28 Jan 2006 - 17:59

Matt Goff on teaching algebra

Matt Goff, who teacher math at a small liberal arts college in, I believe, Alaska, left a great comment about his teaching methods and about how they've changed recently.

All the boldfaces are mine.

I have been reading this site for the last month or so and feel that I've gotten some good ideas and information from it. There are three separate (but related) perspectives that I take when thinking about this information:

1. I teach math at a small open enrollment liberal arts college. Many students are poorly prepared in math. In a typical year, half (or more) of the incoming students will place in Basic Math or Basic Algebra (the equivalent of Algebra I). Even after they arrive, they often struggle to be successful. For example, I have taught a class of 11 where 10 of the students had failed to complete the course previously. It has become clear to me that I could probably be a more effective teacher by making some changes (more on this later).

2. Many of the students who struggle in my math classes are Elementary Education majors. 5 of the 10 students mentioned previously were Elementary Education majors. College Algebra (they can usually make it through Basic Algebra eventually) seems to be a real stumbling block for many of them. However, beyond that, they are required to pass Trigonometry before taking a Math for Elementary Teachers course and final a Math Methods course. Reading these pages as well as having kids that are nearing school age (see below) has really caused me to evaluate how I view these students and their progress (or lack thereof) through their required math coursework.

3. I am planning to homeschool my kids (now ages 4.5 and 2.5). I'm not sure how I came to this decision, I think it has partially grown out of my own experience going through school (I was a 'gifted' student, but my mom had to regularly fight with the school district regarding my schooling. The recurring theme seemed to be concern that by accelerating I would either run out of stuff to do or get in over my head. I'm pretty laid back and I guess when I started thinking about the possibility of conflict with the school district, it felt like I might rather just teach them myself. From that starting point, the idea grew on me and now I feel like it's likely to be a very rewarding experience for them and me.)

Upon seeing over half of a class need to repeat college algebra, I felt like I needed to change some things. In all but one case, the students had not done the work that was expected of them, so in a sense, it was their fault. They are in college after all, and it seems like I should be able to assume they can take responsbility for their own learning. I have finally realized that I can't. For whatever reason, they are just not learning how to be effective learners before they get to me. I seem to be one of those folks who is highly suited for learning in the school environment. Many learning strategies either came to me naturally or were not necessary for me in the first place. I think this is why it took me so long to realize that a lack of such strategies and/or meta-learning might be why students were not being successful.

The typical approach I have preferred to take to teaching is as follows: Introduce a section and assign homework. The next class (we meet three times a week) I take questions on the homework assigned the previous class period. Typically, I would plan to spend up to half the class doing this. It's my feeling that explanations will be more effective if students have already engaged the material. Students then have until the next class period to finish up the assignment and turn it in. The remainder of the class period is spent introducing the next section. Homework is collected and graded on completeness as most of the answers to the assigned questions are in the back of the book. Tests are given at the end of each chapter and students are allowed to turn in test corrections to get half-points back on problems them missed. My reasoning for this was that mid-term tests can and should be a learning tool. I figured that if they could use the test (and corrections) to firm up the knowledge that had been weak on and mastered it by the final, that was good.

Although the better students did fine, there were some problems with this approach for others. Students did not do the homework the day it was assigned and consequently the question time was not very helpful for them. Students did not use the answers in the text as an effective study aide. I eventually came to the conclusion that some of them did not really know how to. I assumed that if students were serious about learning, they would self-evaluate (using answers in the text) and ask questions and/or do more questions to make sure they understood the material. I generally found out they did not know what they were doing when they took a test. In hindsight, it has become clear that this was probably too late for many of them; especially when their lack of progress was masked for a couple of chapters because they were getting by on half-remembered knowledge from previous courses (either in high school or college) that overlapped with the early chapters of my course. They really did not know what they didn't know, and even worse, they didn't seem to know how to figure out that they didn't know it (until it was made clear to them in the form of a failed test).

Largely as a result of frustration with the poor performance of my students and the things I have read on this site, I am trying a new approach in my college algebra class this semester. Rather than giving a class day for asking questions on homework and then collecting it the second class after it was assigned, I am giving a quiz on the homework the class after it was assigned. Already there have been a few things that I have caught that I was able to go back and explain.

(I'm pulling this whole section of Matt's comment out and boldfacing it because I JUST LOVE IT:)

I've required that each student meet with me once a week (an advantage of small schools, for sure) to go over homework (which I am requiring that they keep organized in a three ring binder along with a log of questions, time spent, and in-class quizzes). One of my goals in the one-on-one meetings is to help them figure out what they need to do to effectively learn the material. They just took the first chapter test today, so it will be awhile before I am really able to tell how succesful this approach is. So far I am cautiously optimistic.

What I like about Matt's approach is that it's sending a clear message to his students that they are expected to try to learn the material to some level of mastery after every class. Students, even in college (as Matt points out), take cues from the teacher's policies about what they are expected to do when. Whether or not a teacher intends it, a student assumes that if the teacher is giving one big test at the end of a section, then it's okay for them to try to cram on ALL the material at the end of the chapter.

The daily quiz is a lot of work for the teacher, but I've come to believe that it's a great, success-creating idea. And it can be set up so that it's a quickish grading job for the teacher. I think it is really, really worth it.

-- CarolynJohnston - 28 Jan 2006

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Someone else commented to me that daily quizzes were a lot of work, but they are easier than grading homework. This is especially the case if the homework is actually graded, rather than just checked for completion.

I have told my students on a number of occasions that I would rather not even assign homework. They should be able to go through the problems in the book, do a couple of each type to see if they know how to do them (checking answers in the back, to make sure), and then do more practice on the items they need more practice on. When I write a homework assignment, it's basically a 'one size fits all' sort of thing. I try to make it long enough that most students will have adequate practice without making it so long that it bores the better students to tears. I'm trying to get the students to understand this point during our weekly meetings, but I don't think most of them are self-motivated enough to get it at this point. They seem to still need me to give them a list of problems to do, and they typically will not do any more than that (and often don't quite complete the assignment).

-- MattGoff - 28 Jan 2006

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They seem to still need me to give them a list of problems to do, and they typically will not do any more than that (and often don't quite complete the assignment).

That's right... their executive functioning is not yet up to snuff. In my experience, early 20-somethings are often just not quite mature enough yet for that (but eventually they get there... sometimes in their 40s!).

But as Catherine has wisely said... the price for poor executive functioning shouldn't be that you don't learn the material (she actually said it about organization, but I'm applying it here too).

-- CarolynJohnston - 29 Jan 2006

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For me, part of the reason for spending vast amounts of money studying a language or maths through actual lessons, rather than spending Will Hunting's $20 in late fees on library books, is that a lecturer will provide the structure that forces me to actually learn.

So from my point of view, say out of a $600 charge for a course, I'm paying about $50 for materials that are better than a library book, about $50 for an expert I can ask questions of, about $300 for motivation and the remainder for the formal qualification to point to.

Perhaps I should be able to motivate myself to sit down and do something hard. But I know from bitter experience that my short-term self will simply procrasinate, do the easy bits and not the hard bits, and generally do not learn half as much as I should. But if I sign myself up for deadlines I do the work.

And though this may be very poor functioning on my part and I may be a very very bad person for not being self-motivated in the short-run, at least I can support myself, I have interesting work which is safe and comfortable, and I now have skills that very few people in NZ share and that my employers seem to value so far (and I've learnt to take jobs that operate by short deadlines.) So I think there's value in universities seeing an important part of their role as providing external motivation to learn.

-- TracyW - 29 Jan 2006

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Despite what I've said which might imply otherwise, I was actually never a good student. I was a student who got good grades (rarely a 4.0, but I finished with over a 3.8), but I make a distinction between that and being a good student. When subject material really interested me, I could spend lots of time on it. Most of the time, I was interested in a topic and so took the class, but the class itself (that is, the lecture and maybe some of the readions) satisfied my curiousity and interest. Fortunately for my GPA, my mind seems to be a fact sponge, and I could generally get away with slacking on homework and/or procrastinating on projects. There were a few occasions where my grade suffered and I had to work a little harder in the second half of the course to pull the grade up to a B for the term.

I can remember two courses I took while an undergraduate that illustrate my (poor) study habits and the range of consequences. When I took Numerical Analysis we did not do any computer programming. We had homework where we were required to do things like 5 or 6 iterations of Newton's method by hand (with a hand calculator). Talk about tedious. Homework was due once a week, and in my typical fashion, I would start it the night before it was due. Facing 8+ hours of homework, I usually bailed on it after finishing only a small part of it. Homework was only worth 10%. Tests were 90% and of course there was not time to have lengthy iterations on them, so if I didn't have the details of a method down, it didn't matter for a test. The concepts I understood, so I did well on the tests and got an A in the class despite getting something around a 25% on homework.

When I took an Introduction to Operations Research, for some reason it did not click. Again, homework was due once a week and I would tend to save it to the last minute (night before, or even the morning it was due). In this case I also had difficulty getting it done. Linear programming especially gave me fits. For some reason I would make 15 constraints when only 2 were necessary. I did poorly on the first couple of tests and had to work pretty hard to pull a B at the end. The interesting thing is, that most of my fellow math majors (many of whom usually struggled more than me) considered this course easy and did much better than me.

I'm not sure why I share this information, except that it probably informs my default attitude towards students. If they don't feel like they need to do all the work, I tend to be inclined to trust that they are capable of figuring out how much they need to do, for the most part. My experience as a student was that I had a sense for just how much I needed to do that only failed me on relatively rare occasions. My experience as a teacher has lead me to realize is there are a lot more students who think they can get away without studying very much than can actually get away without studying very much. I guess we might call that misplaced self-confidence. I'm trying to learn to be more assertive (blunt) in telling students when I think their confidence is misplaced (and why I think that).

-- MattGoff - 29 Jan 2006

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To follow up more specifically on what TracyW^? said. I can definitely see the value in a class as external motivation. Until late in my graduate school career I felt classwork always provided necessary structure for me. I tended to avoid indpendent studies because I knew they were difficult for me to complete. It took me 5 years to finish a dissertation that I probably could have finished in 1 year, if I had been better at diligently applying myself. (To be fair, I did get married, have kids, and get a job in those years.) It was only near the very end that I started to feel like I would be better off learning things on my own rather than sitting through a class. (Part of the reason the dissertation took so long was that once I proved the interesting results, the tedium of writing took over and I was far less motivated to do that.)

I am happy to provide the structure for students to learn. I recognize that the ideal self-motivated student is exceptionally rare (I wasn't one myself, for sure) and many students look to the course to provide some deadlines. This is why I have always assigned homework.

Homework assignments are uniform for a given class, student needs are different. I would be happy to see students do more or less than assigned, as needed for their understanding. This only works if they have a reasonable sense of what they need for their understanding. A fair number of students seem to be lacking this sense (or it is poorly calibrated). With others, I get the impression that they know what they need to do, they just don't feel like doing it.

-- MattGoff - 29 Jan 2006

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Having taught classes at U. of IL many moons ago, I was surprised, while filling in for an ailing teacher at a local community college, at the level of cluelessness shown by many of those students. Even freshmen at the University had a sense of how things worked in terms of getting through college and using it to your best advantage. Maybe it was due to the fact that most were living away from home while the community college kids largely lived at home.

Many times I had to remind these "kids" that they were actually paying to be here. There was no doubt that some were going to fail and they seemed disconnected as to how that might affect their GPA. Right before the deadline to drop I tried to encourage a few of them to consider this option rather than wreck their GPA with an elective they cared nothing about. It was as though no one had ever spoken to them about any of this, or that their GPA might ever come up in a job interview.

After one quiz in which the same unprepared handful of students failed, I gave the lecture about being on your own and making good choices, etc. The class (a generic music appreciation course) was an easy A if they either read the chapters or listened in class. I actually had a mother call into the dean to complain that I had been too tough on her kid. That was a first.

There was definitely a huge range of college student out there back 20 years ago. I wonder if it isn't even worse now.

-- SusanS - 29 Jan 2006

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That's right... their executive functioning is not yet up to snuff. In my experience, early 20-somethings are often just not quite mature enough yet for that (but eventually they get there... sometimes in their 40s!

Martha Denckla told me that the brain finally reaches full maturity at age 35!

She also pointed out that age 35 is the youngest our Constitution allows a President to be.

She said that people have an intuitive understanding of brain development in that sense......we all kind of 'know' that age 35 is different from age 20 or 25.

-- CatherineJohnson - 29 Jan 2006

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the price for poor executive functioning shouldn't be that you don't learn the material

That's one of the incredibly useful aspects of ktm for me, which is that it allows me to figure out what I think.

I've been VERY confused on the 'responsibility' issue, because, obviously, KIDS SHOULD BE RESPONSIBLE.

And, obviously, Christopher is now at an age where he is beginning to pull away from his parents (well, from his mother if not his father), is oriented toward his peer group first and foremost, has more ability to organize himself, etc.

But a core part of me just goes nuts at the thought that he's going to get out of math not knowing anything about math because he forgot he had a review sheet.

So I've been confused.

When I finally managed to put it that way - the consequence for screwing up shouldn't be that you don't get to learn - the whole thing became much, much clearer to me.

That formulation will be a big help whenever I talk to teachers & the principal — although the fact is, they've now taken charge of the situation.

It's no surprise to them that 6th graders are clueless.

It's possible they hadn't quite pegged Christopher as being as clueless as he is. (AND CHRISTOPHER: IN CASE YOU DECIDE TO READ THIS ONE DAY: I DON'T THINK YOU'RE CLUELESS! I THINK YOU'RE A CLUELESS SIXTH GRADER! SOON TO BE A NOT-CLUELESS SEVENTH GRADER!)

I was thinking the other day that Christopher probably 'shows' better than he is.

In many ways he's an only child, since both his brothers are autistic, and he's got the kind of 'responsible personality' that the siblings of handicapped kids often develop......so he's oriented to adults, talks to adults, automatically helps kids who need help.....and he's pretty tall for his age. (He's one of the youngest kids in the grade, but he's tall.)

They may not have been perceiving him as disorganized & spacy.

I wasn't picking up on this myself.

-- CatherineJohnson - 29 Jan 2006

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The daily quiz is a lot of work for the teacher, but I've come to believe that it's a great, success-creating idea. And it can be set up so that it's a quickish grading job for the teacher. I think it is really, really worth it.

Since I am posting the solution key to every even question for each lesson, I can create a quiz of yesterday's lesson in about five minutes. Now that I have done it once, it is all there for next year.

The process takes fewer minutes than taking up homework. At the end of the week, the kids staple their assessments together and take them home for a signature. Since all the information is in Excel, I can email mom and dad a line graph of their child's marks. But, the most significant part is the ability to instantly see were the errors are being made by the students.

I am think about teaching my next unit, geometry, the same way.

-- SmartestTractor - 29 Jan 2006

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Smartest Tractor

If you feel like taking the time to write up a Smartest Tractor In A Nutshell, I'd love to post it!

-- CatherineJohnson - 29 Jan 2006

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Which reminds me, I wanted to get your answer key up front.

It's beautiful.

-- CatherineJohnson - 29 Jan 2006

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Matt Goff

Fortunately for my GPA, my mind seems to be a fact sponge, and I could generally get away with slacking on homework and/or procrastinating on projects.

I've been wondering about these kids who seem to get through spialing & non-teaching to mastery courses for years and make it through unfazed.

I was one of those kids, too — and, like you, I'd probably have to say I was a lousy student per se.

I keep coming back to memory.

I had a fantastic memory as a child & as an adult (I think writers often have spectacular memories; at least that's what I think I've seen).....

I think I just 'remembered stuff.'

-- CatherineJohnson - 29 Jan 2006

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In fact, I went to school when memorization was required.

I could memorize LOTS of material very, very quickly.

It was easy.

Probably the same quirk of brain make-up.

'brain like a sponge'

-- CatherineJohnson - 29 Jan 2006

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My mom actually had a photographic memory as a child.

She could turn to the correct page in her mental image of a book, and copy the answer from the page.

-- CatherineJohnson - 29 Jan 2006

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For some reason I would make 15 constraints when only 2 were necessary.

I don't even know what this means and I love it!

-- CatherineJohnson - 29 Jan 2006

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I am happy to provide the structure for students to learn. I recognize that the ideal self-motivated student is exceptionally rare (I wasn't one myself, for sure) and many students look to the course to provide some deadlines. This is why I have always assigned homework.

If writers didn't have deadlines, nothing would get written except blogs.

And blookis.

-- CatherineJohnson - 29 Jan 2006

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Possibly no one here has heard the expression guillotine deadline.

I have heard this expression.

There's a reason for that.

-- CatherineJohnson - 29 Jan 2006

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Smartest Tractor In A Nutshell

I am not sure what you mean.

-- SmartestTractor - 29 Jan 2006

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Hey Matt, appreciate your point, and its good to hear that you're not one of those people who believe that everyone should be able to learn without structure (I occasionally run across arguments that grades are all about ranking students and should be dropped so people actually focus on learning things - the arguers appear to be immune to the dangers of procrasination).

Homework assignments are uniform for a given class, student needs are different. I would be happy to see students do more or less than assigned, as needed for their understanding. This only works if they have a reasonable sense of what they need for their understanding. A fair number of students seem to be lacking this sense (or it is poorly calibrated). With others, I get the impression that they know what they need to do, they just don't feel like doing it.

This is what happened to me. I had gotten great grades at high school without needing to struggle to understand anything. It was rather a surprise to hit university and suddenly run into things I actually needed to work at to understand them. It took me a while to redevelop my sense of how much study I needed to do. My high school wasn't particularly dumbed down, it had just all been too well within my abilities.

And then there's that long struggle - I know I should study, and I will, tonight, when I get home. After I've cooked dinner. And read the newspaper. And hey, of course I'll meet you at the pub to celebrate your birthday. I'll just do that study tomorrow...

-- TracyW - 29 Jan 2006

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Smartest Tractor

She means she would like a nutshell writeup of your classroom methods!

-- CarolynJohnston - 30 Jan 2006

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TracyW^?, I suspect most people can learn without structure. It's just that most of us don't care very much about learning the things we are 'supposed' to learn. (: In the extreme example, it's the student who can tell you everything that's happened in Professional Wrestling over the last 10 years (and they've only been following it closely for 5), but can't tell you what was covered yesterday in class.

I think genuine (internalized) motivation and/or passion to learn can work wonders, even among those of us who are typically procrastinators. I'm not sure how to inspire genuine motivation however (and while showing practical context and applications may cut down somewhat on the "what use is this?" complaints, I'm pretty sure it's insufficient to inspire motivation for most people).

-- MattGoff - 30 Jan 2006

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She means she would like a nutshell writeup of your classroom methods!

Hey!

I have a TRANSLATOR!

-- CatherineJohnson - 30 Jan 2006

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I suspect most people can learn without structure.

People can definitely learn without structure when they're motivated to do so.

When I get 'hyperfocused' on a subject I learn huge amounts about it pretty quickly.

I've never found a way to force myself to be hyperfocused, however (and I suspect there isn't one).

John Ratey was FANTASTIC on this subject.

He constantly said: make your environment do the work, not your frontal lobes.

I never observe that maxim to the degree I want to......partly, I guess, because I still don't know how.

If you have to learn something you're not hyperfocused on (or not highly motivated to learn), you're very well-advised to structure your environment in such a way that it 'pulls' Good Study Behavior out of you.

That's what Matt is doing for his students.

He's structuring an environment that will 'pull' better study habits out of them.

He's creating an environment that will 'do the work.'

-- CatherineJohnson - 30 Jan 2006

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In the extreme example, it's the student who can tell you everything that's happened in Professional Wrestling over the last 10 years (and they've only been following it closely for 5), but can't tell you what was covered yesterday in class.

We have possibly two people in our household who can do this.

-- CatherineJohnson - 30 Jan 2006

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"Possibly no one here has heard the expression guillotine deadline."

When I was a periodicals editor, the term was "drop-deadline". 8-)

I did that job for long enough to develop a real defense-in-depth approach to deadlines:

"I'd like to get all your new information in by ...."

"I need your information by ... to make sure it gets in the next issue."

"I know I said that I need your information by ..., but you know we build in a little bit of slop in the schedule to handle the occasional late arrival."

"I've had a few other people late this issue, so I still have a little bit of time. Can you overnight it to me today?"

"I'm sending the book off to the printer tomorrow; if you can fax me the new stuff today, I should still be able to get it in."

"Don't worry, I can insert it at blueline. Of course, I'll have to charge you for the blueline change."

"I'm sending the bluelines back to the printer today. If you send it direct to the printer, we can still get it in. But you'll have to pay for all the printer's extra work."

"Nope, it's too late for this issue, but send it anyway; the next issue's deadline is tomorrow."

8-)

-- DougSundseth - 30 Jan 2006

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drop-deadline

same difference

only less bloody

-- CatherineJohnson - 30 Jan 2006

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oh my gosh

that is HILARIOUS

yup

been there done that

SEE, what you REALLY needed to do was HIRE MATT, PUT HIM ON AN AIRPLANE, and have him GIVE YOUR WRITERSS A FORMATIVE ASSESSMENT-SLASH-POP-QUIZ every morning

-- CatherineJohnson - 30 Jan 2006

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TracyW?, I suspect most people can learn without structure. It's just that most of us don't care very much about learning the things we are 'supposed' to learn. (:

For me the question is what sort of things can I learn without structure?

My brain will do its best to avoid tackling difficult problems, until confronted with a deadline. And my brain's best is very good indeed when it comes to procrasination.

So I can learn history, politics, etc, quite happily. But I won't learn maths or arguments that depend on maths without a deadline.

I think genuine (internalized) motivation and/or passion to learn can work wonders, even among those of us who are typically procrastinators.

Yes, but I've learnt not to rely on it. If I did, I would fail to achieve a number of long-term goals.

And the weird thing is that, once I actually get down and focus on a problem, I quite enjoy the process of doing so. I don't hate studying maths, but the short-term bit of my brain will try to avoid actually doing so.

I am a strong believer in Steven Pinker's theory that we have multiple selves, with different goals, who struggle for control of the body.

-- TracyW - 30 Jan 2006

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In a Nutshell is attached below.

-- SmartestTractor - 01 Feb 2006

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In a Nutshell has been updated.

-- SmartestTractor - 04 Feb 2006

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They seem to still need me to give them a list of problems to do, and they typically will not do any more than that (and often don't quite complete the assignment).

I was a math major. My favorite math professor at MIT taught Algebra/Group Theory. On the first day of class (even though we were all upperclassmen) he handed out a list of problems that corresponded the material he was going to teach. That list of problems were practice problems in the book.

He explained that this was a list of problems that should be able to be done rotely. They were small and simple, and succeeding at the homework would require these problems to be second nature. The problem sets were weekly and separate--and ranged from doable to extremely difficult. but this list was a way for US to understand if we had understood.

By giving us this list, he helped us to build up mastery because when you know nothing, you can't see the difference between a simple and difficult problem.

For various reasons, I tended to find these problems very difficult, but I did them over and over (as well as many others) until I mastered them. He was a great teacher because he was right--he knew which questions formed the building blocks for mastery, and how to encourage us to learn those blocks so we could succeed.

I don't think it's unreasonable for your students to need a list of problems from you when they have no idea which problems are things 5th graders should be able to solve and which are college level math. You may know, but their ignorance is such that they don't. The more you can do to separate out the building blocks--even in high school algebra 1--from the more difficult challenges, the better. Neither adults nor children can discern that on their own. This is why "self taught" studies often fail to make the connections that constructivists tell us occur naturally.

The more you can provide mechanisms my which to train them to self evaluate, the better. No one has even given them that before. If they were taught in constructivist ways, they have no core knowledge on which to hang the things they are trying to learn. Without the scaffolding, the building will fall down.

-- KtmGuest - 09 Feb 2006

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ktm Guest

Thanks so much for this.

I'm sick as a dog today (Saturday) but will try to get it pulled up front later on.

I'm interested in what kinds of problems your teacher gave you — i.e. what did you need to be able to do with automaticity?

I should keep a list of all the problem types in KUMON.

KEY WORDS TO POST KTM GUEST MASSACHUSETTS INSTITUTE OF TECHNOLOGY

-- CatherineJohnson - 11 Feb 2006

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The daily quiz is a lot of work for the teacher, but I've come to believe that it's a great, success-creating idea.

I'm a HUGE advocate of this, based entirely in my struggles with every other form of self-discipline.

It's true of me, and I suspect of just about everyone else, that I need DAILY HABITS.

If I don't make my bed every day, I stop making it altogether. (I'm in the 'stopped' mode now, ALTHOUGH I'll add that Jimmy and Andrew unmake the bed the minute I make it, so that's a major disincentive.)

If I don't exercise every day, I stop exercising. (I've been at a '10' on that, and am now in the process of slipping — though I predict I'll ramp up the effort to get back to once a day.)

I still haven't developed a once-a-day-check-Christopher's-binder-and-assignment book habit. That's half the battle right there; I need to do this on a daily basis.

Once you're doing something on a daily basis, it becomes a habit, which means it's far easier to do.

KUMON takes advantage of that aspect of human nature. With KUMON, you're not supposed to take any days off at all. No Sundays, no holidays.

You just keep going, 10 to 20 minutes a day, day in and day out.

I didn't do KUMON sheets in Los Angeles, and it was amazing how hard it was to re-establish the habit!

SO a once-a-day quiz is going to get students into the habit of daily study.

Obviously, writing 5 quizzes a week is going to be rough (though I believe Gambill uses the 3 most difficult problems from the homework set, yes? Even so, you have to do all the organizational work of setting up a new system.)

But once you've got the system in place & the quizzes written, you're there.

-- CatherineJohnson - 11 Feb 2006

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I had a long talk with my neighbor yesterday, who is a clinical psychologist & statistician.

She pointed out — I'd forgotten this — that Gambill doesn't even look at students' homework if they pass the test.

In our math class, kids are docked points if they don't turn in their homework. The teacher doesn't make them re-do it, and doesn't assess them to find out if they know how to do it.

Until very recently, Christopher was handing in all of his homework, because we sat with him, helped him do it if he couldn't, then checked the answers & made him re-do it if his answers were wrong — WHICH THEY INVARIABLY WERE.

The teacher graded strictly on whether he showed up with the homework.

She had no idea — none — that he didn't know how to do the problems he was turning in.

My neighbor pointed out the obvious: the focus should be on the student's knowledge, not on the clerical fact of Homework Turned In/Homework Not Turned In.

-- CatherineJohnson - 11 Feb 2006

WebLogForm
Title:	Matt Goff on teaching algebra
TopicType:	WebLog
SubjectArea:	CollegeMath, HighSchoolMath
LogDate:	200601281256

Attachment	Action	Size	Date	Who	Comment
InaNutshell.pdf	manage	42.6 K	06 Feb 2006 - 22:57	SmartestTractor	updated