Thank you for the links Barry.

It's going to take a while to go through the transcripts because it just makes me so upset.

President of MIT Susan Hockfield, said in her opening comments:

"Now we all understand that there isn't one single, easy answer for improving American math education. It's a complex system's problems with multiple factors. Part of the complexity is that there is no single typical student."

AAAAARRRRRGGGGGHHHHHH!

The assumption is that the problem has nothing to do with common sense, a good basic curriculum, grade-level expectations of mastery, and teacher competence. There is nothing complex about this.

The real question is why are kids in fifth grade if they don't know the times table?

-- SteveH - 04 Nov 2006

The real question is why are kids in fifth grade if they don't know the times table?

Because they're ten years old. Duh! ;-D

-- BrendaM - 04 Nov 2006

Steve,

I understand what you mean about it taking a long time to get through the transcript. I'm having the same problem reading the textbook assignment for my ed school class. We're reading a book by a guy named Cangelosi, called "Teaching Mathematics in Secondary and Middle School". Excerpt from Chapter 4:

"Because mathematics is widely misunderstood to be a linear sequence of skills to be mastered one at a time in a fixed order, some people think teaching mathematics is a matter of following a prescribed curriculum guide or mathematics textbook. ... Textbooks present information and exercises on mathematical topics, but typical textbook presentations are pedagogically unsound from a constructivist perspective and inconsistent with PSSM's Curriculum Principle. Thus, textbooks should be used only as references and sources of exercises--not religiously followed page by page."

"Word problems from mathematics textbooks provide convenient exercises for students to experience some--but not all--aspects of real-life problem solving. With a real-life problem, students are confronted with puzzling questions they want to answer. Textbook word problems...present puzzling questions, but rarely are they questions students feel a need to answer."

With respect to the first quote, this is why I don't get excited about NCTM's new focal points. If as NCTM says, "nothing has changed" then NCTM still believes the content should be taught using constructivist techniques. And people like Cangelosi will continue writing drivel like this and ed schools will keep teaching it.

-- BarryGarelick - 04 Nov 2006

The real question is why are kids in fifth grade if they don't know the times table?

When I asked my fifth grade neighbor(she's a friend of the family), when she learned her times table she said third grade. Then I quizzed her on a few. The ones she did know she skipped counted. However, she exclaimed, "I do know that 1 x 1 = 1 because it looks like a barn door." What? You know, and she drew me a picture of a square with an X in it.

The multiplication homework she showed me had 27 problems...she missed five and 8 were incomplete.

Her mother is a friend of mine and is worried she isn't learning math. She had her assessed for a learning disability. There wasn't one.

Her concern was due to a conference she had with her child's third grade teacher. Around May of third grade, the teacher told my friend her daughter needed a tutor. She was shocked! Why did the teacher wait until May to tell me there was a problem? So frantically she found her a tutor.

My question is how could this kid pass our state test in third and fourth grade? We have some of the best SOL scores in the state.

--PaulaV

-- PaulaV - 04 Nov 2006

My question is how could this kid pass our state test in third and fourth grade? We have some of the best SOL scores in the state.

--PaulaV

Because the SOLs keep getting revised and dumbed down.

-- NicksMama - 04 Nov 2006

My question is how could this kid pass our state test in third and fourth grade? We have some of the best SOL scores in the state.

Because the skills that are necessary for success in algebra aren't necessarily what's showing up on the state tests. Since they want to see written-out strategies and baby statistics, teachers feel forced to stop and teach those concepts and skills. Some of the actual math I've seen on the tests look really simple for the age they're testing.

To prepare for the state tests in 5th grade, my math son spent a day working on how to draw out a problem with a big graph filled with X's as a means of "showing his work." Problem was, he and his cohorts could solve the problem mathematically in two seconds flat because they understood how to do so in the abstract (which would be the goal of any math testing, I would think). But they had to go backwards to get by any questions like this on the test. For them, it was like spending a day in a class two years behind them. They were bored out of their minds with the busywork and the entire notion of pretending they were slower than they were, but their teacher had to protect them. These state tests have often been used for placing the kids in the appropriate levels.

-- SusanS - 04 Nov 2006

Catherine,

It would be great (with all your free time!) if there was a math panel link on KTM with access to everything posted so far, including the posts you did on who everyone was. Of course, you could be laughing uproariously at this, but I thought I'd throw it out there.:)

-- SusanS - 04 Nov 2006

The math panel is finally taking off. The second link that Barry provides is especially interesting.

The first link is interesting because the textbook publishers all get up and speak about why the books have grown and where their influences for the books come from (state standards, NCTM).

The second one gets into Singapore's success and like Barry said, it gets a bit heated (at least for mathematicians.)

-- SusanS - 04 Nov 2006

It would be great (with all your free time!) if there was a math panel link on KTM with access to everything posted so far, including the posts you did on who everyone was. Of course, you could be laughing uproariously at this, but I thought I'd throw it out there.:)

that's just what I was thinking - how come I can't find stuff on my own website??

I have to think this through....

I think Barry has put everything up.

-- CatherineJohnson - 05 Nov 2006

It's going to take a while to go through the transcripts because it just makes me so upset.

Every once in awhile I decide to pace myself.

-- CatherineJohnson - 05 Nov 2006

Then I forget.

-- CatherineJohnson - 05 Nov 2006

Part of the complexity is that there is no single typical student.

boy oh boy, my eyes have been opened.....

the "no single kind of student" thing lets them get away with murder

that's why I keep coming back to Engelmann

for Engelmann there is a single kind of student

only difference is speed of learning of novel material in a novel field

after that, it's just teaching stuff to mastery

-- CatherineJohnson - 05 Nov 2006

when you go through a school system the way have, one foot in special ed the other in regular ed, the utter lack of responsibility for outcomes is blinding

and it's not just a lack of responsibility.....the people who work in and lead schools are responsible people (it's complex! there's not one kind of educational bureaucrat!)

it's that after all this time people don't believe it's possible for one human being, a teacher and/or a principal, to be responsible for another human being's (student) learning

our schools have been inputs operations for so long they don't actually know that it's possible to teach content

-- CatherineJohnson - 05 Nov 2006

part of the retreat to understanding - and I now see it as a retreat - is that you can just say the kids understand if they have so much as a glimmer of comprehension in their eyes

That was a key moment back at the beginning of Christopher's 4th grade year

He was getting 74s on math tests, and the math teacher said to me, "Don't worry, he understands the concepts."

I believed it.

It felt kind of wrong, but at the same time it made sense to me, the same way it makes sense to everyone else.

That's our problem.

-- CatherineJohnson - 05 Nov 2006

Because mathematics is widely misunderstood to be a linear sequence of skills to be mastered one at a time in a fixed order, some people think teaching mathematics is a matter of following a prescribed curriculum guide or mathematics textbook.

yeah, I guess that's why I'm getting 800s on practice SAT math tests after teaching myself Algebra 1 & geometry with Saxon math

-- CatherineJohnson - 05 Nov 2006

I'm going to take a few more tests, then start putting word out that Saxon is the book if you want your kid to get high scores

heh

-- CatherineJohnson - 05 Nov 2006

Her mother is a friend of mine and is worried she isn't learning math. She had her assessed for a learning disability. There wasn't one.

Her concern was due to a conference she had with her child's third grade teacher. Around May of third grade, the teacher told my friend her daughter needed a tutor. She was shocked! Why did the teacher wait until May to tell me there was a problem? So frantically she found her a tutor.

No more tutors.

Teach to mastery, or charge the district for the tutors.

I wonder if that's what we ought to push for. There's an anti-fields slogan going around, "Books not Bats." We'll make it "Tutors not anything else ever because two teachers for every single class is pretty damn expensive"

That'll look good on a bumper

-- CatherineJohnson - 05 Nov 2006

Mastery is the word that is missing from many educators vocabulary. If you read those links from Barry, it's fascinating the way a couple of people (teachers, I think) talk, in all seriousness, about exploring the algorithms, including the standard ones. This from a teacher who loves TERC, I think.

Another one also used the word explore to describe the learning of algorithms. Mastery must be connected too much to Kill and Drill for them or something. They did not hear the parent or the college professor who complained about kids not being able to do algebra because of a lack of basic skill mastery.

Some of these teachers seem to have no idea that EXPLORING the algorithms (including the standard one!) can lead to one big mess by middle school. They don't see it at all. They don't see the rise of the tutoring centers as having anything to do with what they're doing. They see happy kids because they're basically teaching math appreciation.

I'm with Steve. I'm going to have to read it a few more times because it is upsetting.

-- SusanS - 05 Nov 2006

some people think teaching mathematics is a matter of following a prescribed curriculum guide or mathematics textbook.

yes, that would be me.

-- BenCalvin - 05 Nov 2006

Prof. Wu, who is on the Math Panel has an interesting recent article on teaching teachers.

A great quote from page 5: "However a common mistake in discussions of mathematics education in the last fifteen years has been to confer blessings on the replacement of mathematics with pre-mathematics."

The whole article does what I think is an especially good job of pointing out that mathematics is not a matter of opinion. Also that hidden assumptions are not a part of mathematics and that, consequently, necessary conditions or assumptions should not be omitted from word problems.

http://math.berkeley.edu/~wu/hardwork1.pdf

-- SusanJ - 06 Nov 2006

yes, that would be me.

Me too.

-- BarryGarelick - 06 Nov 2006

I'm working backwards from the second meeting. It's slow. I'm on page 92 of 154. Some initial comments:

1. Sol Garfunkel is a piece of work.

2. Most speakers (not on the panel) have an agenda. They are pushing something in which they have a vested interest. It's quite amazing.

3. Stanley Ocken cuts through all of the crap and gets right to the point. Good for him!

-- SteveH - 06 Nov 2006

Susan,

Thanks for the Wu link. I'll read that along with all the math panel updates in my spare time. It gets addictive, this math education stuff.

With a real-life problem, students are confronted with puzzling questions they want to answer. Textbook word problems...present puzzling questions, but rarely are they questions students feel a need to answer.

Feels circular to me. Problems students want to solve = good; problems kids don't want to solve = bad. There, that should help illuminate the good from the bad for math educators. Since my daughter doesn't want to solve the EM, EM must be bad.

-- LynnGuelzow - 06 Nov 2006

I stuck with it and finished the second session.

It seems that those who are in the industry of education see things only from the inside out or from their own agenda. A few of the TERC supporters (teachers and math specialists) talked only in general or relative terms. They are happy with improvement. Most saw the problem only as teacher development and not curriculum. (of course) None of them looked at the big picture of getting to mastery in algebra or absolute (externally-defined) goals. It was only Stanley Ocken who got straight to the point.

In the panel discussion phase, my feeling was that they have way too much on their plate. There are too many side issues that will cloud the final report. There will be too many ways to pick and choose how to solve the "complex problem" of math education.

They do talk about defining what a proper curriculum should be (espeically leading to algebra), but they worry about the politics of defining a "national" curriculum. There was talk of calling it a "template". They really can't be wishy washy about what they are doing. I think it was Wu who said that they are perfectly capable of defining algebra and what is needed to get there. Politics is a separate issue.

I think they shouldn't worry about that issue either. There are other ways of doing the same thing. Look at high school with the AP Calculus test. This is an externally (nationally!) defined test that now drives the curricula in the honors tracks in most high schools. Parents and kids all know about AP courses. They talk about how many kids take the AP test and what their scores are on the test. The key is that the test is externally defined and administered. High schools can have all of the other math tracks they want, but they better provide a good AP track.

Unfortunately, the AP track is good only for those who can get there. We need the same sort of externally-defined test for the lower grades. Just like they have the SSAT test for kids going on to a private high school, they should define an AP(?) Algebra test for eighth graders. This will provide an externally defined and administered test (goal) for the lower grades. Public high schools can use the results of this test for more accurate placement of students. Placement is currently a big problem for high schools. Kids get all A's in lower school math and then are completely overwhelmed when they get to the AP track in high school. Lower schools won't be able to get away with this if they have an externally-defined test.

The problem is that most lower schools live in a context-free and accountability free world. They either dump the kids and problems off to high school, or they try to ramp up the curriculum very fast in 7th and 8th grade, leaving only the most able (or externally supported) kids as survivors.

An externally defined and calibrated 8th grade algebra goal would be a big step. Too often, lower schools get away with all sorts of weak algebra and pre-algebra courses. However, the bigger problem is full inclusion and their unwillingness to separate kids by ability.

How do you get lower schools to stop social promotion and expect mastery of specific material at each grade? They WILL NOT do this. Their only solution will be to ramp up the curriculum in 7th and 8th so that only the best will survive.

I see this as the fundamental conflict. It's not about teacher preparation and it's not about money. As long as they see math as some sort of complex process rather than simple hard work, many perfectly able kids will be left behind.

-- SteveH - 06 Nov 2006

Feels circular to me. Problems students want to solve = good; problems kids don't want to solve = bad. There, that should help illuminate the good from the bad for math educators. Since my daughter doesn't want to solve the EM, EM must be bad.

Kids don't like to do a lot of things. Too bad. What does the author do when confronted with kids who are confronted with the traditional problem that he eschews and finds it puzzling enough to want to answer? Oh, well, that's probably an honors student, he's likely to say. They're going to get it no matter what. Right.

-- BarryGarelick - 06 Nov 2006

If you read those links from Barry, it's fascinating the way a couple of people (teachers, I think) talk, in all seriousness, about exploring the algorithms, including the standard ones. This from a teacher who loves TERC, I think.

MASTERY is the missing word.

MASTERY & FORMATIVE ASSESSMENT.

I read the second transcript - wonderful! (I'll get some passages posted)

I think probably I'll put links to everything on the Recommended Reading page.

Yes, Stanley Ocken was great - I loved his line about how students when they get to college seem to have "forgotten" what they've learned.

That's the issue.

I talked to our math teacher dad yesterday. He showed me all his teaching materials!

Wow!

It was interesting, because while he is obviously a master teacher, and is teaching the Phase 4 course privately to his own child and to other people's kids, I don't think he'd ever heard of distributed practice.

He seemed to have invented his own form of it, which was to incorporate previous skills in everything he taught subsequently. The Prentice-Hall book does that.

That's a good approach - but I wouldn't be surprised to find that the Saxon approach of spending a lot of time practicing skills "in isolation" (horrible phrase), in their simplest forms, ultimately produces better "outcomes."

(help! help! I need new words!)

It was interesting, too, because the math teacher brought up spiraling as the safety net for kids who didn't learn things the first time around.

The way he talked about spiraling was very interesting.

To him (I don't think I'm misrepresenting) spiraling was just THE WAY IT IS.

He clearly doesn't have any choice. The curriculum spirals, so he has to spiral.

He's built in as much practice as a teacher humanly could, but he's done this somewhat "empirically" - i.e. he's learned that this works.

I'm thinking that if teachers & principals had directly read Willingham's two articles (on practice & inflexible knowledge) even teachers at the top of their game would be able to improve student learning.....

The Saxon books are fascinating to me not just as a math student, but as a person who writes about the brain.

You can see that he has explicitly & thoughtfully incorporated the findings of cognitive science into the structure of his books.

Working with them is such a pleasure.

-- CatherineJohnson - 06 Nov 2006

it is critical and possibly easier to find out why so many entering college students seem to have forgotten the algebra they learned in school

Stanley Ocken
page 86

-- CatherineJohnson - 06 Nov 2006