Charles

thanks for the link - I'll pull the whole article next week, when I get my two freebies again.

I'd already pulled an article from Ed Week, and it's the wrong one.

-- CatherineJohnson - 26 May 2006

I just saw that the National Math Advisory Panel is meeting today and tomorrow (June 28 & 29) in Chapel Hill, NC. Tomorrow, there is an open session with public comment. Here is a link to their agenda. Math Panel Agenda. There is a link at the bottom of the agenda to e-mail the panel. nationalmathpanel@ed.gov

Does anyone think it is worthwhile to e-mail the panel with a public comment?

-- LynnGuelzow - 28 Jun 2006

this appeared today at Education Week
but infuriatingly you need a subscription
to read the bloody story. anybody got such a thing?

June 28, 2006 Web Extra Women’s Association Demands Removal of Researcher From National Math Panel An advocacy group that promotes increased participation for women in mathematics is calling for the removal of the vice chairwoman of a newly formed national panel studying how to improve student performance in that subject, citing objections over research she conducted in the 1980s on gender differences in math reasoning. (June 28, 2006.)

-- VlorbikDotCom - 29 Jun 2006

wait. what's this? "two freebies"?
i'd better look into this matter further ...

-- VlorbikDotCom - 29 Jun 2006

yeah, okay, so here it is:
the Association for Women in Mathmatics
is collecting signatures for a petition
asking the Bush administration to remove
Camilla Persson Benbow from the Advisory Panel.

more from the AWM webpage on this story

seems like a pretty bad idea to me.
anyhow, i found it. sorry i blew up.

-- VlorbikDotCom - 29 Jun 2006

"Open Session for full Panel to discuss the Task Groups’ progress and coordination of the Task Groups’ agendas."

They already have task groups? It's hard to email comments when I don't have a clue what is going on.

-- SteveH - 29 Jun 2006

I just found that there are transcripts of the first meeting and a Summary of Math Panel's First Meeting available on the ed.gov website.

Here are the four subgroups or task groups that I think they established at their first meeting.

1. Conceptual Knowledge and Skills
2. Learning Processes
3. Instructional Practices
4. Teachers

The panel looks like it is going to meet every six weeks for three meetings, the Chapel Hill event being the first of these 3 meetings. I think it is great that they are putting up transcripts and summaries on the ed.gov website. A little government transparency is so refreshing.

-- LynnGuelzow - 29 Jun 2006

Thanks for the link Lynn. I'll give it a look.

-- SteveH - 29 Jun 2006

Thanks Lynn,

Liping Ma just cuts right through it now, doesn't she.

"Ms. Ma said that it puzzled her that they are talking about doing research to find out if seventh and eighth graders can learn real algebra when they have been learning real algebra in other countries for years."

-- SusanS - 29 Jun 2006

catherine:
i've just been following all those links
you created for the various panel members: wow.
what an amazingly useful piece of research.
mathreasoning.com should probably appear
at "vern williams" instead of the newpaper piece.

-- VlorbikDotCom - 30 Jun 2006

Who is this person? mathpanelwatch

He or She does NOT like Vern.

I like Vern.

-- BeckyC - 30 Jun 2006

Liping Ma just cuts right through it now, doesn't she.

Susan, Yes!

So I read through the whole thing... I was amused to note that a "Mr. Berch" is sure that we can't teach some little kids the same way we teach other little kids, and he seems intent on keeping this thought before the panel.

-- BeckyC - 30 Jun 2006

BeckyC^?, I love Vern. Also, Schmid. I've been reading the transcript of the first meeting -- I'm thrilled Wilfried Schmid is on the panel "some of the elementary curricula in the United States are a disgrace."

I think it takes courage to look at the NSF folks at the meeting and tell them "I think there is a great deal of money being wasted, and NSF, EHR is doing tremendous damage to mathematics education in the U.S."

I can't wait to see what happened at this latest meeting.

-- LynnGuelzow - 30 Jun 2006

"Algebra – what is it, what’s needed to be successful in it, when should it be taught and learned, is it for all or for some and are their more than one algebras?"

It will be interesting to see how this goal pans out. I wonder why there has to be a high-powered panel to answer this simple question. All of the problems in math start in the lower grades and the inability of schools to get many students to a real algebra course in 8th grade. It is less an issue of traditional versus constructivist and more an issue of low versus high expectations and competence. If they look at this as strictly a math issue, they will fail.

I don't know where this "more than one algebras" comes from. Reasonable people might disagree about what exactly should or should not be included in a proper course in algebra, but my feeling is that this isn't what they are talking about.

This is not just a technical or mathematical discussion. There are many educational philosophies and assumptions at war here. The best result would clarify this situation and put the choice (and money) into the hands of the parents.

-- SteveH - 01 Jul 2006

I feel really ignorant in this debate on "what is algebra." I thought I knew, but now I am lost. My son has just completed 8th Grade algebra, it included slopes, variables, solving for x in a variety of situations. That seemed like algebra. . . but, was it?

So, what is the issue? I really don't know what is controversial about this. What do the constructivist v. the traditionalist have to say about what is "algebra."

-- LynnGuelzow - 01 Jul 2006

Vern Williams was the one who brought up defining algebra before doing anything else. I wonder if there isn't more of a problem with this then we realize. Perhaps this is another growing reform idea. Algebra courses now need to be watered down to prevent ill-prepared students from failing.

Smartest Tractor's link above on Vern Williams is quite funny.

-- SusanS - 01 Jul 2006

I am a MAJOR fan of Vern.

-- CatherineJohnson - 02 Jul 2006

Do we need to collect signatures to keep Camilla Benbow on the panel???

-- CatherineJohnson - 02 Jul 2006

How do you find common ground between two opposing philosophies? Besides, a proper solution is not found by looking for common ground - a balance. Would this mean Everyday Math supplemented with more mastery worksheets? This might improve a student's ability, but it won't get them into a good algebra course in 8th grade. Will it eliminate spiraling and social promotion? The goal is not just slightly better math grades.

I'm back to this insight in the wake of 6th grade.

You just can't teach math via some-of-this, some-of-that. YOU CAN'T.

That's what we tried to do this year, only because we were so overwhelmed that we couldn't teach a separate curriculum at home.

It didn't work.

Reactive teaching probably lets kids pick up more fluency in certain skills.....but that's it.

If there's any way we can possibly pull it off - and some of that will depend on how stable Christopher remains & how mature he can become fast - we'll use Saxon Math from now on.

He's going to have to teach himself math, at least until he gets to high school.

The only way to do that is to use the Saxon books, and to do each and every problem in each and every lesson.

You can't "supplement" your way to knowledge, not under these circumstances.

-- CatherineJohnson - 02 Jul 2006

Lynn

I've been flummoxed by "what is algebra"?

I think Wu (I may be misremembering) defined it, in an AMERICAN EDUCATOR article, as "arithmetic with letters" - as an abstract form of arithmetic.

Then Parker & XXXX defined it as "the study of functions."

Lately I'm coming to think that "abstract arithmetic" and "study of functions" are actually fairly close to being the same thing.....that is, they are linked by the notion of the "variable," which implies that often there is a set of solutions that work, as opposed to one numerical answer.

All you math people - is this wrong?

Thanks!

-- CatherineJohnson - 02 Jul 2006

V - thanks!

I've got to pick up the house (people coming over) - I'll make a note to myself to get that done.

I loved your observation at Math Teach the other day (I think it was Math Teach)

-- CatherineJohnson - 02 Jul 2006

"Ms. Ma said that it puzzled her that they are talking about doing research to find out if seventh and eighth graders can learn real algebra when they have been learning real algebra in other countries for years."

heh

-- CatherineJohnson - 02 Jul 2006

Catherine,

You should go take a look at mathpanelwatch.org (or com, I can't remember.) The writers of the blog have very strong opinions and do not like Vern Williams. Interesting ad hominem tone used when discussing him.

-- SusanS - 02 Jul 2006

Thanks!

I'll take a look...

-- CatherineJohnson - 02 Jul 2006

oh, that's the mathematically sane guy

I think he's just one person - is that right?

I've come across him before....

-- CatherineJohnson - 02 Jul 2006

"Lately I'm coming to think that "abstract arithmetic" and "study of functions" are actually fairly close to being the same thing..."

They are similar in that both are forms of abstraction. A variable (usually) abstracts a number, where a function abstracts an operation. In computer programming terms, a function is a subroutine call; you feed it an input, and it returns an output based on the rules embedded in the function.

E.g.:

f(x) = x² + 1

If x is 3, then f(x) is 3² + 1 = 10.

If x is y + 4, then f(x) is (y+4)² + 1 = y² + 8y + 17

-- DougSundseth - 02 Jul 2006

Doug! Thanks!

I need to get your comments up front — where I won't forget them & can find them again....

-- CatherineJohnson - 02 Jul 2006

is MathPanelWatch done by the same person
(if indeed, it's only one person) as Mathematically Sane?
maybe. all i know is it looks just like
this shortlived astroturf site from June of 03.

meanwhile, i just wish they'd get on with
watching the math panel. i mean, the meeting
was days ago! let's have a report!
anybody? barry?

-- VlorbikDotCom - 04 Jul 2006

Sorry; I wasn't at the NC meeting. I was at the first meeting in DC.

The issue with algebra is pretty much as Vern described it. There are some courses called "algebra" which are suped up arithmetic courses. This has been a criticism in Maryland for the last few years. It is dumbed down, so that the school district can say that their 8th graders are taking algebra.

Also if you go to Mathpanelwatch (which is linked above), and look at the report of the first meeting, you'll not that the author criticizes Schmid for his omission of "patterns" and "generalization" in what algebra should cover. This is precisely what Vern is getting at. The weak definition of algebra (which Vern calls "mush") has it that algebra is about patterns--nothing (or very little) about polynomials, slopes of lines, symbolic representation, fractions and the like. So having students see the "pattern" in a sequence like 2, 4, 6... is considered part of algebra to these folks. A big part. The "generalization" I suppose comes in because the student is suppose to generalize a rule for the "pattern". Of course, there are an infinite number of rules that can apply, besides the obvious one of f(x) = 2x. Looking at the first three terms, sure, doubling the first three numbers will work. But suppose the rule is 2x + (x-1)(x-2)(x-3). You'll get 2, 4, an 6 for the first three numbers but for 4, you'll get 14. So 14 can be the next term in the sequence. So can 8. So can virtually any number you want.

I'll try to find out from Vern and others what happened at the second meeting. (Vern lives right behind me, by the way).

-- BarryGarelick - 05 Jul 2006

Mathpanelwatch has posted an e-mail from CPB to other panel members that suggests standards for evidence as they look at the scientific basis for research. Apparently, the constructivist crowd is worried that methodological designs that are scientific, consistent with best practices, with results that are triangulated and replicated will knock out some of their favorite programs.

From this observer's perspective it sounds a lot like the What Works Clearninghouse standards of evidence that have been set so high as to be essentially useless for making policy.

Interesting. .

-- LynnGuelzow - 05 Jul 2006

here's linda moran on panelists
ma, shmid, and whitehurst.

hey, who the heck is this?
there's a lot of KTM-relevant stuff here!

-- VlorbikDotCom - 07 Jul 2006

Barry While waiting for a transcript of their June meeting, I read the full transcript of the May meeting and I am convinced that I have a better charge for the committee...

1. VERN will tell us what he thinks algebra is.
2. VERN will tell us what instructional practices he uses to teach students of all races.
3. Then we go check with LIPING to see if she agrees.
4. If LIPING agrees, we let VERN write it up because he's got style.
5. And the panel is done, six months early.

For instance,

MR. WILLIAMS: I'm looking at the critical skills and skill progressions for students to acquire competence in algebra. I think we perhaps need to decide what algebra is, and if we can decide what algebra is, maybe we can decide whether students need a very excellent grounding in arithmetic skills. Because some people's definition of algebra, you don't really need to teach much of anything in grades K through six. If you look at some of the state standards and their testing, what they call algebra is basically putting a few ideas together and maybe discussing the rain forest. But if you are expecting the kids to be able to do an algebra course and to think algebraically, then we need to go in a specific direction as opposed to having the students prepared to do basic mush in seventh and eighth grade.

is much more fun when read in full than in summary. I'm all for specific directions.

Susan, here is the exchange between DEBORAH, VERN, and LIPING, in which LIPING is puzzled:

MS. BALL: Can I go back to my other comment that I didn't make before? I just would like to flag that as a panel, or at least as a panelist, I want to be very careful as we move into questions of ability, learning disabilities, the advanced student, because we live in a society in which race, which hasn't been mentioned so far, and ethnicity, culture, socioeconomic status interact dramatically with how we label students. And I'm very uncomfortable with us not finding ways to intersect those as we move into that territory, because the data on the enrollment of students into these programs and the intersection of culture and race is troubling. And I would like to make sure that as a panel, we aren't blind to that as we move into that question about quote "different abilities" and what we mean by ability in this society and school system.

MS. MA: May I make an observation? I am originally from China. I had my own middle school education in China, and now I moved to here. I have an observation which is that now we are talking about letting students learn real algebra and we want to do research to find out how children can do that, but in many countries over the world, they are already doing that, like those seventh graders, eighth graders are already learning algebra, and based on my study during recent years, at least I found that Russian students, Indian students, students from Singapore, Taiwan, Japan, and China, they are already doing that. So I was wondering what -- it really puzzles me that we want to find out how children can do it. On the other hand, people are already doing that or have been doing that for many years. So it's really a puzzle -- it really puzzles me.

MR. WILLIAMS: That's an excellent point. In fact, I teach students from Korea, from China, and they seem to not have a problem. Their parents don't need to do research. The country that they're from, they didn't need to do research. They have the attitudes, and their teachers had the content knowledge to teach the subject.

-- BeckyC - 08 Jul 2006

To me, DEBORAH is just blowing a lot of smoke, like in this exchange where she frets about whether the panel is going to get involved in defining a curriculum:

MS. BALL: I just think that if we become a curriculum committee where we're defining a course, we're in big trouble. I don't think that that's how I read our charge. And before we agree on that, I definitely want to hear other people's thinking. I see us as needing to talk about the nature of the domain we call algebra, which is the way I interpreted your comment, Vern. But I don't subscribe to the idea that we're going to define a course. I find that very problematic. I don't think that that's the charge of this group. And I stand to be disagreed with, but I'd like to hear that discussion. Because two different things are to say, “What's this domain of mathematics?” [and] “What are the skills involved?” I do think we need to talk about that. I don't think that means we should define the course.

I don't quite get it. How does she separate "domain" and "skills"? By the time you define what the core skill competencies are in a domain that everyone agrees to call "Algebra I", haven't you got the blueprint for a curriculum?

-- BeckyC - 08 Jul 2006

If I look at this in the most optimistic light possible, it could be that Ms. Ball fears that if the panel openly supports one type of curriculum over another that it will be hard not to be dismissed by whichever side of the "math war" that you are rejecting. Maybe she's trying to be political about it all. A lesson learned from the uproar following the "exemplary" and "promising" labels attached to particular math curricula in years past?

Would it be enough to state that a curriculum needs to teach certain concepts and skills systematically to mastery without undue repetition ("spiraling") in order for it to be an "algebra" course?

-- LynnGuelzow - 08 Jul 2006

There's no question in my mind that she is extremely intelligent, she has taught children in the classroom, and she has the best of intentions. I think she is absolutely serious.

But I think Deborah is too political -- too diplomatic. She had a lot to say at the May meeting, and most of it was: wait! we can't go there! we're not ready! it's a huge problem! In that case, we'll never be ready, by definition.

Deborah is talking about digging through years of research and simultaneously proposing years more research. She is in her element on a government panel!

Liping and Vern and others are convinced "by their own lying eyes" that not only have they seen algebra; they can tell you what algebra is and what our kids need to know to get there. I don't think it's helpful for this panel to dwell on teacher training issues or socioeconomic factors... if they can't even agree on the mathematical target.

I've read Deborah's recent exhortation to the teaching community in defense of specialized mathematical training for teachers... which means testing teachers to see if they learned the specialized mathematics they were supposed to learn. And you can tell she is walking on eggshells. She knows, I know, everybody knows that testing is offensive to teachers.

I've also read her 1999 article whose title Beyond Being Told Not Tell pokes fun at the TERC manifesto, Beyond Arithmetic. It's a candid analysis of times during classroom discussions when a teacher might need to grab the wheel from students who are about to drive the whole class off of the conceptual road.

-- BeckyC - 09 Jul 2006

Perhaps this should actually be a help desk question... So the MAA sponsored a group called Common Ground, and its reports were published just last year. Anthony Ralston, who wrote the case against long division has summed up his opposition to finding any common ground with Milgram and others. Does this point to where the National Math Panel is headed? A sad and useless end... or is there be a way up and out? What do Milgram and Wu know that I don't know about what they hope the panel will accomplish?

-- BeckyC - 10 Jul 2006

A taste of Anthony's objection to teaching the arithmetic of numerical fractions:

“The arithmetic of fractions is important as a foundation for algebra.” Many of you may think this statement is innocuous but I don’t. No one doubts that any non-trivial study of algebra must involve arithmetic with algebraic fractions. But while students should learn about reciprocals and the conversion of fractions to decimals and vice versa before college, it does not follow that prior study of the arithmetic of numerical fractions, even if still remembered by the time algebra is studied, is a good or necessary prelude to this. Indeed, the addition, subtraction and, particularly, the division of algebraic fractions is rather easier than the same operations for numerical fractions. So what if students come to algebra without knowing the arithmetic of numerical fractions? Just teach it as part of the algebra course. Not only are the algorithms generally easier but the more mature high school students will learn them more rapidly than middle school students. Then, if you wish, apply the algebraic algorithms to numbers.

-- BeckyC - 10 Jul 2006

Anthony makes a great case for school choice.

He goes on to say after the above quote:

"Research mathematicians need to understand that college and university mathematics educators generally, as well as many secondary school mathematics teachers, know and understand school mathematics. And research mathematicians will have to accept that the mathematics education community generally knows considerably more than they do about appropriate pedagogy for school mathematics."

Take that!

This "apppropriate" pedagogy apparently involves not teaching fractions until algebra:

"So what if students come to algebra without knowing the arithmetic of numerical fractions? Just teach it as part of the algebra course. Not only are the algorithms generally easier but the more mature high school students will learn them more rapidly than middle school students."

Apparently, algebra doesn't happen until high school. Opinions disguised as pedagogy and college learning.

Right. Anthony can go set up his own little experimental private school and see how many students he gets.

-- SteveH - 11 Jul 2006

"Does this point to where the National Math Panel is headed? A sad and useless end... or is there be a way up and out?

I don't want to see officially sanctioned "Balanced Math". It does, however, force the Ed School constructivists to defend their opinions in a more rigorous fashion. The best that the low expectation, fuzzy math crowd can do is to declare that this is their opinion.

There is actually no need for common ground, as in a common path for math. The best one can expect would be to have the panel define a rigorous course of algebra for 8th grade and the math required to get there. It should be a curriculum that provides an entry way to the high school AP Calculus track. If the fuzzies want to push their own opinions and curricula for math, they can do so, as long as they provide both paths and let the parents decide.

Common ground is a wrong goal. School or curriculum choice is the correct goal.

-- SteveH - 11 Jul 2006

So what if students come to algebra without knowing the arithmetic of numerical fractions? Just teach it as part of the algebra course

Sure. No prob.

I watched as more than a few kids got whalloped in high math algebra 1 due to being unclear on procedures (and concepts) from K-6. It didn't have to be. Which kids can take in all of that new material and newly learn how to manipulate fractions at the same time?

My own math head son lost a few procedures during the year, but he is capable of learning them within a week at most. However, we had to catch what was happening by hovering over every homework problem and checking every quiz that came home (not many did) to see if any gaps were forming. How many parents are going to do that? How many actually can?

The difference in his grade would have been big enough to put him in trouble for going on to Algebra 2 from our perspective. He squeaked out an A, but without his father it would have probably been a C or maybe lower. With his confidence destroyed we would eventually have had to consider holding him back.

-- SusanS - 11 Jul 2006

Which kids can take in all of that new material and newly learn how to manipulate fractions at the same time?

I'm thinking that waiting to teach fractions until high school is a terrible idea... but then again, I don't have a PhD^? so I'm not the one writing opinions that are given space on the MAA website.

Or maybe Anthony is not the wild-eyed radical he seems, but a hard-nosed realist, since it turns out that high school chemistry teachers say they have to teach the arithmetic of numerical fractions for the entire first month of Chemistry!

curriculum choice is the correct goal

This is the dog I have in the fight. I can pick up the pieces from Investigations in our elementary school. But I can't see how I'm going to pick up the pieces from Connected Math in middle school, and IMP in high school. Even though I have the mathematical background to do so, there aren't enough hours in the day! Taxpayers are forced to pay for instruction they don't want inside of the school day, and to buy instruction they do want outside of the school day. Is this the definition of a black market? :)

-- BeckyC - 11 Jul 2006

Yes! from Wikipedia,

Black markets develop when the state places restrictions on the production or provision of goods and services. These markets prosper, then, when state restrictions are heavy, such as during a period of prohibition, price controls and/or rationing. However, black markets are present in any known economy.

-- BeckyC - 11 Jul 2006

"Or maybe Anthony is not the wild-eyed radical he seems, but a hard-nosed realist, since it turns out that high school chemistry teachers say they have to teach the arithmetic of numerical fractions for the entire first month of Chemistry!"

Only if a realist is one who thinks reality is what walks into the classroom and not the sum total of all of the past years of low expectations and bad curricula. If many students don't know certain material, then the reason can't possibly be bad teaching or bad curricula. They are just not developmentally ready ("mature") yet. Do these people really send their kids to public schools?

-- SteveH - 12 Jul 2006

Perhaps I shouldn't call him a realist, but a cynic: Let the chemistry teachers do it since they're doing it anyways...

If he thinks of himself as a realist, you are right: he is a die-hard developmentalist.

Either way, it seems irresponsible.

I doubt Anthony Ralston has a child in school; and if he does, his child may be gifted, and not be in need of instruction like my children are in need. I'm willing to bet that a lot of mathematics PhDs have a huge blind spot when it comes to recognizing the painstaking and systematic instruction that average children require in order to achieve a useful competence in quantitative analysis.

If he has children, I would be delighted to hear personal anecdotes about how his child surmounted the difficulties of learning math by discovery. I'd be delighted to hear how Deborah Ball's children learned math. Or Skip Fennell's kids. I want to see evidence, not from some massive governmental study but from the successful postgraduate careers of children of the true believers. Unsullied by tutoring or Kumon.

They can come comment here at KTM -- we like to hear what has worked for other people's children. :)

-- BeckyC - 12 Jul 2006

Jeff Mervis of Science Magazine seems to think that the Common Ground document and the recent talks between NCTM and mathematicians is a signal that the math wars are over. Not sure everyone agrees with that. I know I don't.

-- BarryGarelick - 12 Jul 2006

Some very involved parents who are on our school committee have kids who do well. Because of this, and their basic belief in public schools, they really don't see any fundamental or systemic problems. They do see problems, but these have nothing to do with fundamental assumptions or curricula. Their kids do well because they are naturally smart, get help at home (or via tutors), or the parents don't expect a lot. I agree that these people seem to have a huge blind spot. They expect that other parents can or will do what they are doing.

Math is different because there are some very smart parents who are really very bad in math. They even acknowledge it. They have no way of judging whether their kids are just not good in math or that the curriculum is poor. Enough kids (one way or another) get into the honors math track in high school that they don't see a problem. They think that real math takes some sort of genetic math brain. Math is cumulative too. Unlike other subjects, you can't miss a bunch of topics and expect to squeeze by in high school.

I think it comes down to philosophy. What do you expect from grades K-8? Many don't expect very much. Learn to read. Learn to write. Learn some math. Learn stuff about history, geography, and science. Music and art are good too. All of the fuzzy, higher-order thinking talk of the Ed School types sounds good.

The Ed School types really seem to believe it themselves. What is incredible, I think, is that they consider it to be based on more than just assumptions and opinion, and that this type of education is for everyone. They even have people talking about "best practices" and "authentic" education. I would be embarrassed to talk about these things.

My opinion is that a number of things contribute to this state of affairs in the lower grades.

1. Many teachers who go into elementary education see themselves as nurturing types, not high expectation types. Perhaps they are drawn by the lack of need for specializing in a particular area of content knowledge and skills. (The need to pass algebra in college.)

2. These teachers do not value directly learning content (memorizing) and developing skills (drill and kill).

3. These teachers (on average) either struggled or did poorly in math. They think that the solution is to do something different from what they remember.

4. There is a curriculum and philosophy wall between grades K-8 and high school. High school is when many more kids, parents, teachers, and schools begin to take education more seriously. Unfortunately, much damage has already been done. The lower grades do not want to push. Middle schools, however, either continue with the warm and fuzzy philosophy or they start putting the screws to the students, but with the same poor and fuzzy curricula. This might depend on whether it is a separate school or part of one K-8 organization.

5. There is a history of curriculum and teaching methods independence. I know of no cases where parents or a school committee forced a school to change either of these. Schools and teachers feel very comfortable making all of these decisions. In fact, they do NOT want parental or school committee involvement.

-- SteveH - 12 Jul 2006

" ...the math wars are over"

The common ground document cannot do that because there are no implementation details. The only thing I saw was this vague comment.

"By the time they leave high school, a majority of students should have studied calculus."

Actually, I don't agree with this. the real goal should be to provide a rigorous course in algebra in 8th grade and a proper curriculum in the earlier grades to get most everyone to that point. If you do that, then the calculus thing will take care of itself.

As far as I can see, the CG work talks about what knowledge and skills are important in math, but it doesn't define grade-level expectations. To provide less wiggle room, they should have recommended a few rigorous algebra books as examples.

There might be common gound on philosophy and generalities, but WHO GETS TO DEFINE THE DETAILS?

-- SteveH - 12 Jul 2006

I say VERN gets to define the details!

One convenient stopping point for the math wars will be when all of the affluent suburban school districts in this country have adopted constructivist curricula that are so comfortable and easy to teach (you just run discussion groups! Because the kids teach themselves!! Isn't that fantastic!!! It's even BESTPRACTICES!!!!) and these districts are simultaneously buying all of the supplements on offer by the publishers of the constructivist programs AND running all of the teachers through implementation workshops... here's the scenario:

First we pay for the work of an adoption committee -- all of those teachers need classroom substitutes over the course of two years in order to attend committee meetings to discuss bestpractices. ||: Then we pay for the curriculum, in which only the teacher gets a textbook, and all of the children get workbooks, one workbook per unit (lots of units!). Then we pay for a summer implementation workshop for all district teachers to strengthen their content knowledge. Then we pay for the manipulatives. Then we pay for the accompanying supplemental skills workbooks that the publisher so helpfully suggests and has on hand, that are synchronised with the unit workbooks which are already in the basket. Then we pay for the reams of paper needed to copy family math letters to go home with the kids. Then we pay for teachers to host family math nights in the evenings to convince the skeptical. Then we pay for the reams of paper needed to copy skill development worksheets out of old textbooks from the 1970s that are kept in a school district vault. (But we don't pay for the time of the parents who come to school to make all these copies and grade them -- that's free. We also don't have to pay for Kumon -- parents are happy to pick up that tab.) :||

So the math wars will be over when all of the money has been made?

-- BeckyC - 12 Jul 2006

To summarize Steve,

1. I will nurture.
2. Learning should be fun.
3. Change is good.
4. Tomorrow is another day.
5. "No parent is going to tell me what to teach!" -- actual teacher's lounge comment overheard.

-- BeckyC - 12 Jul 2006

Jeff Mervis of Science Magazine seems to think that the Common Ground document and the recent talks between NCTM and mathematicians is a signal that the math wars are over.

Only if people like Hung-Hsi Wu can find and close all of the loopholes in the National Math Panel's definition of the K-8 mathematics instruction children must get to be ready to learn algebra in 9th grade. Loopholes that constructivists are forever finding and driving trucks through.

For example, at our school, the teachers have hit up the parent group to pay for "balanced literacy" materials that the state and district no longer provide. So reports like that by the National Reading Panel won't prevent teachers at affluent schools from teaching any old way they want, and charging parents for it, but it sure does prevent teachers at poor schools from teaching any old way they want. The money in our state is following the mandate for the inclusion of direct, systematic phonics instruction in K-3 reading programs, as a result of reports from the NRP. I'm thinking the Reading First initiative.

So... is there any "research" that shows that instruction in the arithmetic of numerical fractions should happen in 4th grade to prepare kids for algebra in 9th grade???

-- BeckyC - 12 Jul 2006

I've just found the second half of this comment thread, so will read the various articles & get them posted.

-- CatherineJohnson - 15 Jul 2006

I was curious about this statement, and I see Steve H has weighed in:

By the time they leave high school, a majority of students should have studied calculus.

My inclination is to disagree with this.....based partly in research I've read about job requirements and partly in the fact that Singapore high school students do not study calculus, but instead become very fluent in algebra.

That makes sense to me, though of course I don't necessarily trust my opinion on this....

-- CatherineJohnson - 15 Jul 2006

I haven't read the long division article yet, but it reminded me of a friend of ours who told us that her son, who is in college, still can't really do long division.

He scored close to an 800 on verbal SAT, which is very hard to do; he was somewhere in the low 600s on math (IIRC).

She doesn't think he can handle even one college level statistics course, so all the social sciences - which he's interested in - are out.

He had progressive ed K-5 and I think may have spent some time doing the KUMON worksheets. (I'll have to check that...)

-- CatherineJohnson - 15 Jul 2006

It's not just engineering and finance that are out.

It's ALL of the social sciences.

That leaves law, journalism, & history.

-- CatherineJohnson - 15 Jul 2006

It's not just engineering and finance that are out. It's ALL of the social sciences. That leaves law, journalism, & history.

Don't be such a pessimist. They can always be a barista at Starbucks.

-- BarryGarelick - 15 Jul 2006

I don't see the need for a majority of people to study calculus in high school. Calculus is good mental discipline and important for some fields of study. But not something that I'd recommend as a universal experience. The mental discipline can come from other rigorous math courses.

In my life, the ONLY time that I ever use calculus is to TEACH calculus.

I'd much rather see high school graduates very fluent in algebra, able to do the math necessary to make wise decisions about personal finance, and able to form meaningful hunches about the data that's served up by the media.

-- RudbeckiaHirta - 15 Jul 2006

That leaves law, journalism, & history.

And Theatre and Recreation. Oh, you meant something you can make a living at.

-- SusanS - 15 Jul 2006

I don't see the need for a majority of people to study calculus in high school.

I tend to agree with that. There is a feeling, however, that without calculus in high school, students can't get into a top flight school (like Harvard, Stanford, Princeton, Yale, etc)

-- BarryGarelick - 16 Jul 2006

FWIW I had excellent instruction in Algebra I, Geometry (with 2-column proofs), Algebra II, and Trigonometry in High School. And I took Engineering Calculus in my freshman year of college, and aced it. The lady who taught Engineering Calculus was a full professor, and she was such a good teacher I have forever after thought that calculus was a subject everyone should learn before they die. !!! Not everybody shares this opinion, I know.

I am a bit skeptical of the quality of the AB or BC Calculus experience in high school.

-- BeckyC - 16 Jul 2006

BC calculus is a good course on par with the engineering calculus taught at most reputable universities. A kid who scores a 4 or 5 on the BC calc exam knows calculus.

AB is watered down to omit the "hard" parts. It would be an OK course for someone headed into a quantitative social science at the undergraduate level -- perhaps someone who wanted to study economics but who had no plans to go to graduate school.

Unfortunately for many of my students, the high schools that they attended offer "calculus" courses that are not AP and where the students don't take any outside exam. Most of these courses are a waste of time: the students would be better off spending that year getting a firmer grip on algebra to prepare them for a real calculus class.

-- RudbeckiaHirta - 16 Jul 2006

Rudbeckia

I'd much rather see high school graduates very fluent in algebra, able to do the math necessary to make wise decisions about personal finance, and able to form meaningful hunches about the data that's served up by the media.

I'm glad to see you say this.

That is exactly my thought. Have kids do enough algebra, for enough years, that it becomes second nature - have them really GET it.

That's a great way of putting it.

-- CatherineJohnson - 20 Jul 2006

i've just found the transcript for the june meeting (here).
the transcript for the may meeting was fascinating—
you could see the whole thing going to hell
right in front of your eyes (as is more or less
in the nature of a committee of any kind in my
[thankfully] limited experience: the real issues
get put aside to work on trivia; i take it that
this is in service of maintaining the status quo).

meanwhile, nothing from MathPanelWatch.

-- VlorbikDotCom - 04 Oct 2006

whoa.

-- VlorbikDotCom - 05 Oct 2006

this thing is amazing.

-- VlorbikDotCom - 05 Oct 2006

(i'm channelling catherine.)

-- VlorbikDotCom - 05 Oct 2006

but no. really. go print it out right now.

sure and some of the speakers are so ill-prepared
that their testimony is mostly just fumbling around.
others are plenty well-prepared provided we agree
that learning to speak edu-buzzwordese like a native
to cover up for having nothing to say counts
as preparation.

but there are quite a few moments of shining honesty.
i didn't expect that. i was particularly impressed
with hyman bass's testimony (& the follow-up;
evidently the panel was impressed, too).
i always kind of took it for granted that he
was some kind of traitor to actual mathematics
since he's always being thrown in one's face
by math-teach's arch-troll MPG as evidence that
even a world-class mathematician can take math ed seriously.
but no. he actually does take it seriously!
ok. gotta do some actual work. long live KTM.

-- VlorbikDotCom - 05 Oct 2006

Vlorbik,

Thanks for link to the panel minutes. This is great stuff. I've just read Bass so far. I liked his point that estimation is harder and requires a more advanced understanding than exact arithmetic.

I also especially appreciated what he said about the difficulty of teaching mathematical modeling. "If you want to do it seriously, you have to pay attention to the integrity, not only of the mathematics, but of the context."

(BTW, you did a great job channeling Catherine!)

-- SusanJ - 05 Oct 2006

It is fascinating stuff. I'm pretty sure that if there had been no KTM I would have never known what anyone was saying due to some of their expert uses of edu-jargon. Too bad there's no video.

-- SusanS - 06 Oct 2006

There does seem to be a lot of discussion on what they need to be discussing.

-- SusanS - 06 Oct 2006

There does seem to be a lot of discussion on what they need to be discussing.

Agreed. When I wrote "great" I had both meanings in mind. Useful insights about math and useful insights about the ridiculous nature of "ed speak" and how we got into this mess.

No one seems to want to deal with the elephant in the room which is whether there is any solution when the teachers don't understand the material. I was interested in the idea where master teachers broadcast a lesson (online?, video-conferencing?) which is then carried further by the classroom teacher (who is hopefully learning along with the students.)

-- SusanJ - 06 Oct 2006

wow - I'll pull the transcript -

-- CatherineJohnson - 06 Oct 2006

i'm channelling catherine.

I'm lol-ing!

you ARE channelling catherine!

-- CatherineJohnson - 06 Oct 2006

or that the world is now saturated with data and a primary role of mathematics is to find patterns in, or if you like, functions to model these data

That's from Bass - very beautifully put, I think

Klein's more recent history of developments in math ed & math wars is a terrific accompaniment to this

Apparently constructivists consciously set themselves against the "physical" uses of math, as in engineering, in favor of the social science uses, as in statistics & data analysis

I'll get links and quotes later....

I'm going to go out to lunch & get a grip.

-- CatherineJohnson - 06 Oct 2006

wow

I can't stop myself - I'm still reading his section - it really is very beautiful

that kind of clarity of mind

incredible

(I'm reading the section about the "legalistic" argument concerning What is algebra & his follow-up on the fact that we haven't had much time to comprehend or imagine a mode of teaching a mathematical modeling form of algebra)

-- CatherineJohnson - 06 Oct 2006