantly better on isolated skills than did the other two groups. There was no significant difference between the groups in performance of skills in competitive games.

Implication. Goals aimed at mastery improve skills at practice. However, the transfer of those improvements to competitive settings is not likely unless there is considerable similarity between the practice and competition situations.

source:
Mastery Learning
Learning in Sports
Volume 3(1) Number, 1997



I wonder whether Willingham would say that these kids hadn't reached expertise and so weren't able to transfer isolated ("fragmented"?) skills to competition.


-- CatherineJohnson - 16 May 2006



PrecisionTeaching 16 May 2006 - 00:09 CatherineJohnson



I've never heard of precision teaching (pdf file)

ABSTRACT

Although educators, policy-makers, business leaders, and the general public have become increasingly concerned about the “basic skills” crisis in American schools, research-based solutions have existed for over two decades in the form of measurably superior teaching methodologies: Precision Teaching and Direct Instruction. In federally validated research, each of these instructional technologies has been shown to produce far greater achievement and self-esteem among students than more traditional teaching practices, with favorable cost-benefit ratios when implemented in schools. These results have been obtained despite adverse socioeconomic influences on students so often blamed for failure in the classroom. These methods have not been widely adopted, partly due to political and philosophical resistance to measurably superior instructional technology among educators.

This article provides overviews of Precision Teaching and Direct Instruction, discusses their origins and research backgrounds, cites effectiveness data, and describes how they can complement one another when used together. It provides sufficient references to the literature and pointers to existing programs to enable interested readers to learn more about each of these measurably superior educational solutions.





Catalogue of School Reform Models: Direct Instruction (chart)



-- CatherineJohnson - 16 May 2006



DifferentStylesOrDifferentSpeeds 18 May 2006 - 19:03 CatherineJohnson



I'm going to be emailing this post to everyone I know.


-- CatherineJohnson - 18 May 2006



TaughtMyDogToWhistle 08 Jun 2006 - 13:24 CatherineJohnson



Englandtaughtdogwhistlesmall.jpg

I taught my dog to whistle.     I don't hear him whistling.        I said I taught him. I didn't say he learned.

source:
Improving learning in mathematics: challenges and strategies
(link to pdf file on this page)



-- CatherineJohnson - 07 Jun 2006



UnderstandingMath 18 Jun 2006 - 14:33 CatherineJohnson



from Peter Alford's website (scroll down)

You understand a piece of mathematics if you can do all of the following:

  • Explain mathematical concepts and facts in terms of simpler concepts and facts.

  • Easily make logical connections between different facts and concepts.

  • Recognize the connection when you encounter something new (inside or outside of mathematics) that's close to the mathematics you understand.

  • Identify the principles in the given piece of mathematics that make everything work. (i.e., you can see past the clutter.)


Wonderful.

In terms of math and the math wars, I especially admire the first principle: you understand mathematics when you can explain mathematical concepts and facts in terms of simpler concepts and facts.

The NSF-funded curricula seem to have been trying for this idea. But they bungled it.

A person who understands something can explain it in different terms. But those terms don't have to be words - and, in the case of math, probably shouldn't be words, or at least not solely words. Alford's formulation is more sophisticated. Being able to explain something means being able to explain it in simpler concepts and facts.

I'm think I'm going to post these principles over Christopher's desk. They're universal. I've been using them for years, without having tried to sort them out or write them down. Alford has made them explicit for me. When I'm writing a book or an article, I know I'm succeeding when I can do these four things.

Seeing past the clutter — that's the big Kahuna.

Temple calls it "finding the basic principle."


dingbatWSJ2.jpg


Saxon Math

Saxon Math probably does a superb job of using these principles to teach math.

This year I learned from Saxon Math, for the first time in my life, that when we find areas we are always multiplying "two perpendicular dimensions." (Saxon 8/7 Lesson 82 Area of a Circle)

Of course, I sort-of knew that.....but I'd never made the connection between finding the area of a square and finding the area of a circle. (Have I mentioned my education in mathematics left a lot to be desired?)

That one observation, in Saxon 8/7, permanently changed my perception of area & volume, permanently increased my comprehension of area and volume, and permanently improved my ability either to remember area and volume formulas or to derive them when I don't remember them.

Saxon used seven sentences, illustrated by geometric figures, to make that observation. This passage embodies all four of Alford's principles:

We can find the areas of some polygons by multiplying two perpendicular dimensions.

  • We find the area of a rectangle by multiplying the length by the width.

    A = lw  [illustration of square]

  • We find the area of a parallelogram by multiplying the base by the height.

    A = bh  [illustration of parallogram]

  • We find the area of a triangle by multiplying the base by the height (which gives us the area of a parallelogram) and then dividing by 2.

    A = bh/2 or A = 1/2bh  [illustration of triangle]

To find the area of a circle, we again beegin by multiplying two perpendicular dimensions. We multiply the radius by the radius. This gives us the area of a square built on the radius.  [illustration of circle]




-- CatherineJohnson - 18 Jun 2006



MasteryLearningAndIq 26 Jun 2006 - 16:59 CatherineJohnson




Through sheer serendipity, I've stumbled across the book with the answers:

Standards and Mastery Learning: Aligning Teaching and Assessment So All Children Can Learn

by J. Ronald Gentile, James P. Lalley.


Learning, in other words, occurs in phases or episodes, and this original learning phase includes (a) the readiness component (described above), (b) learning to initial mastery, and (c) forgetting....it is clear that forgetting is the inevitable result of initial learning, even when a high mastery standard of, say, 80% to 100% correct is required. When the degree of original learning is less than mastery, say, 60% to 80%, then forgetting is likely to occur more rapidly or be more complete. If it is less than 60%, it is questionable to speak of forgetting at all, because learning was inadequate in the first place.




why do we have to learn all this stuff?

Finally, an answer:

Students show that they understand this principle implicitly when they ask, “Why do we have to learn this stuff anyway? We’ll only forget it.” Our typical answers, “Because it will be on the test” or “Because I said so,” are not satisfactory. In fact, we have been able to find only one satisfactory answer to the question, and it was supplied in one of the first empirical studies of learning/forgetting (Ebbinghaus, 1885/1964). The answer is that relearning is faster—that is, there is a considerable savings of time in relearning compared with original learning. Furthermore, there is a positive relationship between amount of time saved in relearning and the degree of original learning, with essentially no savings when original learning is below some acceptable threshold (which we earlier argued was 60% or less).




fast learners, slower learners, memory, IQ

Suppose, however, that we ask how IQ relates to all of this. We already know, for example, that IQ is moderately but significantly correlated with memory. But suppose we randomly assign half the students to have to achieve a preset standard, while the other half (within the same IQ range) are exposed to the same material but do not have to achieve the preset standard. What happens to the correlation between IQ and surprise delayedretention test scores?

A dissertation study on this very premise was completed recently, under the senior author’s direction, by Marianne Baker (1999).... for original learning, a short story was read aloud to fourth and fifth graders individually, immediately followed by a free-recall test on specific items of information as well as comprehension of ideas in the story. For the mastery group, this process was repeated until each student scored between 75% and 90% correct. The nonmastery group heard the story once and did the free-recall test. A week later, both groups were surprised with a written test of memory for the same items. Then students relearned under their respective conditions and finally were tested for retention again after 14 days and 28 days.

Table 1.2 shows the remarkable results regarding intellectual traits and memory.5 Under nonmastery conditions—that is, a single exposure for original learning, recall after 7 days, a single relearning opportunity, and then recall after 14 and 28 days—the correlations between intellectual traits and recall are all positive and significant. That is, higher-ability students tend to remember more, as society has come to expect.

In stark contrast, imposing a mastery standard of 75% to 90% correct on original learning and then again at relearning renders those standardized intellectual measures nonpredictors of how much is recalled: The correlations hover around zero and are all nonsignificant.

What mastery to a high standard can do, in summary, is virtually bypass the effects of IQ for specified educational objectives. What is recalled about educational lessons is more dependent on how well the material is mastered than on such traits as rate of learning or general intellectual abilities.


I believe it.

I'll have more later. The preface and first chapter (pdf file)) are available online.

I'm ordering the book.



in a nutshell

  • learning occurs in phases or episodes

  • all initial learning results in forgetting

  • learning to high mastery means immediate recall of 80% to 100%

  • learning to "low" mastery means immediate recall of 60 to 80%

  • below 60% you haven't learned; when you encounter the material again you'll be starting over again [ed.: hoo boy. we're looking at a big, honking Phase 4 math reteach-fest this summer.] [UPDATE 12-6-06: Actually, we're not. C. is now much faster at learning math; he's managing to absorb and, I think, hang onto some of the content in Phase 4 Grade 7.]

  • IQ is moderately correlated with memory

  • high-IQ allows one to recall more after one exposure: "higher-ability students tend to remember more, as society has come to expect"

  • high mastery to a standard of 75% to 90% on original learning plus one relearning erases the correlation between IQ and memory


"What mastery to a high standard can do, in summary, is virtually bypass the effects of IQ for specified educational objectives."





saml.jpg


MORE COMING ANON



-- CatherineJohnson - 24 Jun 2006



JohnDeweyAtEdspresso 26 Jun 2006 - 20:01 CatherineJohnson




Kicking the Ed School Blues


The fan mail is rolling in and paparazzi are following me to work every day despite the great lengths to which I’ve gone to protect my identity.

[snip]

Of all the comments, two in particular stand out. One from a friend who asked if I thought I was making a difference with this little venture into blog space. The other asked whether I thought I’d be making a difference teaching in a system that prevents effective math teaching in a world infiltrated by NSF, NCTM/ed school dogma and math police.

I don’t know the answer to the first question. But I’m in ed school, where there are no wrong answers.



Good one.

Moving right along —

...what is the chance for change with only a few enlightened teachers battling the math police?

My answer to the second question is based on the fact that I’ve never had an original idea in my life. Being part of the baby boomer generation means that whatever so-called original idea is in my head is also in the heads of thousands of other people. Which means that many people getting ready to retire and who have science or math backgrounds may also be looking into teaching.


Whoa.

That's my experience exactly.

I'm a walking cliche. Always have been, always will be.

I keep telling Ed, who is not a walking cliche, "Look, if I'm obsessing over X that means five zillion other people are obsessing over X, too. Either that, or they're about to start."

It's true.



Unfortunately, when it comes to television I'm an outlier.


it's always worse than you think

In the class I just took, the professor one night espoused the ubiquitous ed school philosophy that one of the biggest hurdles to conquer in teaching math is students’ math anxiety.

[snip]

The ed school of thought holds that if you just relax and get over the anxiety, the greater truth will prevail. Not a word about how inadequate preparation may play a role. “At-risk” students are particularly vulnerable to math anxiety according to ed school wisdom. One instructor the professor knew was quite good with such students. He told how she gave each student a name having to do with a concept in algebra. One student was called “perfect square trinomial”, another was “binomial”, and so forth. (They may have had name tags). Their task was to learn how each of them “related” to one another, thus forcing them to learn what these terms meant.


Time to blow up the ed schools.


edspresso search: Dewey letters

John Dewey at edspresso, part 1
John Dewey at edspresso, part 2
John Dewey at edspresso, part 3
John Dewey has the stomach flu
John Dewey at edspresso Letter #5

John Dewey at ktm
John Dewey at ktm part 2
John Dewey experiences stomach flu
John Dewey writes again

johndewey


-- CatherineJohnson - 26 Jun 2006



ShortStoryByVernWilliams 15 Jul 2006 - 19:19 CatherineJohnson




One night I walked into the 43/8 dimension and actually believed the following:

  • We should write about math but never do math.
  • Correcting students' papers using red ink is a threat to children's self esteem and that red pens should be banned from all public schools.
  • Howard Gardner was right about his multiple intelligence theory (I think that he claims about nine at the moment) and that schools should value bodily-kinesthetic ability and the intelligence of self as much as mathematical and linguistic ability.
  • The war on intellectual excellence is a great thing. It will make us all equal.
  • Teachers Unions are actually concerned about students.
  • Advanced courses and gifted programs should be banned because they are elitist and unfair. Since everyone is gifted in their own way (see Howard Gardner), why have special gifted programs?
  • There are no bored students in US public schools.
  • We can teach thinking even when there is no content to think about.
  • We should treat members of politically protected minority groups as victims.
  • We should never view our students as individuals but as members of racial and ethnic groups.
  • We should buy into the latest educational fad even if it's based on political correctness and has nothing to do with learning or common sense.
  • There is no money wasted on administration, specialists, and useless programs. In fact, we should have more of each.
  • I should join the NCTM.
  • I should join the NEA.
  • I should feel guilty because I teach smart kids.
  • I should feel really guilty because I enjoy teaching smart kids.


cont'd



a_Bio-pictureWeb3.jpg

National Mathematics Advisory Panel
(nationalmathematicsadvisorypanel)


-- CatherineJohnson - 15 Jul 2006



ThreeStrikesRuleAgainstPureDiscovery 04 Aug 2006 - 19:26 CatherineJohnson




I'm hoping Ed can pull the full text of this article on guided discovery versus pure discovery:

Should There Be a Three-Strikes Rule Against Pure Discovery Learning?

The author's thesis is that there is sufficient research evidence to make any reasonable person skeptical about the benefits of discovery learning--practiced under the guise of cognitive constructivism or social constructivism--as a preferred instructional method. The author reviews research on discovery of problem-solving rules culminating in the 1960s, discovery of conservation strategies culminating in the 1970s, and discovery of LOGO programming strategies culminating in the 1980s. In each case, guided discovery was more effective than pure discovery in helping students learn and transfer. Overall, the constructivist view of learning may be best supported by methods of instruction that involve cognitive activity rather than behavioral activity, instructional guidance rather than pure discovery, and curricular focus rather than unstructured exploration. (PsycINFO Database Record (c) 2006 APA, all rights reserved)

Mayer, Richard E.

Mayer, Richard E.: University of California, Santa Barbara, Department of Psychology, Santa Barbara, CA, US

American Psychologist. 59(1), Jan 2004, 14-19.



Barry is well-versed - or on his way to becoming well-versed - in the distinction. I want to learn more.


-- CatherineJohnson - 03 Aug 2006



LovelessOnEducationPhilanthropy 04 Aug 2006 - 20:27 CatherineJohnson




The title of my paper is how program officers at education philanthropies view education. It is inspired by a 1997 study of education professors done by the Public Agenda Foundation in New York City, and in that particular survey, what Public Agenda found was, and I quote from the study: "Professors of education have a distinct, perhaps even singular prescription for what good teachers should do, one that differs markedly from that of most parents and taxpayers."

[snip]

The study concluded with the following. Quote. "While the public's priorities are discipline, basic skills and good behavior in the classroom, teachers of teachers severely downplay such goals."

So what I decided to do was give the same survey to program officers at education foundations, and in a nutshell, what I found was that they too are far outside the mainstream, on some issues [program officers are] even farther outside the mainstream than education professors.

[snip]

You can see in these bottom... six different classroom activities. These are sort of mainstays of progressive education. These are thing that come under criticism by progressives over the last 100 years.

Take a look. Should kids be given--this is the percentage that responded that more of this would be a good thing. Should kids be given more homework assignments? Only 21 percent of the program officers felt that they should be given more homework.

41 percent. The education professors are tougher on homework. Penalties for students who break the rules. Only 19 percent of the program officers. 37 percent, again about twice as many of education professors. And in a minute I'm going to show you what the general thinks about these things.

The title of the public agenda report was Different Drummers. The program officers at the philanthropies appeared to be even more different than the different drummers, at least on issues of discipline and basic skills. Those are the two main differences.

Memorization, endorsed by only 11 percent of the program officers. Prizes to reward good behavior in the classroom. This is Alfie Cohn's [ph] big problem, he has a big problem with that. Only 11 percent. And then multiple choice exams, not popular at all.

source:
With the Best of Intentions: Lessons Learned in K-12 Education Philanthropy



character ed

Look at the question on schools fail to teach religious values. If you see that as a serious problem or not. Only 6 percent of program officers think that's a problem. Among traditional Christian parents, not surprisingly, 70 percent see as a problem.

But even in the general public, almost half, 47 percent, think it's a serious problem.



I'm surprised to discover that, if I had to choose, I would come down on the "serious problem" side of this issue.

I don't want public schools to teach religious faith, though I support vouchers for religious schools and I wish to heck our schools would teach the Bible as subject matter content.

Biblical literacy: a good thing.

On the other hand, I don't want public schools teaching values - namely narcissism and yay-me blather - that directly contradict my own religious values. At Main Street School (grades 4-5) the kids apparently recited some kind of self-respect affirmation each and every morning, after the Pledge of Allegiance. Christopher can't remember the words now, and neither can I, but he thinks he had to say something like, "I am an amazing person." Every single morning. I am an amazing person.

Then, at the 5th grade graduation, the superintendent read an "Alphabet of Values" - "A is for Achievement" - that kind of thing. Most of it was nice, but the entry for L was awful:

L: Love yourself first and always.

It may have been even worse; it may have been "Love yourself first and best."

blech

I was sitting there thinking, "So what happened to Love thy neighbor as thyself?" (Which leads me to think it probably was "Love yourself first and best.")

As far as I'm concerned, there are many, many occasions in life when loving yourself first is a very bad idea. Anyone who a) gets married and b) has kids is going to experience these occasions.

Probably anyone going into the teaching profession is going to experience them.

I don't want my kids being taught to love themselves first. I also don't want them spending a lot of time thinking, "I am an amazing person." As a matter of fact, I would go so far as to say that spending any at all time thinking the words I-am-an-amazing-person is a terrible idea, and I could probably support my view empirically if I had all day to scan the archives of the PERSONALITY AND SOCIAL PSYCHOLOGY BULLETIN. (I have no idea whether this particular study does or does not support the anti-I am amazing person viewpoint. I think it might.)

So, yes.

At this point I'm thinking a failure to teach "religious values" is a problem.



some good news

Loveless:

The program officers with teaching experience are closer to the mainstream public views.


This jibes with my feeling that teachers are more likely than their superiors to think radical constructivism is a crock. Hirsch has a nice observation to the effect that while no one has been able to defeat ed school ideology, no one's been able to defeat reality, either. Students learn the way they learn.

Teachers are in the trenches.



question from the audience

QUESTION: Hi. My question sort of is which side are you on, or actually, which side are the philanthropists on in regard to the education wars that are being fought across this country, often under the name of the reading wars or the math wars. You know, to what extent are they facilitating the reform agenda and to what extent are they facilitating maybe the opposite.

MR. LOVELESS: I don't mind taking a stab at that. For the most part, they're on the neoprogressive side, which in the--I edited a book, a couple years back, called The Great Curriculum Debate, and it's about the wars in both math and reading that have occurred over the last 15 years, whole language versus phonics, and in math, math reform or NCT and math reform versus more basic emphasis on arithmetic and other traditional mathematics.

And for the most part, the philanthropies have supported, financially, the neoprogressive side.



So the question is, given the fact that lots more money poured into the schools over the past decades hasn't improved them, can lots more money poured into the schools make schools worse?

My feeling is yes. It's possible to have too much money.

This reminds me of the various studies showing that rich people undergo all kinds of unnecessary surgery. My line on that used to be, "You go into Cedars-Sinai for a c-section, you come out with a nose job."

In context - i.e. living baja Beverly Hills - it was funny.



-- CatherineJohnson - 03 Aug 2006



NationalMathematicsAdvisoryPanelUpdate 02 Sep 2006 - 15:31 CatherineJohnson





Robert Siegler


Ed can pull the article, so I'll take a look. Given my immersion in the world of non-math teaching, this line from the abstract to Siegler's article on children's learning is chalk on the blackboard for me (chalk on the electronic whiteboard, I meant to say):

Learning has many sources; one that is particularly promising for educational purposes is self-explanations.

I've come to feel that in math ed - though not in other subjects - this proposition is almost completely false.


From Seigler's homepage:

My colleagues and I have built computational models to illustrate how young children can make such intelligent decisions and also to show how the decisions improve as knowledge and skill improve.


He's not anti-content.




NCLB: one law, two philosophies

Meanwhile, Education Week has a terrific article on NCLB (registration required): What Works vs. Whatever Works: Inside the No Child Left Behind law’s internal contradictions by Mike Petrilli.

[T]he No Child Left Behind Act is the result of an uncomfortable truce between two groups of school reformers: the “what works” camp and the “whatever works” camp. The law is an amalgam of their ideas, and their ongoing competition will shape the contours of No Child Left Behind version 2.0.

First, let’s examine the what-works crowd. These reformers look across the education system and see its failings in terms of ignorance and ideology. They decry the pedagogical fads that sweep through our schools, bemoan educators’ resistance to scientifically proven reading-instruction methods, and abhor the quasi-religious nature of disliked educational “philosophies” such as constructivism and “multiple intelligences.” They seek to bring order to this chaos through the dispassionate eye of science. Using medicine as their model, they aim to employ rigorous research methods to determine what works, and then to use the force of law and regulation to ensure adoption of these methods throughout the land. After all, they say, we don’t allow doctors to wing it when they are practicing brain surgery; we expect them to use best practices in order to save lives.

The stamp of what-works advocates is clear throughout the No Child Left Behind legislation, but especially in two of its most controversial provisions: the Reading First program, and the “highly qualified teachers” mandate. The former requires schools to use funds for a narrowly defined type of reading instruction—namely, that which has been found by rigorous research to be effective. The U.S. Department of Education has dutifully implemented the program in this narrow, prescriptive way, leading to much gnashing of teeth and complaints of bullying. But for leaders of the what-works coalition, such as the former federal reading czar, G. Reid Lyon, anything else would amount to malpractice.

Then there’s the “highly qualified teachers” provision of the law, which demands that all teachers be able to demonstrate their subject-matter knowledge. This, too, is said to be based upon rigorous research, though even admirers of the mandate must admit that the evidence is somewhat flimsy. (Most studies linking subject-matter knowledge to teacher effectiveness have examined math or science at the secondary level; their applicability to elementary school, much less to subjects such as art, geography, or economics, is unknown.) But again, the what-works coalition borrows from the language of medicine, insisting that we wouldn’t allow doctors to practice if they didn’t have the relevant credentials. Surely we need teachers who are similarly well-qualified.

The whatever-works camp holds a very different worldview. These reformers look out across the education system and see its failings in terms of incentives, power, and politics. They decry the daily decisions made by school boards and district leaders that benefit adults instead of children (especially poor children). They abhor the red tape and bureaucratic inertia that keep educators from innovating. They don’t particularly care what happens inside the “black box” of classroom instruction; they just want children to be well-educated at the end of the day. They seek to right the system through the classic management model of “tight-loose”: Be tight about the results you expect, but loose as to the means. Put differently, the whatever-works camp combines accountability for student learning with flexibility around everything else. Using the entrepreneurial sector as its model, this camp aims to create a marketplace of schools, free to experiment, compete, and improve. After all, there’s a reason that America has the strongest economy in the world, they assert, and if we can empower educators with significant freedom (in return for getting results), they, too, will rise to the occasion.

The stamp of whatever-works advocates is also clear in the NCLB legislation. The very heart of the law is its accountability system, built into the Title I program, which was designed to create incentives for schools to boost student learning and close achievement gaps. Most important, the design of “adequate yearly progress,” with its disaggregation of test scores by racial groups, was meant to help local communities overcome the political barriers that keep resources and attention from flowing to needy children. In the spirit of “whatever works,” and in return for this increased accountability, the rules around the use of Title I funds were relaxed dramatically, and many more schools were given permission to use their federal dollars for “schoolwide” reforms. New “transferability” provisions were included in the law, too, allowing states and districts to move federal funds from one program to another. Just show us the results, Congress seemed to say, and we’ll leave you alone.

Is it any surprise, then, that educators feel whipsawed between competing demands? On the one hand, the federal government is saying to do whatever works to boost student learning, and on the other hand it’s saying to do things in a certain prescribed, preapproved way.

The result is frustration and anger. Imagine a poor, rural Title I school that is doing whatever works to get great results. In this case, it hires a former engineer from the local coal mine to teach 8th grade mathematics. She’s a natural, and her students’ test scores go through the roof. But because she didn’t major in math, she’s not considered “highly qualified.” How is that school’s principal going to feel when the feds come knocking, telling him to replace the teacher or risk being “out of compliance”? Or consider an elementary school whose reading results are soaring but which dares to use a reading program not on the state-approved Reading First list. Should the school’s principal be punished for insubordination, or celebrated for innovation and inventiveness?

What does all of this mean for the next version of the No Child Left Behind Act, due to be reauthorized in 2007? Surely both camps will try to consolidate their gains, further push their agenda, and avoid surrendering ground. The what-works camp will seek to expand its influence beyond reading to other areas, such as math. (This is especially true if the newly named National Mathematics Advisory Panel can identify rigorous evidence to support certain approaches to teaching math.)

[snip]

The whatever-works camp will try to expand on the transferability provision, perhaps allowing all of a state’s federal funds to flow through a simplified Title I formula. It will try to make it easier for schools to earn waivers from federal laws and regulations. And, perhaps most importantly, expect this camp to push for a larger role for charter schools, whose “accountability in return for flexibility” design epitomizes the whatever-works approach.




in a nutshell

what works

  • Reid Lyon, reading czar

  • Reading First

  • qualified teachers mandate

  • analogy to medical practice


whatever works

  • analyze failure of schools in terms of "incentives, power, and politics"

  • “tight-loose” management model

  • marketplace of schools

  • pro-charter




Coming off of Animals in Translation, I was a whatever works person.

I favored tight-loose because of McDonald's success reforming the meatpacking industry using Temple Grandin's 10-item animal welfare audit. Temple created simple metrics such as "No more than 3 in 100 animals can boo in distress." Just 10 items, all focused on the animals. Nothing about employee training, nothing about non-slip plant flooring, nothing about plant maintenance schedules. That was the "loose" part. A typical government regulator-type will audit at least 100 different aspects of a plant, and Temple has seen the results in countries where that's the case. The results aren't good.

When the audit went into effect, plants thought it was far too strict to pass. McDonald's told plants that if they didn't pass, they'd be off their supplier list. That was the "tight" part. Not only did plants figure out how to pass the audit, a lot of them ended up exceeding the standards. Most plants passed the audit using the same management, the same workers, even the same out-of-date equipment.

So I'm a believer in "tight-loose."

But I no longer believe that a tight-loose approach will reform the schools. Charters & vouchers might, over the long haul, put so much pressure on existing schools that they're forced to change. Might. But I'm not hopeful. As far as I can tell people don't give up core values to increase market share, and neoprogressive ideology has been a core value of U.S. ed schools for nearly 100 years.

They're not going down without a fight.


nationalmathematicsadvisorypanel



-- CatherineJohnson - 04 Aug 2006



TwoSides 12 Aug 2006 - 14:53 CatherineJohnson




Shortly after posting a link to Michael J. Petrilli's What Works vs. Whatever Works: Inside the No Child Left Behind law’s internal contradictions (registration required) it struck me: there are only two sides, and neither of them is neoprogressive.




-- CatherineJohnson - 04 Aug 2006



NixOnColumbiaTeachersCollege 07 Aug 2006 - 20:41 CatherineJohnson




new old schoolteacher is guestblogging for eduwonk. Until June she was, I believe, a graduate student at a school of education in NYC which I take to be Columbia Teachers College, although her blog doesn't currently identify the institution.

Columbia Teachers College, the employer of William Heard Kilpatrick, is Ground Zero for curricular & pedagogical awfulness. E.D. Hirsch argues that Kilpatrick, not John Dewey, is the real founder of progressive education.

Here is new old school teacher:

I am currently attending the KIPP Summit 2006 in New Orleans, attended by all the KIPP schools as well as other excellent charter schools and charter school networks (for example, Uncommon Schools and Achievement First). It is awesome. Compare some of the AERA presentations I talked about yesterday with these, presented over the last few days here in New Orleans:

--"Basics on Advising College-Bound Students"
--"Analyzing Test Scores"
--"Activities and Questioning with Bloom's Taxonomy"
--"Informal Assessment of Reading Difficulties"
--"Overview of Expository Writing, Parts I and II"
--"A Typical Day in Math 8"
--"Developing Number Sense"

These sound a little more practicable and useful than a session on Taiwanese mail-order brides, don't you think? Yesterday I learned a ton of great strategies for creating a safe, calm, effective learning environment and how to deal with students with difficult behavior. Today in 1.5 hours I learned exactly how to teach my kids to write summaries from fiction or non-fiction and how to highlight text effectively (college, hello!). THIS IS WHAT I ALWAYS WANTED from grad school and NEVER GOT. And was so sad about that I had to write an angry blog full of tirades. It's $30,000 worth of tragic.


That's $30,000 to not learn how to teach.


My favorite W.H. Kilpatrick saying:

activity leading to further activity without badness

That's the project method.



kilpatrick.jpg

The Columbia School of Pragmatism
William Heard Kilpatrick UNESCO



-- CatherineJohnson - 07 Aug 2006



EngelmannOnHowManyWordsADay 08 Aug 2006 - 19:03 CatherineJohnson




Ken left this passage from Engelmann in the Comments thread to 15 words a day:


Engelmann thinks that Hirsch's estimates are way too high. He think's it's more like 30,000 words total and 3 new words a day.

The numbers: Hirsch selects 60,000 as the number of word meanings for the top-of-class student. I did a very unscientific experiment that may be way out in left field, but I came up with a smaller number. I didn't have a top-of-class high-school student handy, but I had a top-of-class graduate student. I opened a college dictionary that had about 70,000 entries to four random pages. I read the words, spelled them, told her the part of speech for those she questioned, and asked her if she knew what they meant. On three of the pages, she did not know all the words. On one page, she did not know bourn, bourrée, bouse, boustrophedon, bouzouki, bowerbird, bow pen, bowsprit. She also didn't know a second meaning of bower (a bow anchor). She probably didn't know bovid, but I gave her half credit. "Could that be something related to a bovine?" "It is an adjective for bovine."

Also, I did not present most capitalized entries because I didn't think they were fair (Bournemouth, Bow bells, Bowditch, Bowen, Bowie State.) I did present Bowie and Bowling Green. I did not present six entries because they were either dialect, slight variations of the same word (two bowman entries for instance), obsolete, or spelling variations (bowlder for boulder). The page had 58 entries. Eleven were discards. Of the 47 remaining, she missed 9.5 (half credit for bovid). So her score on that page was 37.5/47 or 80%. Her performance on the other pages was 100%, 65%, 39%. The low-scoring page had lots of sodium words, which she could identify only as a substance composed of sodium. (She got sodium chloride, sodium fluoride, sodium glutamate, and Sodium Pentothal, but she was not able to identify the others.) Also, I threw out a lot of items on this page-variant spellings, obsolete words, capitalized words I didn't know and that seemed trivial, affixes, and obscure slang words. She also missed sociometry, socal, socman, sokeman, sodalite.

Indeed my decisions were less than operationally delineated, but if we assume that 15% of the entries are not fair and that the top-of-class person would get average 80% on the others, the total number would be something on the order of 48,000, which is quite a bit less than 60,000. Personally, I don't believe it's that high. Also of interest is that a very extensive analysis of morphology for spelling, conducted in the '70s, came up with a number of 30,000 words that seemed to be fairly exhaustive.

At least some cognitive scientists favor this range over the one that Hirsch suggests. Biemiller and Slonim (2001) concluded that the learning rate of new words for the top-of-class student is more on the order of about 3 words per day, not 8-18. So there seems to be far from perfect consensus on number of words. Also, Biemiller endorses explicit, direct instruction. So there isn't perfect consensus on methods for inducing vocabulary.




Three new words a day sounds much more likely to me, based on nothing more than instant reaction.

I just noticed that Ken is back on the job!

Can't wait to read.



Fischgrund on divorce and SAT scores
how much reading a day?
robust vocabulary instruction (400 words a year)
Vocabulary Workshop levels & grades
15 new words a day
Engelmann says it's 3 new words a day



-- CatherineJohnson - 08 Aug 2006



NctmReformsAgain 14 Sep 2006 - 16:52 CatherineJohnson




In today's Wall Street Journal ($):

Arithmetic Problem
New Report Urges Return to Basics In Teaching Math
Critics of 'Fuzzy' Methods Cheer Educators' Findings;
Drills Without Calculators Taking Cues From Singapore
By JOHN HECHINGER
September 12, 2006; Page A1

The nation's math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics.

In a report to be released today, the National Council of Teachers of Mathematics, which represents 100,000 educators from prekindergarten through college, will give ammunition to traditionalists who believe schools should focus heavily and early on teaching such fundamentals as multiplication tables and long division.

The council's advice is striking because in 1989 it touched off the so-called math wars by promoting open-ended problem solving over drilling. Back then, it recommended that students as young as those in kindergarten use calculators in class.

Those recommendations horrified many educators, especially college math professors alarmed by a rising tide of freshmen needing remediation. The council's 1989 report influenced textbooks and led to what are commonly called "reform math" programs, which are used in school systems across the country.

The new approach puzzled many parents. For example, to solve a basic division problem, 120 divided by 40, students might cross off groups of circles to "discover" that the answer was three.

Infuriated parents dubbed it "fuzzy math" and launched a countermovement. The council says its earlier views had been widely misunderstood and were never intended to excuse students from learning multiplication tables and other fundamentals.

Nevertheless, the council's new guidelines constitute "a remarkable reversal, and it's about time," says Ralph Raimi, a University of Rochester math professor.

Francis Fennell, the council's president, says the latest guidelines move closer to the curriculum of Asian countries such as Singapore, whose students tend to perform better on international tests.



So maybe it wasn't such a great idea after all for IUFSD to ban my Singapore Math course.



new timeline

According to their report, "Curriculum Focal Points," which is subtitled "A Quest for Coherence," students, by second grade, should "develop quick recall of basic addition facts and related subtraction facts." By fourth grade, the report says, students should be fluent with "multiplication and division facts" and should start working with decimals and fractions. By fifth, they should know the "standard algorithm" for division -- in other words, long division -- and should start adding and subtracting decimals and fractions. By sixth grade, students should be moving on to multiplication and division of fractions and decimals. By seventh and eighth grades, they should use algebra to solve linear equations.

Here's the Singapore sequence.




Lutherans turning into Catholics

A recent study by the Thomas B. Fordham Foundation, a Washington nonprofit group, found that only two dozen states specified that students needed to know the multiplication tables. Many allowed calculators in early grades.

Chester E. Finn Jr., the foundation's president and a former top official at the U.S. Department of Education, blamed the earlier math-council guidelines for state standards that neglect the basics. He described the new advice as a "sea change," saying that "it's a little bit like Lutherans deciding to become Catholics after the Reformation."

Understanding math, rather than parroting answers to poorly understood equations, was the goal of the council's controversial 1989 standards. Those guidelines called on teachers to promote estimation, rather than precise answers. For example, an elementary-school student tackling the problem 4,783 divided by 13 should instead divide 4,800 by 12 to arrive at "about 400," the 1989 report said. The council said this approach would enable children using calculators to "decide whether the correct keys were pressed and whether the calculator result is reasonable."

"The calculator renders obsolete much of the complex pencil-and-paper proficiency traditionally emphasized in mathematics courses," the council said then. In 2000, in another report, the council backed away somewhat from that position.

Still, in response to the earlier recommendations, many school systems required children to describe in writing the reasoning behind their answers. Some parents complained that students ended up writing about math, rather than doing it.

As the debate heated up, concern grew about U.S. students' math competence. In 2003, Trends in International Mathematics and Science Study, a test that compares student achievement in many countries, ranked U.S. students just 15th in eighth-grade math skills, behind both Australia and the Slovak Republic. Singapore ranked No. 1, followed by South Korea and Hong Kong. Fueling concern about the quality of elementary and high-school instruction: one in five U.S. college freshmen now need a remedial math course, according to the National Science Board.





low-income students

This is very exciting. The AIR report (pdf file) led me to believe that Singapore Math had been a flop in low-income schools because the student mobility is so high (and see Hirsch on this subject, too):

If school systems adopt the math council's new approach, their classes might resemble those at Garfield Elementary School in Revere, Mass., just north of Boston. Three-quarters of Garfield's students receive free and reduced lunches, and many are the children of recent immigrants from such countries as Brazil, Cambodia and El Salvador.

Three years ago, Garfield started using Singapore Math, a curriculum modeled on that country's official program and now used in about 300 school systems in the U.S. Many school systems and parents regard Singapore Math as an antidote for "reform math" programs that arose from the math council's earlier recommendations.

According to preliminary results, the percentage of Garfield students failing the math portion of the fourth-grade state achievement test last year fell to 7% from 23% in 2005. Those rated advanced or proficient rose to 43% from 40%.

Last week, a fourth-grade class at Garfield opened its lesson with Singapore's "mental math," a 10-minute warm-up requiring students to recall facts and solve computation questions without pencil and paper. "In your heads, take the denominator of the fraction three-quarters, take the next odd number that follows that number. Add to that number, the number of ounces in a cup. What is nine less than that number?" asked teacher Janis Halloran. A sea of hands shot up. (The answer: four.)

Ms. Halloran then moved on to simple pencil-and-paper algebra problems. "The sum of two numbers is 63," one problem reads. "The smaller number is half the bigger number. What is the smaller number? What is the bigger number?" (The answers: 21 and 42.)

In this class, the students didn't use the lettered variables that are so prevalent in standard algebraic equations. Instead, they arrived at answers using Cuisenaire rods, sticks of varying colors and lengths that they manipulate into patterns on the tops of their desks. The children use the rods to learn about the relationship between multiplication and geometry. The goal: a visceral and deep understanding of math concepts.

"It just makes everything easier for you," says fifth-grader Jailene Paz, 10 years old.


Cuisinaire rods for bar models!

That's so cool!




TERC time

The Singapore Math curriculum differs sharply from reform math programs, which often ask students to "discover" on their own the way to perform multiplication and division and other operations, and have come to be known as "constructivist" math.

One reform math program, "Investigations in Number, Data and Space," is used in 800 school systems and has become a lightning rod for critics. TERC, a Cambridge, Mass., nonprofit organization, developed that program, and Pearson Scott Foresman, a unit of Pearson PLC, London, distributes it to schools.





parents don't get it part 1

Ken Mayer, a spokesman for TERC, says many parents have a "misconception" that Investigations doesn't value computation. He says many school systems, such as Boston's, have seen gains in test scores using the program. "Fluency with number facts is critical," he says.





parents don't get it part 2

Polle Zellweger and her husband, Jock Mackinlay, both computer scientists, moved to Bellevue, Wash., from Palo Alto, Calif., two years ago so their two children could attend its highly regarded public schools. She and her husband grew suspicious of the school's Investigations program. This summer, they had both children take a California grade-level achievement test, and both answered only about 70% of the questions correctly. Ms. Zellweger and her husband started tutoring their children an hour a day to catch up.

"It was a really weird feeling," says their daughter, Molly Mackinlay, 15. "I do really well in school. I am getting A-pluses in math classes. Then, I take a math test from a different state, and I'm not able to finish half the questions."

Eric McDowell, who oversees Bellevue's math curriculum, says parents misunderstand Investigations.


If it weren't for the parents, teaching would be a great job.




math wars and war wars

In the Alpine School District in Utah, parent Oak Norton, an accountant, has gathered petitions from 1,000 families to protest the use of Investigations. His complaints began more than two years ago, when he discovered at a parent conference that his oldest child, then in third grade, wasn't being taught the multiplication tables.

Barry Graff, a top Alpine school administrator, says the system has added more traditional computation exercises. Over the next year, Alpine plans to give each school a choice between Investigations or a more conventional approach. Mr. Graff, who says Alpine test scores tend to be at or above state averages, expects critics to keep up the attacks and welcomes the national math council's efforts to provide grade-by-grade guidance on what children should learn.

"Other than the war in Iraq, I don't think there's anything more controversial to bring up than math," he says. "The debate will drive us eventually to be in the right place."



wow

I bet things are hopping over at math-teach & math-learn.

[pause]

hmm

No action thus far.

Once Wayne Bishop posts this baby, we'll be in a shooting war.





update: Bishop's got it!

let the fun begin



what Singapore students can do at the end of 7th grade



-- CatherineJohnson - 12 Sep 2006



BattleLines 26 Sep 2006 - 19:57 CatherineJohnson




Midway through today's TIMES report on the state's fourth grade slump:

E. D. Hirsch Jr., the author of a recent book, “The Knowledge Deficit,” said students do not learn enough vocabulary and content knowledge at younger ages.

Daniel P. Keating, director of the Center for Human Growth and Development at the University of Michigan, said schools should prepare students earlier for the more abstract and sophisticated reasoning required in middle school.

“Perhaps the early preparation is not anticipating that shift to having those higher demands,” he said, adding that tests for younger children do not measure those skills. “All of a sudden we’re looking for the kinds of skills that just haven’t been assessed earlier.”


Note: one of these men is a developmental psychologist "whose research focuses on integrating knowledge about biodevelopmental processes, population patterns in developmental health, and social factors affecting individual and population development."

The other is a college professor who has spent a lifetime researching education, creating a superb core curriculum for K-6 students, and researching and writing new content in his own field of research.

The psychologist doesn't know anything about education or curriculum and is giving his best guess.

The curriculum specialist is stating the consensus view of cognitive scientists who've been researching this subject and publishing their results in refereed journals for many years.

Guess which man is winning the argument.


Irvington slump
NY scores slump
battle lines



-- CatherineJohnson - 22 Sep 2006



HowToCureMathAnxiety 23 Oct 2006 - 00:00 CatherineJohnson





So I mentioned that the Yonkers school system graduated Christian from high school with a 3rd grade level of math knowledge — and that last week I'd started him on the 4th grade Saxon Math book, Saxon 5/4.

It's working.

He breezed through the first lesson.

Then he breezed through the second lesson.

Then he breezed through the third.

Now he comes in, deals with the kids, and, after dinner, pulls out his Saxon Math books and does the lesson in 15 or 20 minutes while keeping an eye on Andrew & watching whatever Christopher has on TV.

This is the way you cure math anxiety.

I think.

You cure math anxiety the same way you remediate gaps, by starting a student back before the point where math got hard. That's the Siegfried Engelmann way; that's the KUMON way.

I don't know that Christian had a full-blown case of "math anxiety."

I don't even know what "math anxiety" is, other than the predictable result of years of lousy math instruction.

Christian was against math when he first started working with the kids.

Now he's neither for math nor against it, as far as I can tell.

He just comes in and does his math.

Long live Saxon.



Speaking of living long, I'm a bit concerned.

The Harcourt website seems to have pulled its online placement tests.

yikes

We need those.

I have copies myself, and I've found two other websites that have them posted (links below). Harcourt has an online test, which is good, but it doesn't give you the flexibility you need and reading online is difficult.

I hope they post those tests again.





Engelmann on student placement in curriculum

Rule 1: Hold the same standard for high performers and low performers. This rule is based on the fact that students of all performance levels exhibit the same learning patterns if they have the same foundation in information and skills. The false belief that characterizes the conventional wisdom about teaching is that lower performers learn in generically different ways from higher performers and should be held to a lower or looser standard. Evidence of this belief is that teachers frequently have different “expectations” for higher and lower performers. They expect higher performers to learn the material; they excuse lower performers from achieving the same standard of performance. Many teachers believe that lower performers are something like crippled children. They can walk the same route that the higher performers walk, but they need more help in walking.

These teachers often drag students through the lesson and provide a lot of additional prompting. They have to drag students because the students are making a very high percentage of first-time errors. In fact, the students make so many mistakes that it is very clear that they are not placed appropriately in the sequence and could not achieve mastery on the material in a reasonable amount of time. The teachers may correct the mistakes, and may even repeat some parts that had errors; however, at the end of the exercise, the students are clearly not near 100% firm on anything. Furthermore, the teacher most probably does not provide delayed tests to assess the extent to which these students have retained what had been presented earlier.

The information these teachers receive about low performers is that they do not retain information, that they need lots and lots of practice, and that they don’t seem to have strategies for learning new material. Ironically, however, all these outcomes are predictable for students who receive the kind of instruction these students have received. High performers receiving instruction of the same relative difficulty or unfamiliarity would perform the same way. Let’s say the lower performers typically have a first-time-correct percentage of 40%. If higher performers were placed in material that resulted in a 40% first-time-correct performance, their behavior would be like that of lower performers. They would fail to retain the material, rely on the teacher for help, not exhibit selfconfidence, and continue to make the same sorts of mistakes again.

If students are placed according to their first-time-correct percentages, they tend to learn and behave the same way, whether they are “lower performers” or “higher performers.” In Project Follow Through, we mapped the progress of students of different IQ ranges. The results showed that regardless of students’ entering IQ, the rate of progress was quite similar across all children and across different subjects. Lower performers learned as fast as higher performers. They simply started at a different place, with material that higher performers had long since mastered. Note that this conclusion may be somewhat biased because we paid particular attention to the instruction for the lower performers. They tended to have better teachers and their instruction tended to be monitored very closely. In any case, they learned at a very healthy rate, one that paralleled that of students with IQs 40 points higher.

The typical practices of placing and teaching students are completely opposed to appropriate placement and teaching procedures. At the University of Oregon, we place teaching-practice students in special-ed classrooms that use direct-instruction programs. During the years that we first offered these practica, we typically worked with teachers who were teaching DI but had not generally received much training. Before we arranged for a placement with a new supervising teacher, therefore, we made sure that the classroom was “appropriate” for our students, which means that the children the practicum students were to work with were placed appropriately and that the teacher was using and modeling appropriate practices. As part of the review of the new classrooms that were candidates for receiving practicum students, we checked the program placement of the students and changed their placement if necessary.

Our estimate is that in the first 40 or more classrooms we used, the children were moved back in DI reading programs an average of 100 lessons—sometimes 120 lessons. The children, in other words, were placed about 3/4 of a school year or more beyond the optimum first-time-correct percentages. Nearly all teachers had children that were seriously misplaced. Furthermore, I don’t recall a single classroom in which children’s percentages required us to move children ahead in the programs. Children were always “over their heads.”

source:
Student Program Alignment and Teaching to Mastery (pdf file)
by Siegfried Engelmann



Children were always "over their heads."

When you design instruction so that children are always in over their heads, you have poor instruction and bad student outcomes.

Period.




in a nutshell

  • students of all performance levels exhibit the same learning patterns if they have the same foundation in information and skills

  • when placed correctly in the curriculum - at a level determined by what they already know and can do - "low performing" or "learning disabled" students learn "at a very healthy rate, one that paralleled that of students with IQs 40 points higher"

  • teachers must provide delayed tests to assess the extent to which these students have retained what has been presented earlier

  • children who are struggling in school are almost always placed far ahead of themselves in the curriculum. They are struggling the same way a straight-A student whose never studied physics would struggle if you dropped him into the middle of a college physics course.




remediating math at the college level

We've had a number of discussions about how to remediate the math knowledge of college kids. Rudbeckia Hirta has written about this often, along with Carolyn &, I think, Steve H.

When Ed and I first discussed what to do about Christian's math, I said I didn't particularly feel like paying for Westchester Community College to teach Christian the math his mom already paid Yonkers to teach him back in grades 6-12.

I said I was thinking about just giving him the Saxon placement test & buying him the books & seeing how it went.

Ed thought that was a bad idea.

(It's fun to be right! It's even more fun to be right on your own blooki.)

Actually, "I told you so" isn't (really) the point. At the time I thought Ed was probably right. I thought handing Christian a couple of Saxon books and telling him to go teach himself math — or trying to teach him myself — was probably nuts. He doesn't (didn't) like math; he couldn't do math; he had no interest whatsoever in the whole question of math....none of this sounds like a recipe for success in self-teaching.

The fact that I went ahead and gave him the Saxon placement test anyway was probably a Bayesian moment. I've been teaching myself math long enough now, and teaching Christopher math, and writing ktm, and reading the Comments that I probably "knew" at the level of the cognitive unconscious that Saxon was a better idea than a $500 "developmental" math course at a community college.

The reason Saxon is probably a better idea (it's early days, I realize) is that the community college doesn't offer courses in 4th grade arithmetic.

They're trying to remediate years of missing math instruction in one or two semesters. I just don't see how it can work no matter how good their teachers are (and I bet their teachers are good). In fact, the effort to close years of math gaps in one or two semesters seems almost inevitably destined to produce more math anxiety than a student had going in.

I'm thinking that just as there is no royal road to geometry, there's no royal road to Algebra 1. People whose math education went completely off the rails back when they were eight have to go back to when they were eight.

At least, that's what I'm thinking at the moment.

We'll see how it goes.


01ec024128a01b30b5abd010._AA240_.L.jpg



Saxon middle grades online placement test
downloadable Saxon placement tests at Learning Things
downloadable Saxon placement tests at Sonlight Curriculum
Rainbow Resource (least expensive source of Saxon Homeschool texts I've found)
teachingtomastery teachtomastery programplacement
Christianlearnsmath



-- CatherineJohnson - 20 Oct 2006



AgainstChallenge 01 Nov 2006 - 19:53 CatherineJohnson




More from Engelmann on teaching to mastery:

Rule 3: Always place students appropriately for more rapid mastery progress. This fact contradicts the belief that students are placed appropriately in a sequence if they have to struggle— scratch their head, make false starts, sigh, frown, gut it out. According to one version of this belief, if there are no signs of hard work there is no evidence of learning. This belief does not place emphasis on the program and the teacher to make learning manageable but on the grit of the student to meet the “challenge.” In the traditional interpretation, much of the “homework” assigned to students (and their families) is motivated by this belief. The assumption seems to be that students will be strengthened if they are “challenged.”

This belief is flatly wrong. If students are placed appropriately, the work is relatively easy. Students tend to learn it without as much “struggle.” They tend to retain it better and they tend to apply it better, if they learn it with fewer mistakes.

source:
Student Program Alignment and Teaching to Mastery (pdf file)
by Siegfried Engelmann



This is a perfect description of Irvington educational philosophy as it pertains to the rapidly dwindling student "elite," i.e. the chosen few who are allowed entry into accelerated and Honors courses.

The kids have to gut it out.

If they can't gut it out, down they go.

They "don't belong."



As a direct result of my experience muscling our family's way through "accelerated instruction" here in Irvington, I have now stricken the word "challenge" from my list.

I don't want to hear "challenge" ever again.

I want to hear "teach;" I want to hear "learn;" I want to hear "assess." That's "assess" as in assessment for learning, not grading.

During our meeting with the principal — which was very good — we raised the question of Irvington's rationing of accelerated courses.

That's another story; I'll get to it later. Suffice it to say that the middle school plans to offer two sections of Regents earth science next year, out of 8 sections altogether. Compare this to the Pelham school district which, a few years back (and possibly still today) had everyone in 8th grade taking Regents science and earning high scores on the Regents earth science test. Irvington has 25% of 8th graders taking earth science and apparently our Regents scores for the kids who take earth science in high school aren't good, or so I'm told.

Spot the difference?

Anyway, Mr. Witazek said he'd already had parents in to discuss the issue with him (good); he also mentioned that he himself had taken earth science in the 8th grade because in his school everyone took earth science in the 8th grade.

He's going to have to spend some serious time figuring this out, because this year the SOP* isn't operative, SOP being that parents wait until after their child has been rejected to complain. We're complaining now.

Since he couldn't promise anything at that moment, he offered the observation that, "All courses can be challenging." This was sincere; it sounds like spin, but it wasn't.

I swatted it back across the net anyway. Time is short. I can't spend any more of my child's middle years swapping edu-language with the administrators who are in charge of his education.

I said, "Everyone who wants to take earth science needs to take earth science. Just telling people that this course or that course is 'challenging' isn't enough. An earth science course is either a Regents course or it's not."

The thing I like about the new principal so far is that he has exactly zero problem with a statement like that. Although he uses a great deal of edu-blah-blah in his official communications with parents, he clearly seems to think that parents are within their rights not to want to talk edu-blah-blah face to face.

Then I delivered my stump speech:

I don't want to hear 'challenging' any more. We've had 'challenging' in Phase 4 math for a year now, and it's a nightmare. All it means is the parents teach the course. Anyone can challenge a child. Just pull something that's over their heads off the internet and tell them to go do it. Teaching a child is what's hard. We want our child to be taught, not challenged.'

He said, "I hear what you're saying," and he meant it.


Since that meeting we've seen tangible changes in the math instruction.

Solutions to the homework problems are given out; kids check their own homework in class. (To me this is preferable to having the teacher collect the homework and correct it at home. These kids are perfectly capable of correcting their own homework as long as the teacher gives them the answers, and this way they get much more timely feedback.)

Then Ms. K finds out who missed which problems and gives each child individual help on those problems. (I'm thinking that as matters improve she shouldn't have to do that as often, because the kids should be getting homework assignments pitched to their level of mastery.)

A couple of days ago she gave a quiz consisting of two problems of the type they'd had on the homework assignment.

This is fantastic progress; it's exactly what we all desperately need; and it's happening because of the new principal.

We are impressed and grateful.

I've mentioned in the comments section that we're thinking the principal's background is a help.

Previously he worked with a disadvantaged student population in Albany schools.

During our meeting he seemed almost stunned to be finding out that he's got parents reteaching courses at home. This widespread practice has become naturalized for us; when there's trouble in a class, people immediately begin to reteach the content themselves; if trouble continues the next step is to hire a tutor. Parents take both of these steps quickly. Unlike a school bureaucracy, we don't wait for "the meeting" to provide "services."

Many parents hire tutors from the same school their child is attending.

All of this seems normal to us.

It does not seem normal to a person who just got off the train from Albany.

So far, I'd say he's making progress in changing the tone and culture of the school. Here is a bellwether: some of you will remember my friend who was spending close to $200 a week on tutoring by a middle school teacher to keep her child from flunking 6th grade.

I talked to her a couple of days ago.

She is now spending half that and she's spending nothing at all keeping her other child afloat.

She may be heading towards dispensing with the tutor altogether.

All of this appears to be happening because of the new principal.



The district needs fundamental reform.

At a minimum, we need a laser focus on student outcome.

What student outcomes will result from the proposed program or pedagogical approach?

And then: what student outcomes did result from the proposed program or pedagogical approach?


And we need to focus always on creating and maintaining the conditions for success.

One of those conditions is to dump the idea that unless a child is being worked to the point of burn-out or swamped by homework problems he has no idea how to do, he's not learning because he's not being challenged.


Teaching to mastery means the child is not gutting it out.




* standard operating procedure


-- CatherineJohnson - 20 Oct 2006



NoOneToWaste 26 Oct 2006 - 20:56 CatherineJohnson




Now that I've been involved in "remediating" at least two people (not counting a couple of the kids in Singapore Math &, I guess, not counting me, either) I've realized that: I am interested in the question of remediation.

It's entirely possible that we have some real research avilable to us in the area of remediation, as opposed to your standard edu-research, which is not research but log-rolling.

If so, this would jibe with my feeling that when it comes to teachers & principals, you want the teacher or principal who's taught special ed.

Christopher's ELA teacher, the one who gave them the SWB and so assignment, has taught special ed.

So has the new principal; special ed is his background, I believe.

And then there's Siegfried Engelmann.

Teachers and administrators who've worked in special ed have spent a great deal of time endeavoring to teach the kids who need teachers, a large point in their favor. They haven't been able to coast on the gifted kids who "breathe it in"; nor have they been able to "teach to the middle."

They've been teaching to the bottom, by definition. I don't mean this statement to hurt feelings; I know special ed kids can be brainy — I've got some brainy special ed types around here. But when a special ed teacher is teaching a high-end special ed kid with strong native intelligence, she's still teaching a kid who has many gaps in his knowledge and probably a roaring case of edu-shame and demoralization along with. Special ed teachers are working with the most challenging population, regardless of how naturally intelligent any given special ed kid may be.

Beyond this, special ed teachers have spent a great deal of time — countless hours of time, in fact, and I am in a position to know — sitting in face to face, legally mandated meetings with parents hashing out what will be taught in the upcoming year. These teachers experience strong external legal, moral, and emotional demands to get content inside their students' heads.

Obviously any good teacher feels internally pressured to get content inside students' heads. Depending upon the school, she may be feeling heat from NCLB & state standards, too.

But special ed teachers live with intense outside pressure from law and from parents.

They've been shaped by different forces.


And then there's the fact that people who choose to go into special ed are the salt of the earth.

I was drafted. They volunteered.


So I've come to feel optimistic the minute I hear that a teacher Christopher is going to have has a background in special ed. My reaction may be common; my neighbor said "Good" the minute she heard that the new middle school principal had a background in special ed.

Anyway, I realized this afternoon that this principle may also apply to education research. It's possible that research into remediation is more serious and less ideology-ridden than research into "literacy" and "mathematical reasoning" and the like.

So I'm going to start paying closer attention to the field.



no one to waste

I've been prospecting for remediation factoids for awhile now.

Here are a couple:

The study found that students who are successfully remediated become productively employed. Almost 16% become professionals; 53.7% obtain mid-level, white-collar or technical positions; 19.8% become high-skill, blue-collar workers; and only 9.2% remain in unskilled or in low-skill jobs.

source:
No One To Waste: A Report to Public Decision-Makers and Community College Leaders

Students who require remediation in reading are at a greater disadvantage than those with a math deficiency (McCabe, 2000).

source:
Remediation PostSec


...about half of the students entering college aren't prepared for credit-bearing college-level work and have to take remedial courses, according to the Department of Education (2001). Overall, more than one million entering college students take remedial courses, says R. H. McCabe in "No One To Waste" (2000). McCabe cites studies that show 20 percent of entering students are underprepared in reading, 25 percent in writing, and 34 percent in math. Students who take remedial courses are much less likely to graduate.

source:
ACTIVITY



It's always interesting seeing the same study characterized as optimistic ("students who are successfully remediated become productively employed") and pessimistic ("Students who take remedial courses are much less likely to graduate") both.

McCabe's study doesn't seem to be available online, but I've found an interview with him.

Remedial students range from those with a minor deficiency in only one area to people who are deeply deficient in all three. There are roughly one million students a year who begin in college and are assigned to remedial courses.

PC: Is that number for all institutions or just community colleges?

RM: In all of them. It’s 29 percent of all of the entering college students. In community colleges it’s about 40 percent, and I do not know of an urban community college where it is not at least half.

[snip]

...the average student takes a little over seven semester credits for remediation, approximately one-fourth of a college year.

PC: What is known about whether, or how well, remediation works? Your report talks about the perception, especially among some state legislators, that we simply are paying for failure one more time?

RM: There is that perception, but more often than not it’s based on faulty premises. First, some of these legislators see continuity between high school and college that doesn’t exist. They think that if students graduate from high school, they should be ready for standard college work. But the criteria for high school graduation do not match the competency requirements to begin standard college courses....

Second, our definitions of success may be too narrow. A variety of studies, including my own, show that between 40 and 50 percent of students who begin in community colleges are successfully remediated. But, the fact is that a high percentage is not going on to bachelor’s degrees, even though remedial programs are really geared for that purpose. Twice as many earn occupational associate degrees or certificates.

If you look at remedial students nine years later, 90 percent are employed in work above an entry-level type of job. Less than two percent are out of work. Remediation in the community colleges is much more occupational and vocational than we have thought, and measures of its success should recognize this.

For the seriously deficient, the program is basically a total failure. Only 20 percent of those students complete remediation, and very few go on to anything after that. Programs for the seriously deficient need to be redesigned altogether.

PC: How do you define “seriously deficient”? Out of the million students mentioned earlier, how many are there?

RM: Seriously deficient students are those who are deficient in reading, writing and math, and are required to take at least one course prior to the standard remedial courses. For example, they simply could not take one remedial math course and be ready—they would have to take a math course prior to that math course. As for numbers, I lack data for all institutions, but in the community colleges I looked at, about one-fourth were seriously deficient.

[snip]

Actually, remediation is the most productive education program we have. With just one percent of the budget, it salvages the lives of a half-million people, and enables them to become positive, con-tributing individuals in our society. It is a particularly good investment because of the country’s changing demography and economy. The part of our population that is growing the most is also the part that is least prepared for college and skilled jobs. We believe in opportunity and access, and we can’t have either without remedial education.

...you assert that remediation is essential for quality, not a detriment to it. Is this true?

RM: It is absolutely true. In regular courses, faculty must expect that students are prepared, and only remedial testing and placement can assure that this expectation is met. If it is not met, then quality will suffer because faculty will be forced to lower their expectations to meet the competencies of the unprepared, or too many will fail.

[ed.: this reminds me of my hypothesis that when you refuse to accelerate gifted children you also refuse to accelerate regular children]

...it is essential to America, morally, socially and economically, that a high percentage of young Americans have education or training beyond high school—as high as 80 percent, in my opinion.

[ed.: I think it's Robert Murnane (not sure) who has shown that the only reason it's essential for 80% of young Americans to have training beyond high school is that high school isn't high school any more. It's junior high. Will attempt to track down the source at some point.... yes, it's Murnane*

[snip]

...teaching less-prepared students is hard and often frustrating work, for they need more personal attention and support. A belief that their job is helping human beings to develop, and that academic work is, in fact, an instrument to that end, is not typical of college faculty.

[snip]

One of the most disappointing things to me is that typically community colleges, where most academically deficient students enroll, do not seem to use the resources that they are given for remedial programs. In fact, they often use mostly part-time instructors without additional and necessary support. They give remediation low priority and run cheap programs.

[snip]

PC: If all of the K–12 improvement programs that the country has been working so hard on are successful, can’t we look to the day when remediation will not be around in higher education?

...I simply do not see reform wiping out the need for remediation in the fore-seeable future. We have to dig in for the long run.

[ed: amen]

[snip]

Testing should recognize a continuum; secondary school testing should be closely related to tests used to place people in college. With regard to under-prepared students, experience together with educational research has produced substantial knowledge of effective learning practices. Typically community colleges do not use that knowledge. They must.

[snip]

Most programs simply identify someone who is deficient in math or reading or writing, and then assign students to subject classes based on test results. That is a great waste of resources and student time; nothing is done to identify the differences in deficiencies within and across subject fields, or to relate deficiencies to the learning program.

We have the capacity to produce diag-nostic assessments and to align each student’s program to the results.

[snip]

A final word, if I may. I was surprised by our data on just how educationally far behind ethnic minorities are. [ed.: No kidding.] There is a monumental problem here that, in my opinion, needs to be addressed with mega effort and resources, not just by schools, but also by states and by communities.




what skills does one need to hold a middle-class job?

RICHARD MURNANE, Co-Author, "Teaching the New Basic Skills:" To qualify for a job that will pay a middle class wage as minimum the graduate needs to be able to read well enough to understand training manuals, basically ninth grade, able to do the mathematics that’s typically included in training manuals, fractions and decimals and line graphs, mastery of that, the ability to problem solve, to take a problem and find what will work, to shape it, to design a solution towards it, and two kinds of what we call soft skills, the ability to communicate effectively both orally and in writing, the ability to work productively with people from different backgrounds, and enough familiarity with computers to have the self-confidence and the knowledge to learn to use new software. You might say these skills are extremely modest, and they are in one sense, and there are lots of jobs that require, that pay good wages that require a lot more than these skills, but there are almost none, outside of professional sports, that do not require at least these new basic skills and also, remember, in terms of whether this is a challenge for schools to provide this, roughly half of American high school seniors are graduating without these new basic skills.

DAVID GERGEN: And if they graduate without them and never get them, they’re condemned to live in very low wages? RICHARD MURNANE: They can find work in most cases but these are jobs that pay six and seven dollars an hour, not enough to support children.

DAVID GERGEN: And if they can get the skills?

RICHARD MURNANE: If they can get the skills, they have a chance at acquiring middle-class jobs and have access to subsequent training when they need it. And these aren’t jobs that will be jobs for--that one holds for twenty-five or thirty years. To a large extent, those jobs have disappeared from the economy, but it will be the opportunity to move from job to job and to earn enough to support kids.


If you don't get these skills in high school, and black and Hispanic students routinely do not, you've got to get them somewhere else.

That somewhere else is going to be our community colleges.

Our community colleges & John Saxon.




* Murnane and coauthor Levey do not appear to hold the view that public school decline has made it necessary for high school graduates to pick up what once were K-12 skills in college:

FRANK LEVY: That’s right. And that’s what makes the problem so hard to diagnose. Schools today are a little better than they were 15 years ago, but the job market skills have just escalated much faster than that. I mean, we have an example in the book, "Looking At a Modern Automobile Plant," and about half of today’s high school graduates couldn’t make the cut-off to be a production worker at a modern automobile plant.

DAVID GERGEN: Say it one more time. Half of the 17-year-olds--

FRANK LEVY: Half of 17-year-olds don’t have the skills necessary to make the cut-off of the production worker at a modern automobile plant today.


-- CatherineJohnson - 23 Oct 2006



OnNotTeachingToMastery 01 Nov 2006 - 16:43 CatherineJohnson




excerpt from: Standards and Mastery Learning
by J. Ronald Gentile, James P. Lalley


Memory by Fast and Slow Learners

One field of basic research that is relevant to mastery learning, perhaps even more than studies comparing mastery-based instruction with traditional forms of instruction, is that of memory by fast versus slow learners. The general problem was introduced in Chapter 1 in terms of learning/forgetting curves, as well as what happens to the relationship between IQ and memory when a mastery standard is required. Consider the question directly (e.g., Gentile, Voelkl, Mt. Pleasant, & Monaco, 1995):

If slow learners can be equated with fast learners in amount initially learned, then what will happen on an unannounced test of memory for that material a day or week later?

a. Fast learners will recall significantly more than slow learners.

b. Fast learners will recall significantly less than slow learners.

c. Fast learners will recall about the same as slow learners. (p 185)

The question has a long history because it is central fo understanding individual differences in learning and memory….

...c is correct....When fast and slow learners are equated on amount of learning, recall is about the same.

[snip]

…the fastest and slowest thirds of the distribution tended to be quite different indeed: The fast learners ranged from 3 to 7 trials (median = 5), whereas the slow learners ranged from 12 to 33 trials (median = 15). Nevertheless, in surprise retention tests days or weeks later, the fast and slow learners were not significantly in average number of words of the poem they recalled.

Gentile et al. (1995) also extended this research to ask what happens to fast and slow learners in relearning to the same 75% to 90% standard. They found, first, that there was tremendous savings in relearning. Fast learners, who on average requird 5.3 trials at original learning, relearned to criterion in an average of only 1.4 trials. The corresponding data for slow learners was 17.4 trials at original learning and, remarkably, only 2.1 at relearning. The 1:3 ratio (fast:slow) advantage at original learning was reduced to 1:1.5 at relearning. All students, the fastest and slowest, were ready to relearn quickly as a result of having initially learned to a high mastery standard. Such data refute the oft-heard argument that there is no time to make sure each student learns to a high level; the savings in relearning time suggests that in the long run, teachers will save time by bringing all students to a high standard at original learning. [emphasis in the original]

The data with regard to memory, however, were a bit more complicated. It happened hat despite the 75% to 90% criterion, fast and slow learners were not exactly equated…Nevertheless, as the learning/memory curves described in Chapter 1 predict, there was much less forgetting after relearning than after original learning.

…What seems clear, however, is that requiring mastery to a high standard at original learning accrues the following benefits: (a) Fast and slow learners will recall about the same amount and are therefore both ready to have their prior knowledge activated in the current lesson (whether it be a review lesson or new applications of the material), and (b) relearning will be faster for all, saving time in the long run.



Table of Contents

Preface (pdf file)

1. Understanding Mastery Learning (pdf file)

2. Examining the Standards: Math, Science, Social Studies, and Language Arts

3. Planning Standards-Based Lessons Using Mastery Learning

4. Implementing Standards and Mastery Learning in the Classroom

5. Professional Development and Mastery Learning

Appendix: What Does the Literature Tell Us?





outputs, not inputs

from the Preface: (pdf file)

The history of standards also reflects federal government versus states’ rights skirmishes, competition among professional organizations (for what will be required and what will be optional for graduation), religious versus secular issues, as well as numerous other political issues beyond the scope of this book.

What does seem relevant, however, is an apparent shift in the goals of standards from inputs to outputs, in Marzano and Kendall’s (1996) shorthand. Whereas previous standards emphasized what had to go into a course (specifics of the curriculum, how material was to be taught, how many credits or Carnegie units it was worth), current standards emphasize what comes out (what students know or can do and how to assure accountability). As Marzano and Kendall (1996) summarized, “The new, more efficient and accountable view of education is output-based; success is defined in terms of students learning specific standards” (p. 17).

Whether the “outputs” view is better or worse, we cannot be sure, though it certainly created a firestorm of rhetoric over the high-stakes testing, perhaps a too-narrow view of accountability that has become linked to the standards movement beginning in the 1980s. Interestingly, the input/output categories have rough parallels with fundamental variables in John Carroll’s (1963) model of school learning, which provides some of the theoretical underpinnings of mastery learning. Those variables are opportunity and perseverance. Opportunity, in rough parallel to input, is the time allowed or scheduled by the teacher to cover the material and induce students to learn. Perseverance, in rough analogy to output, is the time the students spend or are willing to spend to learn. Although both of these are important to and predictive of achievement, perseverance becomes the bottom line: Teachers have been successful to the extent that they induce students to do what they need to do to learn.

We bring this up here to point out that the mastery philosophy on which this book is based is potentially compatible with current views of standards, but it has developed methods for measuring and motivating students to persevere until they achieve those standards.

Sadly, many advocates of standards, not to mention those who are charged with implementing them, know little or nothing about implementing mastery learning: its philosophy, its evolution, what makes it work or undermines it, its varieties. [ed.: don't know of don't care to know?] Thus, although the movement toward higher academic standards carries with it assumptions about learning, development, and measurement that have traditionally been central to the theory and philosophy of mastery learning, the standards movement has neither embraced mastery learning nor shown evidence of having learned from its successful or unsuccessful practices.





learning & forgetting

from the first chapter: (pdf file)

Learning, in other words, occurs in phases or episodes, and this original learning phase includes (a) the readiness component (described above), (b) learning to initial mastery, and (c) forgetting. Although forgetting has not been mentioned up to now, it is clear that forgetting is the inevitable result of initial learning, even when a high mastery standard of, say, 80% to 100% correct is required. [ed.: which is why it makes so much sense to spend one day teaching dimensional analysis going into the state test, assign no homework problems, and never mention the topic again] When the degree of original learning is less than mastery, say, 60% to 80%, then forgetting is likely to occur more rapidly or be more complete. If it is less than 60%, it is questionable to speak of forgetting at all, because learning was inadequate in the first place.1

Students show that they understand this principle implicitly when they ask, “Why do we have to learn this stuff anyway? We’ll only forget it.” Our typical answers, “Because it will be on the test” or “Because I said so,” are not satisfactory. In fact, we have been able to find only one satisfactory answer to the question, and it was supplied in one of the first empirical studies of learning/forgetting (Ebbinghaus, 1885/1964). The answer is that relearning is faster—that is, there is a considerable savings of time in relearning compared with original learning. Furthermore, there is a positive relationship between amount of time saved in relearning and the degree of original learning, with essentially no savings when original learning is below some acceptable threshold (which we earlier argued was 60% or less).

...[C]onsider the experience we teachers have. The first year of teaching a unit, we have a lot to learn (even though many prerequisites have already been mastered in college and student teaching). The next year, when we reach that unit again, we find we’ve forgotten quite a bit. Fortunately, relearning is faster, and we find ourselves reorganizing the material, coming up with new examples, and so forth. The next year, forgetting has been less yet, and thus there is greater savings in relearning. By the 10th year, the material is almost totally recalled, with examples virtually falling off the tongue. The material seems so easy by this time that many teachers can now be heard complaining, “The students are getting dumber and dumber every year.” Sadly, this is one of the negative effects of becoming expert in something: We lose empathy for the novice. (Note the parallel to what happens once a nonconserver on Piaget’s tasks becomes a conserver: e.g., the 8-year-old who understands that the amount of water does not change when poured into a taller, thinner glass cannot recall that she expected more in the taller, thinner glass when she was 5). This is also what distinguishes a mere expert from a teacher: An expert can do it; a teacher can do it but also remembers what it takes to progress from novice to expert.

Beautifully put. I would add that this is what distinguishes an expert nonfiction writer from a nonexpert.

For the negative example of how these learning/memory concepts form the basis for mastery learning, consider some students whose original learning is 50% or less. Their forgetting in Phase 1 will be at least as rapid as it will for those who mastered the material and, because they learned so little, more complete. Furthermore, there will be little or no savings in relearning during Phase 2. Then, if this material is treated as a review (“This was covered last year”), less time will be spent on relearning (and after all, students who mastered originally will need less time). Thus the relearning episode for those who need it most will also be substandard, leading to relatively little residue in memory and therefore little or no savings for Phase 3 relearning. By Phase 3, the motivation to learn this material will also be eroding (“I was never very good at this”), an issue we shall explore in more detail in “Learned Helplessness.”


The bottom 3rd learners are probably routinely being put into states of learned helplessness; I would expect to see learned helplessness in a number of the middle 3rd, too. In the case of accelerated math here in Irvington, I believe that we have some children in the top 3rd who have been pushed into states of learned helplessness for doing and learning math.

That is what their parents report.

The tearful mother who asked, at the Parent Revolt meeing in winter 2005, "What are you going to do to repair my child's self esteem?" deserved an answer.

What she got instead was: "I don't understand why your children are so thin-skinned."

That was it.



schools creating "comas"

A summary of the long-term effects of the difference between mastery and nonmastery at original learning is provided in Figure 1.2. After four or five episodes, when learners in Part A say to those in Part B, “I forgot more than you ever learned,” the sad fact will be that they are telling the truth. A close look at the curve in Part B shows that after four or five episodes, those persons—they can hardly be called learners—have learning/forgetting curves that resemble the brain waves of comatose patients.





learned helplessness, mastery learning, and math

Let’s return for a moment to the students in Figure 1.2B. If their first experience in learning fractions, say, is unsuccessful, they will forget all or most of it. Next year, they may even claim that they “never had this stuff before,” and they will probably believe it. On the second time through, if they are still unsuccessful (which is likely, because teachers usually spend less time reviewing previous material than was spent on initial learning), they will demonstrate little savings and forget again. By the third and fourth exposures to the material, they at least remember they had it before, but may stop trying and explain their lack of motivation with statements such as “I was never very good at math” or “Why do we have to learn this stuff anyway? I’m never going to use it.” Learned helplessness has set in.

[ed.: I want to stress that "learned helplessness" is a well-established concept in psychology — and that it was first demonstrated in animals. These experiments, which I studied in college, are wrenching to read. The most upsetting, which couldn't be done today, involved rats who were, iirc, yoked together and shocked. One of the rats could turn off the shock, or escape it somehow. The other rat was helpless. He received the same level of shocks as the "actor" rat, but he couldn't turn them off.

After going through this experience, the rats were put in a tub of water with a platform somewhere in the middle. (again, working from memory - details may be wrong) The "actor rates" - the ones who'd been able to turn off the shocks, swam to the platform and scrambled out of the water. The helpless rats didn't even try to save themselves. They sank into the water and drowned.

I believe that today, in our schools, spiraling curricula are putting children into states of learned helplessness.

Until someone proves me wrong, I stand by that perception.]

Under laboratory conditions, learned helplessness is developed by first exposing animals or humans to a series of experiences in which failure is inevitable and beyond their control (e.g., Peterson, Maier, & Seligman, 1993; Seligman, 1975). Later, when success is now possible and personally controllable, the victim does not even try. On the emotional level, there is a heightened state of fear, which if prolonged, can easily turn into apathy or depression. On the behavioral/motivational level, there is no perseverance or willingness even for trial-and-error searches (because “Nothing I do ever satisfies these people”). On the cognitive level, there is no discovery of what works, no understanding or organization of an information base, and a long list of defensive excuses or causal attributions, such as “I was never very good at this” and “I could do it if I want to, but school sucks” (the former a primarily female attribution, the latter male; e.g., Dweck & Licht, 1980). It is also more self-protective to adopt a strategy of not trying—or pretending not to try—than to try and not succeed.

Math seems to be a field particularly vulnerable to learned helplessness, because new topics and courses seem to be quite different from previous ones (from multiplication of whole numbers to fractions, arithmetic to algebra to trigonometry, etc.). Even having great success at earlier levels does not immunize against having difficulty on a new topic. Thus even being a “good” student or having 100% success does not guarantee against learned helplessness later, particularly if what students have been good at is memorizing without understanding.

But those primarily at risk for learned helplessness are those who come to school and have not mastered fundamentals (as mentioned earlier). If we teachers cannot diagnose their problems correctly— and early—they are almost destined to fail to master the new tasks. Sadly, to continue the math example, many teachers are not skilled enough themselves to diagnose a child’s problems with addition and subtraction as being a deficit in rational counting or one-to-one correspondence. Thus these students comprise the population in Figure 1.2B.

Is there a cure? As in health, prevention is easier than cure.


Didn't Steve H say this?

I believe that the phenomenon of learned helplessness explains why it was important for Christopher and Christian both to teach themselves using a Saxon book. Christian is emerging from his state of learned helplessness vis a vis math so fast it's startling. Same thing for Christopher, except with Christopher we're talking about prevention. Even after all the mishegoss of last year, his slow but steady march through Saxon Algebra 1/2 almost certainly prevents him from developing a state of learned helplessness in the first place. His previous work with Saxon Math 6/5 probably innoculated him against developing learned helplessness last year.

I think I've told that story.

Christopher does not know that Ms. Kahl selected "Finds subject matter difficult" from the Comments Bank. When I mentioned it one day, thinking he'd read his report card, he said indignantly, "She did not put that on my report card!"

He doesn't have learned helplessness.




how to cure math anxiety, part 2

With his learned-helpless dogs, Seligman (1975) literally had to drag them across the barrier to escape electric shock, anywhere from 25 to 200 times, before they once again tried to explore and control their environment. With humans, whose patterns of thought (“I was never very good at this”) may reinforce the helpless-behavior patterns, dragging is more figurative than literal. In any case, the cure for helplessness is competence, and only when students are succeeding do feelings of self-efficacy, self-control, and self-esteem begin to follow (see also Bandura, 1977, 1986).


Saxon Math is the answer.



memory & IQ

Table 1.2 shows the remarkable results regarding intellectual traits and memory.5 Under nonmastery conditions—that is, a single exposure for original learning, recall after 7 days, a single relearning opportunity, and then recall after 14 and 28 days—the correlations between intellectual traits and recall are all positive and significant. That is, higher-ability students tend to remember more, as society has come to expect.

In stark contrast, imposing a mastery standard of 75% to 90% correct on original learning and then again at relearning renders those standardized intellectual measures nonpredictors of how much is recalled: The correlations hover around zero and are all nonsignificant.

What mastery to a high standard can do, in summary, is virtually bypass the effects of IQ for specified educational objectives. What is recalled about educational lessons is more dependent on how well the material is mastered than on such traits as rate of learning or general intellectual abilities.




(wrong) conventional wisdom about mastery

Critics usually cite three points in opposition to mastery learning:

1. It helps slower students at the expense of the faster students.

2. It is too oriented toward basic knowledge and skills at the expense of creativity and higher levels of thinking.

3. It requires too much work of the teachers.


[snip]


That fast learners are bored to tears waiting for slow ones to catch up is far too true of many educational programs, including badly implemented mastery programs. It is not true at all of Keller’s (1968) individualized mastery plan, in which students complete course units at their own pace. For group-based mastery schemes, such as Bloom’s (1971), it would be true only if mastery were misconceived solely as passing minimum competency tests, with no incentive for students to use their new competencies for higher-level intellectual purposes.

[snip]

  • A grading system that earns a minimum passing grade—that is, a C or 70 for passing the initial mastery test with at least 75% to 80% correct. Under the concept of mastery as a beginning rather than as an end state of learning, even a test score of 100% is just the initial phase of learning-forgetting curves. Thus it should earn an entry-level grade. Not passing the mastery test should have a grade of zero or “incomplete” attached to it so that, like driver’s tests, initial mastery is conceived as an all-or-nothing affair: Either you get your license, or you do not.

  • A set of enrichment activities that use but go beyond the basic knowledge, skills, and principles required for mastery. This includes reports on how these principles are applied in real life, creative projects and experiments, further readings or advanced problems to be solved, cooperative investigations or debates, and—most important—tutoring others (we really learn something well when we teach it). Such activities, because they provide overlearning, distributed practice, organization and construction of knowledge, and the like, earn bonus points when adequately completed: Add 5 to 10 points for each project to the minimum pass of 70, or move from C to B for one advanced project and A for two or three such projects.


This is where I get off the boat.

This passage equates "mastery" (75% to 80% correct on a test) with "expertise." A child who has scored 80% correct on an initial test of mastery has not reached the level at which he is ready to start constructing knowledge, applying principles to real life, or solving "advanced problems."

What is happening here — and, again, until someone proves me wrong I'm going to stand by my opinion — is that constructivist teaching practices are being used to mask the fact that the fast kids are being slowed down to the slow kids' pace.

It's significant that these authors do not once reference Siegfried Engelmann's work.

There's a reason for that.

I think the reason is the Siegfried Engelmann directly confronts the question of maximum efficiency of learning for everyone, not just for the slowest third.



against enrichment

I'm fast reaching the point where I don't want to hear "challenging" and I don't want to hear "enrichment":

A commonly held belief regarding mastery is that for it to be successful, there must be a highly effective, if not innovative, remediation component. Although we do not underestiet the importance of remediation, it is our assertion that the strength of any mastery program is contingent on its enrichment component. The reasoning behind this assertion is at least twofold. The first issue is that a common criticism of mastery is that it focuses on those students who initially fail to master the objectives at the expense of moe capable students who often easily master those same objectives. One can certainly find examples of this. However, we suggest that poor planning, rather than mastery learning, is at fault. Teachers need to develop engaging enrichment assignments that are pertinent to their objectives and not seen as busy work by students…Contrarily, students in need of remediation will often need to simply revisit and revise previous assignments and not be in need of additional materials. However, what they likely will need is additional instruction from the teacher or classroom aide. These resources will only be available to these students if other students are engaged in appropriate enrichment activities....


...which, presumably, "other students" will be engaged in entirely on their own!

Because they've reached mastery!

So they can zip right through Bloom's Taxonomy without further ado!

Thus a comprehensive enrichment program is not only a critical component of a mastery learning system but also an effective classroom management tool. Furthermore, enrichment activities need not be narrowly defined as something that occurs following mastery. When scheduling permits, it is appropriate to allow students who have yet to master the critical objectives to engage in enrichment activities. This seems appropriate for at least two reasons: (a) The enrichment activities may assist the student in achieving the critical objectives, and (b) the enrichment activities may provide motivation for that student’s learning.


enrichment = classroom management



in conclusion....

....first of all, the thing to remember here is that no one is currently doing this in U.S. public schools.

No one is "teaching to mastery."

That's the rhetorical purpose of the book, to persuade educators to start teaching to mastery.

Why aren't schools teaching to mastery now?

Because everyone and his brother knows that if you teach to mastery in a mixed-ability class — and mixed-ability classes are taken as a given — you're going to be moving very, very slowly:

"The fast learners ranged from 3 to 7 trials (median = 5), whereas the slow learners ranged from 12 to 33 trials (median = 15)...[for a ratio of] 1:3 (fast:slow).

The fastest third of the class masters material 3 times as quickly as the slowest third. (We're not even talking gifted here. Just top third, middle third, bottom third — which is the way a real class "falls out" in the real world,* leaving aside a tiny number of genuinely gifted children.)

So say you're studying two-digit multiplication, and the fastest third has got it after a median of 5 trials, which we can probably define as lessons-with-practice.

The slowest third still has another 10 trials (lessons-with-practice) to go while the fastest third does — what?

Investigates two-digit addition?

Solves real-world problems using addition?

Teaches two-digit addition to the slowest third?

Gentile & Lalley's answer to all of these questions is yes. The fastest third has got two-digit addition after a median of 5 trials, so now they spend the next 10 trials investigating, solving real-world problems, and tutoring their slower peers.

This is what Gentile & Lalley are proposing.

That is a huge drag on the wheel for the fast kids, one not likely to go unnoticed by parents who are going to come in loaded for bear.

Why do real-world teachers and schools not "teach to mastery," as teaching to mastery is defined by Gentile & Lalley?

Real-world teachers and schools do not "teach to mastery" for exactly the reason they give: teaching to mastery in a mixed-ability classroom, and the mixed-ability classroom is a given, would slow the entire class down to the pace of the slowest third of students.

Almost certainly real-world teachers and schools are splitting the difference by teaching to the middle.

Gentile & Lalley don't tell us how much faster the middle group learns than the slowest group, so let's split the difference ourselves. Let's assume they're literally in the middle; let's assume that the same material it takes the fastest learners a median of 5 trials to learn takes the middle learners a median of 10 trials and the slowest learners a median of 15.

If you have the fast-thirds, who've hit mastery after 5 trials, sit around enriching themselves while you teach another 5 trials to the middle, and then you move on, you might reach something like mastery with 2/3 of the kids, without inciting the fast-thirds (or their parents) to riot.

Meanwhile the spiraling philosophy apparently allows everyone to tell himself that the slow-thirds will see the material again next year so it's OK they didn't master it this time; the constructivist philosophy tells educators nobody should be committing anything to memory anyway; and Bloom's taxonomy tells us (or can be interpreted to tell us) that the important thing is for everyone to comprehend-apply-analyze-synthesize-evaluate....and the entire judicial system of the United States of America has spent the past god-only-knows how many years ruling that the school isn't responsible for getting content inside kids' heads, because "it could be something about the child" — and there you have it.

Nobody is "teaching to mastery," nobody apart from teachers who close their doors and try to do it anyway, in spite of the towering odds stacked against them.

Worse still, if people did start teaching to mastery, this is what it would look like.

"Teaching to mastery" would mean the fastest third learn at exactly the same pace as the slowest third, then spend 2/3 of their class & homework time being enriched.

Not "being" enriched; enriching themselves. The teacher and her aide, if she has an aide (questionable) is going to be busy with the slower-thirds while enrichment is taking place.

The fast-thirds are going to be spending 2/3 of their class & homework time enriching themselves, and the middle-thirds will spend 1/3 of class & homework time doing the same.

No wonder parents (and teachers) want smaller class size.



So this is where we get differentiated instruction, now the essence of an Irvington public school education and part of our strategic plan.

Our teachers are all to teach 3 different groups of kids in each and every class & in each and every subject.

That is their job.

We're not going to have formative assessment or teaching to mastery (except, again, from teachers who buck the odds, or try to).

We're just going to have differentiated instruction. Three different levels of classroom instruction delivered to three different groups of kids.

Plus a whopping big load of enrichment for the fast-thirds and the 1 or 2 truly-gifteds.

Parents have no say — none — in these decisions, which profoundly affect our children's lives.

The district is the decider.




0761946144.01._AA240_SCLZZZZZZZ_.jpg



Standards and Mastery Learning: ERIC abstract

* Mrs. Panitz told Ed and me about this back when Christopher was in 4th grade. She said every classroom falls naturally into 3 groups; teachers expect this. She said that the Phase 3 classes all had 3 such groups; so did the Phase 4 classes. That was one of the main reasons why, as she thought about it a bit, she realized Christopher should move to Phase 4. He was at the top of the top 3rd of his Phase 3 class, which meant that at a bare minimum he ought to be able to hold his own in the bottom third of the Phase 4 class. We figured he could probably be in the middle of the pack with the extra work we gave him at home, and in fact he probably did quite a bit better than that when he moved to Mrs. Woeckener's class. I think he may have been in the top third of her Phase 4 class in 5th grade. I would guess he was towards the "bottom of the top," but I think he was in the top third.

on not teaching to mastery - Gentile & Lalley
Engelmann on diversity and teaching to mastery
IQ is a range, not a point

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-- CatherineJohnson - 25 Oct 2006



EngelmannOnMasteryAndAbilityGrouping 21 Nov 2006 - 17:55 CatherineJohnson




A number of us have been kicking around the question of ability grouping and teaching to mastery in the Comments thread for the on not teaching to mastery post.

Sometime last night it struck me that I'm not understanding the issue, by which I mean I haven't managed to pull all the fragmented data points floating through my mind into a coherent account of how teaching to mastery affects ability grouping.

Gentile and Lalley propose a model in which the "slow-thirds" are taught to mastery, while the faster-two thirds are occupied with enrichment tasks.

You probably won't find many parents of the faster-two thirds willing to take that deal, which I imagine is part of the reason why schools "teach to the middle."

But I think this way of looking at things isn't quite right — even according to Gentile & Lalley's own evidence. Here's Engelemann:

2. The [grouping] steps are levelers of individual differences. Not all students who stand on the fifth stair [in the curriculum] are the same age, learn at precisely the same rate, have equal intelligence, or exhibit the same “style” of learning. However, every student who is firmly on the fifth step is the same with respect to the program sequence. Each has the skill repertoire and knowledge needed to take the next step and reach that step within 30–45 minutes of instruction. Because students could not reach the fifth step without specific skill and knowledge, the stairway structure of a well-designed program serves as a leveler. All students with a particular skill profile are placed on the same stair. Certainly, the program design does not guarantee that all students will progress at exactly the same rate; however, greatest individual differences occur on the very beginning levels. On higher levels, after students have mastered a battery of skills and knowledge, the difference in rate of ascent for appropriately placed students is far less because all students tend to have enough skill to master the new material at around the same rate.

source:
Student-Program Alignment and Teaching to Mastery (pdf file)
by Siegfried Engelmann



"after students have mastered a battery of skills and knowledge, the difference in rate of ascent for appropriately placed students is far less because all students tend to have enough skill to master the new material at around the same rate"


This is a radical concept — radical meaning paradigm-shifting.

What he's saying is this:

Once students have learned a certain amount of material within any given subject matter, the difference in learning speed amongst the fast-thirds, the middle-thirds, and the slow-thirds is much lower than it was back when they were trying to learn brand new material.



I believe this.

First of all, we saw this ourselves with Christopher last spring.

All of a sudden, in math, he was faster. Ed would reteach a concept at home, and he'd get it.

We didn't know quite what to make of it at the time, but clearly he'd hit Engelmann's tipping point. At the end of the course he'd managed to master enough material to be able to pick up new material faster. (I hit this point myself awhile back, using Saxon Math....)

Second, we know that the big difference between "fast learners" and "slow learners" is in learning, and then remembering what you've learned not too long afterwards. A fast learner "picks things up fast," and then holds onto them better.

We know this because Gentile and Lalley cite research showing this, but we also know this from life.

When I was growing up, my dad had a farm hand who was a slow learner. It's possible his IQ would have put him at the high end of what is considered mental retardation.

His "problem," from my folks' perspective, was simply that he was a slow learner.

His problem was not that he forgot to do things he knew how to do.

That would have been unthinkable — and if you search your own experience you'll find the same thing. It's not normal for people at any level of IQ and ability to forget things they know how to do well.

In fact, forgetting-how-to-do-something-you-seemed-to-know-how-to-do-well is a huge issue in autism. There are heartbreaking stories of autistic kids suddenly losing huge amounts of knowledge or know-how they had previously "mastered" to a 90% criterion. I don't think anyone understands how this happens, or what it means. But the fact that teachers and parents are shocked and saddened when it occurs tells you how much we take solid-memory-of-mastered material and skills for granted. Our folk psychology tells us Gentile, Lalley, and Engelmann are correct: people are very different in their ability to learn new material quickly. People are not different in their ability to remember material and skills they've learned very well.

The language we use offers further evidence.

We speak of "fast learners" and "slow learners."

We don't speak of "high forgetters" and "low forgetters."

We don't speak of "high forgetters" and "low forgetters" because they don't exist (apart from "forgetful" people, who, when it comes to learning, can be fast, slow, or in between.)


Third, we all know that it's harder to learn brand new material in a brand new field than to learn brand new material in a field you know something about.

No need to belabor this point.




background knowledge as the leveller of learning differences

What Engelmann is doing is using a student's background knowledge to allow the creation of somewhat-mixed ability groups in which learning rates for new material are roughly the same.

I'm guessing that the reason one can do this is that at some point students have mastered a "map of the world" — at some point students have a very well practiced and mastered structural understanding of the particular field being taught. UPDATE 11-20-2006: I believe the term for this is "schema."

This is not easy to acquire, btw. I say this as a nonfiction writer who frequently has to attempt to acquire such a structure in order to write about a subject I haven't studied.

Once you have built a "map of the field" inside your memory, it's much easier and faster to slot in a new fact, analysis, or skill being taught in class.

This is my guess, at least.




diversity through teaching to mastery

All schools and probably most parents value diversity.

We're not comfortable with the notion of hiving kids off into top-thirds, middle-thirds, and bottom-thirds, and then keeping them there for the 13 years of K-12. At least, I'm not. UPDATE 6:31 pm: This statement is far too broad. I think it works if I say that "we" - we meaning American culture and Americans in the aggregate - have a core egalitarianism that may or may not affect our feelings about tracking & grouping....Also, in my own case, I've seen the down side of tracking, which is a school deciding that a child "is a 3" (direct quote) and then enforcing said child's 3ness.

Unfortunately, differentiated instruction is simply another way of hiving kids off into the standard 3rds while keeping them physically together inside the same classroom (and piling a whopping big workload on the teacher). No effort is made, under a differentiated instruction model, to accelerate the slower thirds. The thirds are assumed to be given to us by God or nature, take your pick; that's just the way things are.

Things could be different.

Every child should be taught to mastery from the get-go, and grouped according to where he or she is in a sequential curriculum.

When kids reach the tipping point at which their learning rate for a subject accelerates, we'll have classrooms filled with different children who possess different intial rates of learning all working together and moving forward at a steady clip.

Diversity through teaching to mastery.




in a nutshell

  • The primary difference between learners lies in different speeds of initial learning of novel material in novel fields or content areas.

  • Teachers and parents alike have long observed that learners fall into one of 3 groups: the "fast learners," the "slow learners," and everyone in between.

  • question: Are truly gifted children, defined as the top 2% or higher of learners, outside these 3 groups? (I don't know.)

  • The fastest third of learners, when learning novel material in a novel field, need 3 to 7 trials to master the material (median = 5). The slowest third need 12 to 33 trials (median = 15). In short, he fastest 3rd learn new material in a new field 3 x faster than the slowest third.

  • If novel material in novel field is learned to mastery, retention is roughly the same. People differ dramatically in speed of learning novel material in novel fields, not in degree of forgetting well-mastered material.

  • All learning requires relearning.* That's what "distributed practice" is about. Individual learners do not show large differences in speed of relearning material that has been learned to a 75% to 90% standard. Again: the large individual differences amongst learners are found in first-time learning of novel material in a novel field, period.

  • from Gentile and Lalley: "Fast learners, who on average requird 5.3 trials at original learning, relearned to criterion in an average of only 1.4 trials. The corresponding data for slow learners was 17.4 trials at original learning and, remarkably, only 2.1 at relearning. The 1:3 ratio (fast:slow) advantage at original learning was reduced to 1:1.5 at relearning. All students, the fastest and slowest, were ready to relearn quickly as a result of having initially learned to a high mastery standard."

  • "What mastery to a high standard can do, in summary, is virtually bypass the effects of IQ for specified educational objectives. What is recalled about educational lessons is more dependent on how well the material is mastered than on such traits as rate of learning or general intellectual abilities." (Gentile & Lalley)


Differentiated instruction is not the answer.

Given the amount of extra work for the teacher and the amount of time the faster kids will necessarily have to spend supervising their own enrichment activities, it may be the problem.

Differentiated instruction assumes that the speed of learning a student brings with him to school is a given.

That's not right.

We should see a student's speed of learning the same way we (ought to) see all aspects of human biology and psychology: as a point on a spectrum.

Just as our schools should endeavor to move a child to the top of his IQ range, schools should also endeavor to move individual students to the top of their range of learning speed.

We can do this by teaching all students to mastery from day one.




* Gifted children, who seem to "breathe content in," may be an exception to this rule. Unfortunately, I don't know enough about gifted children to hazard a guess. For everyone else, including the highly intelligent amongst us, learning involves relearning.

on not teaching to mastery - Gentile & Lalley
Engelmann on diversity and teaching to mastery
IQ is a range, not a point



-- CatherineJohnson - 27 Oct 2006



NationalMathAdvisoryPanelLinks 21 Nov 2006 - 18:07 CatherineJohnson




meetings




email updates

about the panel

homepage




where you can find links

I'm posting links to the Math Panel homepage, transcripts, & ktm posts here:



You can find both pages on the menu to the left.

If all else fails you can search posts using the keyword nationalmathematicsadvisorypanel with no spaces between words. (Works pretty well with spaces, too.)

I'm thinking this is about as findable and redundant as I can make the links now...unfortunately, you will have to remember some constellation of the words "national mathematics advisory panel" to find these links (that could be iffy for me these days....)

But I think I've just raised the odds of re-finding the transcript links considerably.


panel members w/links
Polite agreement or something we can use?
National Math Panel announcement
National Math Panel update
short story by Vern Williams

nationalmathematicsadvisorypanel


-- CatherineJohnson - 07 Nov 2006



PrecisionTeachingPart2 09 Dec 2006 - 15:13 CatherineJohnson




My neighbor the statistician just sent me this link to a site on precision teaching.

I thought it sounded familiar, then discovered I'd posted an abstract awhile back.....

I like the words "precision" and "teaching" so much I could almost go for this just because of what it's called, sight unseen.

Precision Teaching: A Brief History



Which reminds me, does anyone know what went wrong with "outcomes-based learning"? (I think that was the term.)

Naturally I keep thinking we ought to be looking at the outcomes of curriculum and pedagogy; then I find out there already was an outcomes-based movement of some kind (while you were sleeping) and it was a fiasco.

What was it?

Why was it a fiasco?




writing objectives

Some of us were talking about writing objectives on IEPs the other day. This page may be useful.



behavioral fluency as mastery, not percent correct

This is cool:

His research was showing "frequency to be 10 to 100 times more sensitive than percentage correct in recording the effects of drugs and different reinforcers" (Lindsley, 1990b, p. 10). He was painfully aware that when researchers applied their methods, even behavioral methods, to academic behaviors of school children, they typically recorded only percentage correct, "the time-honored educational measure."

[snip]

"Our first class-wide frequency recording was in a Montessori class for special education children...Elaine Fink showed we could effectively use rate of response with curricula as varied and as difficult to measure as Montessori materials. Clay and Ann Starlin showed an entire first grade class could correct and chart their own academic work on standard celeration charts...Ron Holzschuh with Dorothy Dobbs and Tom Caldwell showed that academic frequencies (rates) recorded 40 times more effects of curricular changes than did percent correct...These and many other studies proved behavior frequencies significantly more sensitive to learning variables in the classrooms than percent correct and percent of time on task." (Lindsley, 1990a, p. 7).



This, too:

Van Ostrom stressed that aims should be meetable and beatable. This suggests that our long-term goals and aims might require mini-aims for some learners as they strive for high fluencies.


That's Saxon Math.

Aims that are meetable and beatable.



-- CatherineJohnson - 06 Dec 2006



LindaMoranListserv 11 Dec 2006 - 19:25 CatherineJohnson




I think everyone here knows about Linda Moran's Teens and Tweens blog.

I've recently (re)discovered that she has a listserv attached to the blog.

I joined last week, and I think some of you might like to join as well. There have been some very interesting posts to the listserv that I don't believe have been posted to the blog itself — and that I don't expect to see posted to the blog itself.




-- CatherineJohnson - 09 Dec 2006

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