Entries from DirectInstruction

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.

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

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.

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:



(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.

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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

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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.

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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)

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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."

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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

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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

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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.

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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:






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





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

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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.

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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:

• boys hate journaling

• JD (& others) on Houghton Mifflin Math & long division

• Susan on grading handwriting (Christopher is going to be reading this one out loud)

• Steve on epiphany

• Suzuki

• teaching to mastery

• 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....

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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.










source:
reciprocals

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ExpressiveWriting 21 Dec 2005 - 18:06 CatherineJohnson








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

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.






compare and contrast





'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.

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IrvingtonPtsaForum 19 May 2006 - 16:07 CatherineJohnson







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

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IfTheStudentHasntLearned 23 Dec 2005 - 22:16 CatherineJohnson









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.

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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

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TeachersStuckOnMastery 16 Sep 2006 - 20:08 CatherineJohnson


from Becky C, a smoking gun:




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

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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.

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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