Matt

I know what you mean about the "big picture," which Temple calls "finding the basic principle."

I continue to read and think about this every day. Reading ktm Comments here at ktm is a big part of this effort.

For me, at the moment, the "big picture" is captured in Engelmann's statement, no doubt in Alfie Kohn's statements about blaming the child, and in the Princeton Charter School's definition of accountability.

As things stand, schools aren't accountable for individual student learninhg.

They're not even accountable, not really, for student learning in the aggregate, although NCLB alters the landscape somewhat in this arena.

In short, we face a confusing social reality in which schools aren't (ultimately) responsible for doing the job they are created and funded to do.

And yet our schools do want to teach children and do want children to learn.

I think you can make the case that everything else flows from the central contradiction that our schools aren't responsible for outcomes, BUT no one - including school personnel themselves, - quite grasps the implications of such a system:

• spiral curriculum: When you're not accoutable for results - for student learning - but at the same time your goal is to produce student learning - a spiral curriculum makes sense. A spiral curriculum is like an insurance policy. The kids who "didn't get it" this year will see it again next year, and the kids who don't get it the next year will see it again the year after that. A spiral curriculum allows the school to be careless about student learning, but to maintain hope that students will learn nevertheless because there's been so much repetition.

• constructivist blather - "All children can learn" "A school is a place where students think, create, problem-solve, etc." — all of these slogans set abstract goals that can't be measured or assessed. When you're responsible only for inputs, but you believe you should be producing outcomes, focusing on unmeasurable outcomes is a means of squaring the circle.

• blaming-the-child - this one's obvious

• blaming-the-parent - this one's obvious, too

• extreme achievement gaps not only between socioeconomic classes, but between the fast-thirds and slow-thirds within each school (more on this t/k)

visit to edu-attorney

parents performing formative assessment

-- CatherineJohnson - 21 Nov 2006

I guess for me it's not just the basic principle I am interested in, but also the 'lay of the land,' so to speak.

To use the example of Kohn and Engelmann again, on one level, it seems like they are polar opposites. Kohn says implies there is too much 'scripting' (using pejorative terms to describe), the means of measuring/assessment are self-perpetuating (schools are good because test scores are high, test scores are high because the schools are good; so focus on trying to improve the school by improving the test scores). Students need to be treated as the individuals they are. For his part, Engelmann seems to argue against many of the things that Kohn seems to advocate as well (I have not read Engelmann so recently, so I can't recall specifics).

However, despite the apparently significant gulf between them, they actually do seem to share a lot of common ground with respect to the responsibility of the schools to students. I was a little surprised by this.

So I'm interested in what the various 'names' in education (reform) think; what are the big differences, is there much common ground? How much of what they say is more of a polemic than substantive criticism? Beyond that, what does the research that is out there actually say and what are its limitations? One of the articles that Kohn wrote commented about the use of the phrase 'studies show...' (and I noticed that he uses it a lot also). He argues that studies don't always show what the advocates claim that they do. It would be interesting to see a summary of research from a critical and unbiased source, though that's probably a pie-in-the-sky idea.

One of the things that Kohn seems to have problems with is the assessment is done. He argues that studies show when students are graded, they tend to focus on getting a grade and become less interested in the material. He brings up interesting (to me) questions about the nature and purpose of assessment, and what it means to be 'well-educated'. He suggests (correctly, in my mind) that students should play a more active role in the curriculum that is taught and the assessments that are used to verify that learning has taken place. I think the further along a student gets, the more the student should be involved in these things. I'm going to work on incorporating this into some of my classes, I think. It seems especially likely to be helpful in the General Education math class I teach, though it will take some thought about how best to implement.

-- MattGoff - 21 Nov 2006

"Is it the curriculum? Is it the pedagogy?"

First, and foremost, it's competence. Second, it's about accepting responsibility for getting all kids from point A to point B (and defining points A and B!). Then comes curriculum and pedagogy - and hopefully, common sense.

"In the big picture of school reform, how do all these people fit in?"

It's nice to have their work and opinions. That's it. There is no need (if ever possible) for common ground.

There is no such thing as "best practices" or common assumptions or expectations. Our town decided to use a very wide full-inclusion, child centered, learning environment for teaching - no tracking at all through 8th grade. Is this right or wrong? Who gets to decide? What is wrong is the assumption that there is some widely agreed upon model of education. What is wrong is that some group gets to make these assumptions for all.

"He suggests (correctly, in my mind) that students should play a more active role in the curriculum that is taught and the assessments that are used to verify that learning has taken place."

The devil is in the details. One of the big problems of education is the technique of schools to argue with vague generalities, but they get to decide on the details. Lots of things sound nice on the surface. That's why the idea of balance works so well when math is discussed. Who could be against balance?

I can't imagine going into an AP Calculus class and telling the teacher that I really want to have some input on curriculum and grading. HA HA HA HA HA!!! Sorry, but let's see some details.

I expect the teacher to know the material. I expect the teacher to know how to teach the material. I expect the teacher to know what is important and what isn't. I expect the teacher to be very clear about what is to be taught and how performance is to be graded. I expect my son to do what the teacher wants. How on earth can students verify (for themselves) whether enough learning has taken place?

"He argues that studies show when students are graded, they tend to focus on getting a grade and become less interested in the material."

"Studies show?"

What, exactly, do they show? Is he saying that grades don't show how much students have learned? That they know the material, but they aren't interested in it? That students could learn more if they graded themselves?

Excuse me while I get a little bit ornery. This sort of fuzziness of curriculum and assessment is a big problem in education.

" ...and what it means to be 'well-educated'."

I sure as heck don't want him educating my son, and I don't want anyone else making these fundamental decisions for me. I don't want to impose my educational beliefs on anyone else, but unfortunately, Ed Schools, public schools, and teachers don't hesitate for one second.

-- SteveH - 22 Nov 2006

"What, exactly, do they show? Is he saying that grades don't show how much students have learned? That they know the material, but they aren't interested in it? That students could learn more if they graded themselves?

Excuse me while I get a little bit ornery. This sort of fuzziness of curriculum and assessment is a big problem in education."

I'm sure that there are plenty of things which Kohn can be criticized for, but I do want to say that some of the apparent lack of clarity of his positions is my fault, if you are responding only to what I have said (rather than your own reading of his writing). So, to let Kohn speak for himself, here is an article where he discusses grading and the problems he sees with it.

"I can't imagine going into an AP Calculus class and telling the teacher that I really want to have some input on curriculum and grading. HA HA HA HA HA!!! Sorry, but let's see some details.

I expect the teacher to know the material. I expect the teacher to know how to teach the material. I expect the teacher to know what is important and what isn't. I expect the teacher to be very clear about what is to be taught and how performance is to be graded. I expect my son to do what the teacher wants. How on earth can students verify (for themselves) whether enough learning has taken place?"

I certainly agree that students do not have the knowledge/perspective to always know what is important or "whether enough learning has taken place." I'm not trying to suggest that teachers have no place in determining assessment. However, it's my impression that currently students have no input into curriculum and/or assessment. It matters very little what they are interested in learning, even if it could reasonably fit within the curriculum.

If a student is in AP Calculus, that course is highly constrained by the fact it is designed to prepare students to pass a calculus test. Obviously in this case the AP Calculus exam (or something similar) is going to be a primary means of assessment. I like to think I have enough perspective in this field to claim that teaching to the AP Calculus exam is not the only approach to teaching the material in calculus.

Currently, the calculus text I use (Calculus in Context) emphasizes a geometrical and algorithmic approach to calculus. With some basic programming skills and geometrical understanding, it's actually not too difficult to consider some problems that are not even possible to solve at all in closed form. Algebraic formulas are taught, but not empahsized, especially for integration. In my experience it's a little strange to spend lots of time learning integration techniques and then find out that there are still lots of functions that you can't integrate.

Having said that, absolutely, the teacher should have the knowledge and background to teach, guide, and evaluate a student. Having students involved in the process (in some way other than just learning what they are told they need to) probably makes it even more critical for teachers to know the field. If the curriculum is tightly constrained and the teacher learns that curriculum, he or she can get away without understanding much outside of the specific curriculum. If students are allowed to push out a little bit, a teacher with a weak background will quickly run into trouble. For example, a teacher who was trained to teach AP Calculus may know how to solve all the kinds of questions that would show up on an AP Calculus exam, but they might have quite a bit of difficulty talking about predator-prey models and ways to look at them. Such models typically do not have closed form solutions, but using Euler's Method it's fairly straightforward to investigate what's going on in such a system and how the parameters effect the behavior (and this approach is accessible by first semester calculus students).

In the bigger picture though, I think it is valid to consider the purpose of education and what children should learn. I know that for myself (and my kids) there are definitely things I want my kids to learn that the schools here won't teach them. Even more so, I'm pretty sure that what they would get from school, they could get far more efficiently from me at home. These are the main reasons I am planning to start homeschooling them in the next couple of years (my son is in Kindergarten this year, my daughter would start Kindergarten the year after next).

By the time students are in college (the level I teach), I would hope that they have their own purpose for going to school (though in my experience, many of them don't; it's just what's expected of them). That purpose should guide their educational decisions. I don't see any reason why their individual interests cannot help shape the curriculum of a general education math requirement, the content of which is highly variable from school to school, anyway. (Of course, this is only really an option for me because my typical class size for this course is about 8 students, not 80).

-- MattGoff - 22 Nov 2006

I let the students in my gen-ed class make decisions about what we're going to cover. Each of our major units has required topics and optional topics, and I let the students decide which of the optional topics we'll do.

My calculus students are voting with their feet about assessment. There is homework due every class period and it is graded on a 0/1 scale: 0 points if you don't turn it in, 1 point if you turn in something and it looks like you tried (even if every problem is wrong!). This homework adds up to 10% of the course grade. (My intention was to offer some free points for "effort" and to balance this out by putting fewer easy problems on the exams.) The current homework average is a touch under 70%. This means that my students are willing to lower their grades by a step (i.e. from a B+ to a B) in exchange for not keeping up with the homework.

-- RudbeckiaHirta - 22 Nov 2006

"I'm not trying to suggest that teachers have no place in determining assessment."

I didn't think that and I didn't suggest it.

"However, it's my impression that currently students have no input into curriculum and/or assessment."

More importantly, parents have absolutly no input! As for student input, teachers can offer assignments that could be tailored to student interests. However, it sounds like you are suggesting much more. As for grading or assessment, my opinion is that the students can assess all they want, but I would give out the grades.

"I like to think I have enough perspective in this field to claim that teaching to the AP Calculus exam is not the only approach to teaching the material in calculus."

Everyone has their own opinion, but what is best for the students? You don't live in an isolated world. Are you introducing all of the topics and skills they need for college? Do the students and parents understand the differences and trade-offs? I can take any rigorous course in math and come up with other topics that are very important.

Since you teach college math, you have a little more freedom to design your course, but you are still constrained by meeting requirements for follow-on courses and requirements of the student's major. Back when I taught college math and computer science, our department meetings spent a lot of time aligning courses. It sounds like your course ideas are more appropriate for an applied math track - that's not wrong, just different.

"For example, a teacher who was trained to teach AP Calculus may know how to solve all the kinds of questions that would show up on an AP Calculus exam, but they might have quite a bit of difficulty talking about predator-prey models and ways to look at them."

And vice-versa. They also might not know much about techniques for finding solutions to optimization problems. Is the material covered by the AP test just different, or, are you saying it's wrong? When you get to calculus and beyond, equally rigorous tracks exist, but the student has to be aware of the direction they are heading.

"In the bigger picture though, I think it is valid to consider the purpose of education and what children should learn."

And who gets to decide those things. If you have the option of homeschooling, that's good for you. Most people don't have that option, but would really like the option of school choice. The affluent get choice, the poor do not.

-- SteveH - 22 Nov 2006

but also the 'lay of the land,' so to speak

oh gosh, yes

and that's where you have a war between Kohn & Engelmann

I haven't read Kohn in awhile, but I think it's right to say that he and Engelmann et al probably do agree on the, or a, central issue, which is school accountability & blaming the child/parent/bad community/etc.

-- CatherineJohnson - 22 Nov 2006

It would be interesting to see a summary of research from a critical and unbiased source, though that's probably a pie-in-the-sky idea.

Actually, I think Carolyn posted one such study way back when.

It was the CA study of all math ed research.

Hang on while I find it.

Here is Carolyn's first post on that survey: California state study

-- CatherineJohnson - 22 Nov 2006

Here's the group:

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

-- CatherineJohnson - 22 Nov 2006

-- CatherineJohnson - 22 Nov 2006

The Kohn article on ed research looks interesting - I'll read.

-- CatherineJohnson - 22 Nov 2006

He suggests (correctly, in my mind) that students should play a more active role in the curriculum that is taught and the assessments that are used to verify that learning has taken place.

Are you thinking now of your college students?

I loved taking courses using the Keller method.

I don't think it's correct to say that the student assesses himself in a Keller course, BUT the student knows absolutely what the assessment criteria are and whether & when he/she has met them.

As I go through the Saxon books I would say that I'm "being assessed" by Saxon - i.e. I'm using all of his tests - and I'm also "self-assessing."

I've taken the CAHSEE (CA exit exam), the Jefferson High entry exam, the NY state Math A Regents, one of the Singapore tests....and a couple of other tests I've found online.

I also, not infrequently, "eyeball" other textbooks and/or assessments to see whether I'm up to speed in others books - i.e. I'm not becoming a "Saxon math learner" as opposed to a "math learner," period.

For me, certainly, given what I do for a living, the ability to self-assess is critical.

-- CatherineJohnson - 22 Nov 2006

However, I think I'd be doing perfectly well without all the extra self-assessing if I were using the Saxon books as a high school student.

-- CatherineJohnson - 22 Nov 2006

What is wrong is that some group gets to make these assumptions for all.

huge problem

AND: "some group" means ed schools, since School Boards tend not to mix in with curriculum and pedagogy

I think I posted the "Curriculum Update" from one of our School Board meetings.

In that meeting 300 parents, some of them employed in math-related fields, show up with a signed petition against adoption of Math TRAILBLAZERS, and the Board blows them off because "teachers are professionals."

Parents have zero say in matters of curriculum and pedagogy - AND curriculum committees act as advocates, not as honest brokers.

Our curriculum set out to choose a constructivist curricuulum (that is stated directly, in one of their PowerPoint presentations); then, after they chose it, they did not disclose any of the difficulties:

• they did not disclose the fact that Math TRAILBLAZERS was rejected for adoption by the state of CA

• they did not disclose the fact that more than 200 mathematicians & physicists, two of them Nobel prizewinners, had formally objected to NSF-funded constructivist texts

It's shocking when you think about it.

A professional doesn't "sell" you on a product by suppressing the arguments against.

Ever.

-- CatherineJohnson - 22 Nov 2006

Nor does a professional impose an experimental treatment (curriculuum in this case) on clients or patients against their wills - and without notifying them that it is experimental!

-- CatherineJohnson - 22 Nov 2006

vague generalities

oh brother

-- CatherineJohnson - 22 Nov 2006

In the bigger picture though, I think it is valid to consider the purpose of education and what children should learn.

E.D. Hirsch has now definitively answered that question for me: the best possible broad liberal arts education.

(I'll eventually get around to posting more about his books....but I have my own answer.)

-- CatherineJohnson - 22 Nov 2006

More importantly, parents have absolutly no input!

amen

this needs to change

-- CatherineJohnson - 22 Nov 2006

Matt

One danger with student choice is what happened to me: I made stupid choices.

I don't think either Wellesley or Dartmouth had required survey courses, so I took things like a "Colloquium" on "Women's Voices" in literature or some godforsaken thing.

So here I am in middle age, severely undereducated with an Ivy League degree.

I don't think that's what you're talking about, but it's definitely a point to bear in mind....

-- CatherineJohnson - 22 Nov 2006

The grades-are-bad research has been severely over-cited as far as I'm concerned. (I was first taught that one study way back in college.)

I find you can never rely on one study (or a couple of studies) for a claim as sweeping as "grades turn you off to learning" (what I was taught was that any external incentive eroded internal motivation...)

I haven't read this article yet, but it's apropos:

Incentives to Learn

I believe this describes a program to pay children in Kenya to learn...

-- CatherineJohnson - 22 Nov 2006

The reason I will always "go with" an Engelmann over a Kohn is that Engelmann so obviously speaks from direct experience of designing curricula that succeed.

Kohn, at least in the essays I've read, always seems fairly far removed from the classroom....

-- CatherineJohnson - 22 Nov 2006

"E.D. Hirsch has now definitively answered that question for me: the best possible broad liberal arts education."

It works for me too. I remember early on when I first came across the Core Knowledge series of books. It was so obvious to me. One could quibble about the exact content, but I was astounded to find out that many in the education world were anti-content and anti-grade-level skills. This culminated in my sending email to two members of our school board and telling them (among other things) that the schools should hand out the Core Knowledge series of books and tell parents that this is NOT the education their kids will receive. I never did hear back from them. They KNOW there are fundamental differences of opinion over educational philosophy. They KNOW that many kids are sent to other schools because of this, but they JUST DON'T CARE. THEY JUST DON'T CARE.

-- SteveH - 22 Nov 2006

the schools should hand out the Core Knowledge series of books and tell parents that this is NOT the education their kids will receive

heh

-- CatherineJohnson - 22 Nov 2006

Hmm. I thought Ken DeRosa^? had an interesting comment about Hirsch on his website. I thought he said that the problem with Hirsch is that he's never actually figured out a way to implement the core knowledge curriculum effectively for all kids.

Maybe I'm misinterpreting, but I think he said that Engelmann thought Core Knowledge was too difficult and not always developmentally appropriate, and that while Engelmann's program had been implemented successfully for children with different abilities, Hirsch's had not.

Hopefully, he'll read this commment and clarify.

-- RobynW - 22 Nov 2006

RH: I let the students in my gen-ed class make decisions about what we're going to cover. Each of our major units has required topics and optional topics, and I let the students decide which of the optional topics we'll do.

That seems like reasonable way to accomodate some student interests even in classes that are large (though I assume it still requires that the whole class do the same thing, even if a good sized chunk of the class would prefer to do something else).

RH: There is homework due every class period and it is graded on a 0/1 scale: 0 points if you don't turn it in, 1 point if you turn in something and it looks like you tried (even if every problem is wrong!).

I used to do a variation on this for my classes, but I switched over to doing daily homework quizzes and not collecting homework.

SH: More importantly, parents have absolutly no input! As for student input, teachers can offer assignments that could be tailored to student interests. However, it sounds like you are suggesting much more. As for grading or assessment, my opinion is that the students can assess all they want, but I would give out the grades.

At the ages you seem to be concerned about, I think it's a good idea for parents to have a great deal of input. At the ages (college) I am more concerned about (until my kids get a little older, anyway), I think students should have a little more independence.

I am suggesting more, but I am not suggesting that teachers give over the ultimate authority for giving out grades. Ultimately that is the responsibility of the teacher. However, I do think it is a reasonable approach to sit down with each student (and parents) at the beginning of the year and discuss what the student should be learning over the course of the year. They can discuss what the State/District/School require, and what the student/parent want. They can discuss what the State/District/School considers to be adequate demonstration of learning, and they can discuss what students/parents would consider proper demonstration(s) of successful learning. Throughout the year, progress could be measured against what was set up at the beginning of the year. Ideally, it seems to me, if the learning objectives (and the criteria for meeting them) were clear and precise, it should be straightfoward to see how the student was progressing.

Perhaps a more fundamental question is what to do about grades at all. Even before reading the article I linked previously, I have been struggling with how to do grades (and what they actually should mean). I use a system of accumulation of points, but allow myself wiggle room (usually to give higher grades than the points might suggest). The problem with this is that it doesn't necessarily reflect what students know at the end of the course, it reflects what they have done over the 16 weeks the course runs. Sometimes, for hard working students, a grade overestimates their knowledge (though this is rare, as I tend to be a tough grader). Other times it underestimates a student's knowledge, especially when you consider that much of their grade is based on material tested on in the middle of the semester that they may have learned better by the end. All in all, my system seems to work okay most of the time, so I've not been in a huge rush to figure out how to change it.

While reading Kohn's article on grading, I realized that I have had many students who exhibit some of the negative characteristics he claims can arise from the practice of grading. Students who become disinterested in the work when they feel an 'A' is out of reach. They do enough to pass, but mainly just go through the motions. More common is the student who gets frustrated early on (maybe due to my weaknesses as a teacher, or perhaps their poor study habits) and gives up because they do not feel like it is possible to get the grade they want/need. It doesn't really seem to matter to them when I say they just need to keep focussing on learning the material and the grade will take care of itself.

-- MattGoff - 22 Nov 2006

So this is what happens when I start a response and have to take a two hour break to teach classes before I can finish it; there's a lot of new stuff that happens in between.

Catherine: I've never heard of Keller courses before, but they sound interesting. I think that if the objectives are clearly stated, it should be fairly clear whether you are meeting them or not, especially if you are honest with yourself. I think learning to self-evaluate is a valuable skill to have. It's probably also a valuable skill to know how to set appropriate goals/objectives. Currently, it seems that students are not taught these skills.

Of course there is a risk of making stupid choices, but we all have to make our own choices eventually. I think it's a good idea to get advice from others, but by the time you are in college, you should be making many of the choices on your own based on your own goals. Thinking back to my choices, I went into math because I liked it and I felt like it offered me the greatest future flexibility. Other than that, I took things that interested me, including music, philosophy, and religion courses.

There are school districts in Alaska that are part of something called the Re-inventing Schools Coalition. This group was started in Alaska by a school district that was failing (its students) miserably in almost every way. Part of their reforms involved bringing in the entire community (not just parents) and giving them real input into the goals for the school district. They have dropped the carnegie credit and grades. They do have clear standards that need to be met for to acheive a given level in each area. Students are not required to meet standards at the same rate (for example, they could finish high school math by 9th grade and still be working at an 8th grade level in writing). Students are expected to understand their learning objectives, play a role in designing some of the assessments for those objectives, and (perhaps most importantly) you should be able to walk into a classroom at any time, and each of the students would be able to tell you what they are doing and how it contributes toward their learning objectives (that is, why they are doing it).

One of the interesting things that has come out of this approach, is the way the values of a community become a part of the education. Most of the school districts are in very rural areas, perhaps covering several communities over hundreds of miles (see Bering Straight School District, for example). Traditional methods of food acquisition (hunting/gathering) are still valued and commonly practiced in many of these communities. One of the things a student might do is put together a project that involves going to fish camp with his grandfather. Before he goes, he will work with his teachers/mentors to put together the objectives for the project and how those contribute to meeting the standards for the school. He will also work with his teachers/mentors to come up with products that will be used to assess the learning that took place. Most likely, such a project would help a student learn things that met standards in several different areas, including math, science, and cultural values.

When I talked to a fellow who has been involved in implementing this model, he emphasized that there was still the expectation that students should be able to do well on the tests. However, his argument was that if the tests reflected the standards, and the teachers/students were committed to learning that matched the standards, the tests would be a mere formality at the end; just one way among many of demonstrating what you know. I like what I have seen of this approach and would like to implement it at least in part in classes I teach. However, as SteveH^? mentioned previously, the devil is in the details.

-- MattGoff - 22 Nov 2006

Here's what Engelmann said about CK:

Core Knowledge, did not show significant gains in achievement with at-risk kids. The reasons for the program's failure are obvious if one looks at the stuff he attempts to teach, which amounts to just about everything. The way he formulated his cultural literacy scheme was to bring in loads of experts. Each had input. The sum of inputs was at best unrealistic. And nobody seemed to say, "This committee stuff is great, but how do we pare this mountain of information down to something that is realistic for at-risk kids?" Look at Hirsch's book, What Your Third Grader Needs to Know. Many high school kids don't know much of this stuff.

Most people with a sane view of education agree with Hirsch that having a broad based store of background knowledge is critical for comprehension and, therefore, learning. The problem, however, is that all that information and associated vocabulary has to be taught somehow and such teaching is not amenable to acceleration. See Becker and this synthesis of vocabulary research.

This is the point Engelmann is trying to make. Sure, Core Knwledge might be a feasible plan for higher performers but there is a logistical problem trying to teach it to lower performers. They don't learn fast enough to squeeze in all that information in the time permitting and we haven't found a good way to accelerate the process, though inroads are being made.

I touched on this topic in a post I wrote earlier today and one about vocabulary research earlier this month.

I think Hirsch has identified a legitimate first principle of education. Increasing background knowledge is a critical compnent of education; however, the actual teaching of all that background information remains, as Becker put it, a problem of "first magnitude."

-- KDeRosa - 22 Nov 2006

I've been thinking on the incentive effects of grading, and comparing it with KDeRosa^?'s discussion of Direct Instruction, and I note an interesting interaction.

My understanding of DI is that students should be getting pretty much full marks (over 90%) all the time. If they're not, the solution is to move them back a few classes until they do.

So, in a DI curriculum, kids would not be graded like in traditional or constructivst curriculum. The most you could say is how much the kid has covered so far, not how well they're doing on what they've covered (since it's going to be the same from kid to kid).

-- TracyW - 23 Nov 2006

In DI they recommend keeping a motivational point system that can be used as the basis of grades.

Here's what the point system is for Reading Mastery III.

Word Attack: Each student reads a column of words. If he reads the column with no errors, he earns 2 points.

Decoding: If the class reads the first 100 words in the story with a 98% error rate of higher and then finish the rest of the story below the expected error rate, they earn 4 points. If they miss the 100 word mark, yet still finish the story below the error rate, they earn 2 points. Otherwise, they earn 0 points.

Comprehension Workcheck: Each student completes independent work consisting of comprehension questions from the story they just read, review questions from previous stories, and skill items.

If the student makes 0 errors, she earns 5 points. 1 or 2 errors, 3 points. 3 or 4 errors, 2 points, and 4+ errors, 0 points.

Bonus: If the student completes all the questions in the independ work without skipping any, he earns 1 point.

Fluency Checkout: Every fifth lesson the students must read a passage from the previous lesson at a rate of 90 words a minute. If the student finishes in time, he earns 7 points for 0 errors, 3 points for 1 or 2 errors, and 0 points for 2+ errors.

Grades can be awarded based on the cumulative tally of bonus points earned.

-- KDeRosa - 24 Nov 2006

"The problem, however, is that all that information and associated vocabulary has to be taught somehow and such teaching is not amenable to acceleration."

The problem I see is not the type of content or the speed/level of content, but that it has specific content at all. This is not what or how our public schools want to teach. At the school committee meetings and the open houses at school, this is NEVER a point of discussion.

-- SteveH - 24 Nov 2006

"At the ages (college) I am more concerned about (until my kids get a little older, anyway), I think students should have a little more independence."

I wouldn't have wanted a group of my college algebra (oxymoron) students giving me their own, individual ideas on material to be covered or assessment and grading. I was not an individual tutor and there would be no way to please them all. If they wanted more independence to explore, I would have suggested an independent study course.

"However, I do think it is a reasonable approach to sit down with each student (and parents) at the beginning of the year and discuss what the student should be learning over the course of the year."

This is not what I am talking about. I can't imagine sitting down with my son's 5th grade teacher to discuss what history is to be taught and what individual expectations and gradings should be set. I would, however, like to have a say in the overall development of curriculum and grade-level expectations. This is quite different. You seem to be suggesting that schools and parents define some variable sort of individual expectations. You seem to be implying that there should be no externally-defined grade-level expectations of knowledge and skills.

-- SteveH - 24 Nov 2006

"The problem with this is that it doesn't necessarily reflect what students know at the end of the course, it reflects what they have done over the 16 weeks the course runs."

Don't make it more difficult than it really is. There is always lots of wiggle room using partial credit on homework and tests. On every question I graded, I used my judgment as to how much the student really understood. This sometimes required deciphering chicken scratches. By the end of the semester, you have a pretty good idea of the capabilities of the student and the grades should reflect that. Whether kids flunked or not usually was pretty obvious, and reflected in the grades - thankfully. However, for a few borderline kids, you have to be careful because you might have to open you grade book and defend your grades. You can't decide that for those with equal grades, some will pass and some won't. You have to rely on your grading scheme and let it decide. You have to rely on the summation of your grading judgment over the semester.

As for knowing more at the end of the semester, you can weight the final exam more. However, as a student, I preferred that the student (me, I guess) who showed consistent hard work and results over the semester got higher weightings on the homework and regular tests and exams. There are all sorts of variations you can use, and which one you use may depend on which course you are teaching. As a full-time student for 20 1/2 years, I saw it all. What students want is a clearly-defined and executed grading system. No surprises and one that hopefully doesn't depend on just a couple of tests or homework assignments.

-- SteveH - 24 Nov 2006

"Students who become disinterested in the work when they feel an 'A' is out of reach. They do enough to pass, but mainly just go through the motions."

That's their loss and weakness, not a problem with your grading system. Either there are some explicitly-defined goals for the class or there are not. I used to tell students that I'm on their side. I want them all to get A's, but there is certain material that has to be covered and certain skills to learn. I couldn't learn it for them.

"More common is the student who gets frustrated early on (maybe due to my weaknesses as a teacher, or perhaps their poor study habits) and gives up because they do not feel like it is possible to get the grade they want/need."

It's your job to evaluate your teaching abilities. I remember doing it every time I graded a set of homework or tests. It's the student's job to not give up. You can suggest that they come to your office hours, but the solution is not to grade more easily or let the student assist in the grading.

"It doesn't really seem to matter to them when I say they just need to keep focussing on learning the material and the grade will take care of itself."

The grade isn't the problem here. If you had a course that didn't give out grades, would they work harder? If you had a course where the student had input into the grading, would that make them work harder? No. If you had a course where the student had more input into the material covered, would that make them work harder? Maybe, but you may not cover what you need to cover and the students would still have difficulty over the hard parts.

Hard work is hard work. The problem is not grades. Covering less difficult material or making the grading easier are not solutions.

-- SteveH - 24 Nov 2006

I wouldn't have wanted a group of my college algebra (oxymoron) students giving me their own, individual ideas on material to be covered or assessment and grading.

There is far less room for this sort of thing in College Algebra due to the way it fits into a sequence. Gen-ed math is usually intended to be a terminal math course outside of the calculus sequence, so there is a lot more flexibility there.

Also, I have the luxury of very small classes, so I have the ability to work with students individually, if they want/need it.

I would, however, like to have a say in the overall development of curriculum and grade-level expectations.

Can you explain what this might entail in practice?

You seem to be implying that there should be no externally-defined grade-level expectations of knowledge and skills.

That's not what I intend to imply. I think there are externally-defined minimum grade-level standards (defined by the State, in most cases, I expect). I'm guessing that a lot of parents want more than that out of their child's education.

Don't make it more difficult than it really is. There is always lots of wiggle room using partial credit on homework and tests....

There are all sorts of variations you can use...

I agree with both of these statements, but I'm not very happy with the idea that the grade can depend signficantly my choice of grading rather than a student's knowledge. If a grade says as much about the teacher as it does the student, it seems a little strange to me to use grades as a means of indicating what a student has learned.

Sure, in the end, what's important is what the student learned, not the grade they got. However, the grades have other consequences (GPA effects scholarship eligibility, for example).

I'm certainly not arguing material should be less difficult or A's given out more easily. I'm saying that grades can be a pretty poor way of communicating what a student has learned, except possibly in the extremes.

As an example of one of the problems I have to deal with on occsaion, I teach a pre-calculus class with a book that covers the material in 4 chapters. The first chapter is exponential and logarithmic functions. The rest of the chapters cover trigonometry and never refer back to the first chapter. I sometimes have students who do miserably in the first chapter and fine for the rest of the course. Points-wise, they can easily earn a low B and have no idea how to deal with exponential and logarithmic functions. I can add wrinkles to the system that allow me to not pass someone in this case, but it doesn't seem like an elegant solution to me.

"Students who become disinterested in the work when they feel an 'A' is out of reach. They do enough to pass, but mainly just go through the motions."

That's their loss and weakness, not a problem with your grading system.

That's an assumption I am hesitant to make. It seems a little too convenient for me to say my (grading) system has nothing to do with it. By the time students get to me, they are pretty well accoustomed to doing poorly in math, for the most part. It doesn't take much for them to decide my class isn't any different than the ones they've been failing to learn in for most of their lives.

Ultimately, it is up to the students to do what they need to do. However, I consider it my responsibility to work on putting together a system (across all classes; including content, presentation, assignments, and grading) that gives them the best possible chance to succeed; and by succeed, I mean that they actually learn the material well, not just that they (barely) pass the class.

I'm in a situation where grades will not go away in any case, so I'm not really looking to get rid of them. But right now, the way I have things set up, students can approach a class by working to accumulate points to pass. I'm not entirely happy with this system (though I continue to use it with some modifications, because it's what's easiest for me).

What I would like to do is set up a very clear and detailed list of things that they should be able to do (and why). Grades will be awarded on the basis of the things they have demonstrated (more than once over time) that they know how to do. Holes in knowledge will not be allowed, though incompletes may be granted for students who have made progress but not enough to pass. Theoretically, I should be able to sit down with a student at the end of the semester and go over thie list. We should both be able to agree that a student has learned any given item. If the student thinks she has, and I am unconvinced, all it would take in many cases is for her to do a couple of problems right there to show what she knows.

-- MattGoff - 24 Nov 2006

I would, however, like to have a say in the overall development of curriculum and grade-level expectations.

"Can you explain what this might entail in practice?"

Our public schools lists a Citizen's Curriculum Committee, but they never (re)formed it. I guess they didn't like the idea of not doing only what they want to do. The ideal case would be to define an individual curriculum and expectation plan for my son. This just won't happen. The next best thing would be to have citizen-based oversight of curriculum, expectations, and any sort of tracking or pull-out. This can be controlled and still doesn't resolve the issues of different educational philosophies or exepectations.

The only real solution is school choice.

-- SteveH - 24 Nov 2006

"If a grade says as much about the teacher as it does the student, it seems a little strange to me to use grades as a means of indicating what a student has learned."

I don't think it says that. If most of my students flunked a test, either I had to explain things better (or differently), or I expected too much from the kids. (usually the latter) The school I taught at was not Harvard and I couldn't go around flunking most students. But I never thought that my grades didn't reflect their knowledge in the course. When you first start to teach a class, there is a certain amount of calibrating that has to go on. After a couple of times teaching a course, there are usually no issues related to grades.

It sounds like you just don't like grades, but as a student, I never liked pass/fail courses.

"I'm certainly not arguing material should be less difficult or A's given out more easily. I'm saying that grades can be a pretty poor way of communicating what a student has learned, except possibly in the extremes."

I would never use the word "extremes". There has to be a way to quantify what you think a student knows. What's the alternative?

"I can add wrinkles to the system that allow me to not pass someone in this case, but it doesn't seem like an elegant solution to me."

When it comes to passing or failing a student, there is no elegant solution. I would have liked to make that decision solely on my own judgment, but I would not like being put in the position of explaining that. It is better to incorporate that judgment using partial credit in all of the individual tests and homework.

For the case where a student does really well in one part of the course, but "flunks" another part, well, you have to properly weight the different parts. Some kids I would pass, but hope they would not go on to the next course in math. I don't know how not quantifying these things would help more than quantifying them.

"It doesn't take much for them to decide my class isn't any different than the ones they've been failing to learn in for most of their lives."

I taught algebra to college students who were in my class only because they had to take the class. It was probably the only math course they had to take, and many dreaded it. First, there was only so much I could do to fix any or all of their problems. Second, I would tell them exactly what they had to do to pass the course. I told them if they did all of the homework and understood it, then they should have no problems whatever. I had few borderline problems.

"Holes in knowledge will not be allowed, though incompletes may be granted for students who have made progress but not enough to pass."

This is nice, but most all of my students who asked for incompletes could have done more during the semester, but they didn't. The problems or "holes" weren't a sudden surprise at the end of the semester. Finishing incompletes was like pulling teeth. Many didn't bother.

-- SteveH - 24 Nov 2006

It sounds like you just don't like grades, but as a student, I never liked pass/fail courses.

I would never use the word "extremes". There has to be a way to quantify what you think a student knows. What's the alternative?

What I meant by "extremes" was the very best performers, and the worst. An 'A' means that a student has pretty much mastered the entire course (and done what I asked throughout). An 'F' means a student has failed to master much of anything (and has done little of what I asked). For grades of 'B', 'C', or 'D', there are several different ways a student can end up with such a grade. For example, a 'C' could mean that the student has an low-adequate understanding of all the material or it could mean they have a good understanding of most of the material, but didn't do all the assignments. The latter person would have a much better chance of being successful in a subsequent course, but there's no way to determine that by the grade.

Grades are essentially a weighted average. As such, they can suffer from the problems that averages have in summarizing data. What I'm suggesting is that there is not so much material in a given course that it's not possible to look at the 'raw' data so to speak. If I want the students to learn a certain set of material, it is possible to consider each of the things they should have learned and evaluate whether or not they have learned (mastered) each of them. In theory, I should be able to leave it at that. In practice, I don't work in a context where that is possible, so I will still need to give students a grade. However, I will feel like giving a grade based on this underlying data of content mastered, will be better than making the assumption that content mastered is adequately reflected in points earned for the course. It should also enable me to provide better feedback. Right now, with points, I can sit down with a student and show where they didn't earn points, but I can't easily sit down and say "here are the things you haven't learned that you need to."

I taught algebra to college students who were in my class only because they had to take the class. It was probably the only math course they had to take, and many dreaded it. First, there was only so much I could do to fix any or all of their problems. Second, I would tell them exactly what they had to do to pass the course. I told them if they did all of the homework and understood it, then they should have no problems whatever. I had few borderline problems.

This is not too different from my experience. This is the approach I take in practice now. However, I'm not satisfied to say this is "good enough" and the students need to work harder to learn the material. I feel like there are ways that I can help them worker harder and, perhaps more importantly, smarter (so they can learn more efficiently). Most of my participation on this website has been geared toward figuring out how to do this. It's certainly a work in progress, and I do not know ultimately what is going to work the most effectively. However, if I don't do everything I can in this way, am I doing any better than the schools that have failed them in the past and justified themselves by saying it is the students, or their families, who didn't work hard enough?

-- MattGoff - 24 Nov 2006

"Right now, with points, I can sit down with a student and show where they didn't earn points, but I can't easily sit down and say 'here are the things you haven't learned that you need to.'"

You can do this on a test-by-test basis. There is a direct correlation between what they don't know and the grade on the problem. Doing this translation back using weighted scores at the end of the semester is probably too late anyways. You could instead, offer other ways (make up tests?) for students to show you that they really understand the material. I wouldn't care how many tests I gave if it motivated everyone to really learn the material. They might be excited to find that they had multiple chances to get an 'A' (or just pass the course). The motivation might be the grade, but the goal is to learn all of the material. If you want to eliminate holes, I think you have to fix them on the way and not wait until the end of the course.

"I feel like there are ways that I can help them worker harder and, perhaps more importantly, smarter (so they can learn more efficiently)."

This is tough to do in college - after so many years. I only had limited success. Most just wanted to get past the course, since it was the last math course they would ever take. The only success I had was in finding new, simple ways to explain things. Students would get excited when something, that seemed so confusing before, became quite clear. Perhaps it just finally sunk in, but I found that spending more time on the basics worked better. (Less is more.) Instead of 10 different ways to use logarithms, I focused on only one or two. Hopefully, if someone brought up logarithms 10 years after college, he/she would remember those simple cases and rules.

-- SteveH - 25 Nov 2006

"Core Knowledge did not show significant gains in achievement with at-risk kids. The reasons for the program's failure are obvious if one looks at the stuff he attempts to teach, which amounts to just about everything."

I agree. I bought a couple of What your _ Grader Needs to Know books. If my kids need to know all this, we're in trouble. Hirsch doesn't even explain how to present the material.

-- RobynW - 25 Nov 2006

wow - I've missed all kinds of good stuff - Ken thanks so much for the Engelmann link on Hirsch (I've been wanting to find that)

I don't think it's the case, though, that Core Knowledge hasn't panned out for at risk kids - ??

I'll have to look it up.

In terms of curriculum design, I would always go with Engelmann.

This is something I haven't mentioned....but while Hirsch is now in my pantheon along with Engelmamm, I think he fails to put across, or perhaps even to formulate, what "background knowledge" or "cultural literacy" actually is for a child (and for an adult).

Hirsch leaves the impression that knowledge is "facts" - i.e. lots and lots of stuff that you know.

I suspect this is where Engelmann gets his dander up - it's too much stuff.

Hirsch, of course, wouldn't say that this is what he believes, but both books (KNOWLEDGE DEFICIT & SCHOOLS WE NEED) leave this impression on the reader.

What Hirsch is missing is the idea of "schema."

A superb education - which I think I received in some subjects at Wellesley and Dartmouth - gives you a cutting-edge and historically informed schema, or "map of the world," in each field you study. (This is why students need to take high quality survey courses.)

I've made an entire career of psychology & even neuroscience writing, all based on the schemas of these fields that I learned at college.

Hirsch talks about "exemplary" facts, but he doesn't tell us why certain facts would be exemplary and certain others would not, apart from the frequency with which they appear in cultural discourse.

I'm going to assume that Engelmann is more focused on choosing the right facts to teach to mastery - and on teaching a schema.

-- CatherineJohnson - 27 Nov 2006

I saw something funny this weekend.

I was looking up GED books, and someone recommended Hirsch's WHAT YOUR THIRD GRADER SHOULD KNOW.

-- CatherineJohnson - 27 Nov 2006

I really like the Core Knowledge series, which my son has been using for a couple of years now. He's learning solidly substantive stuff about interesting and useful things that will provide a sound foundation for further learning in the future.

Kids can learn much more in a shorter period of time than we usually expect; we should use that capability to its fullest extent.

-- DougSundseth - 27 Nov 2006

oh my gosh - lots of good stuff here - BUT I MUST WORK!

TRACY:

My understanding of DI is that students should be getting pretty much full marks (over 90%) all the time. If they're not, the solution is to move them back a few classes until they do.

So, in a DI curriculum, kids would not be graded like in traditional or constructivst curriculum. The most you could say is how much the kid has covered so far, not how well they're doing on what they've covered (since it's going to be the same from kid to kid).

Absolutely - at least as I understand it.

I've GOT to get around to writing a post about the Keller method.

In the Keller method each student studies on his own (I took two Keller courses in college); you don't move to the next topic until you score 90% on a test.

Everyone gets As, because an A is mastery.

A B is not.

This is a massively radical idea for parents (and teachers).

Parents here all feel constrained to say, "I don't care if my child gets As."

Ed once said this! To Scott Fried! He actually said, "We'll take a C"!

That's how powerful the "social expectation" is. This happened at the end of 5th grade, as Scott was rushing off from the parent-transition meeting.

Ed had pigeonholed him and was letting him know Christopher had to be placed in Phase 4 math in 6th grade.

Scott said, "If you'll take a C."

And Ed said, "We'll take a C."

THEN I SAID ARE YOU OUT OF YOUR MIND???

But I know why he said it. Scott was racing off, refusing to stop and talk, and he'd laid down a condition as he blew out of the room - and Ed took it.

-- CatherineJohnson - 28 Nov 2006

I keep telling parents, and I'm going to keep on telling parents, "Everyone should get As."

By which I mean: everyone should master the material being taught at a 90% level.

The only meaningful difference amongst learners at this stage is rate of learning novel material in a novel field.

Period.

-- CatherineJohnson - 28 Nov 2006

btw, I'm not doctrinaire about any of this stuff - Ed has used grades to very good effect in his college classes; I've seen that boys love to compete for grades & prizes; etc.

I have a wide pragmatic streak - whatever works.

However, I'm not willing to compromise on teaching to mastery, which means a 90% criteria, which means an A.

That's my line in the sand!

If people wanted to figure out some other way to make distinctions & reward faster learning, or extra learning, or more complex learning - great.

But I want my school to tell all of us what the core curriculum is, and to make sure everyone masters it to a 90% criterion.

-- CatherineJohnson - 28 Nov 2006

I think Hirsch has identified a legitimate first principle of education. Increasing background knowledge is a critical compnent of education; however, the actual teaching of all that background information remains, as Becker put it, a problem of "first magnitude."

-- CatherineJohnson - 28 Nov 2006