National Council of Teachers urges streamlined math curriculum

Tessellation on Tessellation, originally uploaded by *Sherry*.

A report by the National Council of Teachers argues that State math curricula need to be streamlined:

The report urges teachers to focus on three broad concepts in each grade and on a few key subjects -- including the base-10 number system, fractions, decimals, geometry and algebra -- that form the core of math education in higher-achieving nations. Some are calling Focal Points the most significant publication in the field since the 1980s.

R. James Milgram, a Stanford University math professor who is among the harshest critics of U.S. math instruction, said the 41-page report aligns teaching "with what is being done with unbelievable success" in other countries. The curriculum would teach a few topics intensely and have students master them and move on rather than teach many topics briefly and repeatedly over several years. [WaPo]

This seems germane to yesterday's discussion of math pedagogy in the US vs. other countries. I'm not an expert, but it seems like a good idea to focus intensively on the most basic skills in the early grades instead of introducing a large number of topics in less detail.

Comments

[Danton]

Great.

Now how about teaching our kids to write well? Maybe hire a few more teachers and decrease class sizes so teachers could spend some time reading and guiding kids through the process?

[mudkitty]

When will they realize you don't teach math, you teach money!

[Njorl]

But what about Roman numerals!?!? Think of the poor children who wind up seeing Star Trek III when they wanted to see Star Trek II.

[Frankenstein]

One word: Kumon.

[dr nobody]

"Now how about teaching our kids to write well? Maybe hire a few more teachers and decrease class sizes so teachers could spend some time reading and guiding kids through the process?"

But it's so much easier to them them to write good. Seriously though, where do you propose finding all these wonderful teachers? Funny how math/science teachers don't bloviate about "guiding kids through the process," even though the same concept is equally applicable -- if not more so -- in their fields. Their just aren't enough competant teachers to hand-hold every student. We have to figure out how to teach students how to learn and that no one is going to do it for them.

[Alon Levy]

Lindsay, the Focal Points document goes too far in trying to simplify matters. Instead of teaching too many concepts too early, it teaches too few too late. We can compare it to traditional math education, which apparently was fairly decent back in the day when people walked 10 miles in the snow to school, uphill both ways.

For example, traditionally, students learn multiplication in first or second grade and memorize the multiplication table up to 10 or 12 by third grade (which if I remember correctly is what also happened with my sister, who's been going to IB schools since the middle of second grade). Focal Points would have US schools only introducing multiplication in third grade and students master it only around fifth grade.

[converger]

I am deeply suspicious of any initiative supported by Milgram. The man has been a tool of the Christian fundamentalist wing of the math wars (I know it's hard to comprehend why math or reading pedagogy would be a religious issue - but it is) for over a decade, and has been tireless in his bizarre assertion that long division - the least efficient of a dozen different algorithms for doing division - is not only the critical basis of any form of advanced mathematics, but that any exposure to a different division algorithm irreversibly destroys any cognitive capacity for understanding mathematics.

Do we need more consistency across state math standards? Sure. Should we be doing our best to converge on best practices across a wide range of learning styles? Absolutely. But the devil is in the details, and the toxic legacy of the math wars makes every report like this one fraught with political intrigue. Be careful out there.

[Firebug]

The reason why we have a shrinking number of science and engineering students isn't because of poor math skills. It's because anyone smart enough to enter these fields is smart enough to see why it is a losing proposition. If we want to increase the number of American scientists and engineers, we need to crack down on offshoring and eliminate H-1B visas. As of now, it's well known that an engineering degree is nothing more than a ticket to the unemployment line if you're over 40 years old - right when people in other professional careers are entering their peak earning years.

Milgram is also full of crap for another reason. The vast, vast majority of people will never have to do long division (let alone factor polynomials or any of the other stuff Milgram says this is important for) in their adult lives. The basic curriculum needs to have enough math for people to be functional adults and to know whether they might be interested in more intense study. Teaching everyone algebra is a waste of time. I'd rather if the traditional Algebra I course were replaced by a course of basic logic in which students were taught how to reject logical fallacies. Or a course on the U.S. Constitution and the structure of American government. Really, there are any number of things that would be a better and more productive use of class time for most students.

[1984 Was Not a Shopping List]

(I know it's hard to comprehend why math or reading pedagogy would be a religious issue - but it is)

This reminds me (as so many things do) of an Onion headline: "Creationists Protest Third Law of Thermodynamics"

Funny--I first read the headline as:

National Council of Teachers urges streamlined myth curriculum

[Alon Levy]

The reason why we have a shrinking number of science and engineering students isn't because of poor math skills.

Actually, the US is performing quite badly compared to other countries. Everyone who goes to academic schools in the European countries I know something about has to learn calculus to graduate (and almost everyone does). In the US only honors students ever learn how to differentiate and integrate anything.

The reason Americans are losing math jobs to Indian and Chinese immigrants is that Indians and Chinese tend to be better at math. Deal with it and stop whining about foreigners taking your job.

[RickD]

It's hard for me to tell whether the recommended changes are going to be useful or not. I'm a bit concerned that multiplication is to be delayed until third grade or later.

An interesting point in the critique Alon mentions is the usage of calculators in schools. Basically, kids don't need to be using calculators, and in fact would probably learn more if they had no access to calculators, but one of the cheapest way for school districts to spend money and appear to be "serious about education" is to buy calculators or computers. When it comes to math, what most schools need is not so much a revision of the curriculum, but better teachers. This is especially true at the secondary school level.

Getting better teachers would require more money, though.

FWIW, Math Ed. really is a distinct field from mathematics in that I can be qualified to use math at a high level in my day-to-day work (I am) and yet not really have an idea about what the best way would be to get most kids to understand the basic methods of math. What topics need to be taught in what order? I really don't know. I went to primary school in the 70s, a bit after the New Math fad had come and gone. My feeling is that primary math education should be based both on training skills by rote and on introducing the larger concepts: functions, geometry, logical reasoning, etc. New Math's problem was that it was too abstract for most of the people teaching it, not to mention the kids who were supposed to learn it.

[Clare]

It's worth bearing in mind that in India, at least, only a very, very small number learn math to the kind of level that they are eligible for engineering jobs either inside, or outside the country. The challenge in the US, with a (happily) well-rooted public education system, is not to get a few to that level -- we can do that -- but to establish what average achievement in math for the entire population should be, and how to achieve it.

[Danton]

"Their just aren't enough competant teachers to hand-hold every student."

"Their" ? "competant"?

Look, the point is that teaching kids to understand the rhetorical nature of texts, and getting them to write more and regularly, are both ways of teaching them to think and think critically.

At any rate, when I was in high school, I wrote a "theme a week"--a two-page paper (typewritten) addressing a topic suggested by assigned reading. The teachers could do this because they had smaller and fewer classes, and more variety in their class assignments. Teaching English in high school is far more regimented now. The teachers have more students in their classes and they tend to teach at one grade level, at least here where I live. Thus, the techer who assigns a two-page paper to all his or her classes winds up having to grade 150-175 papers a week. That's simply untenable.

[Clare]

It was a two-hour late start in school today, so I asked my 15 year-old daughter her thoughts on math instruction at school. She felt that it was pretty good in elementary school, when they had plenty of time during the day to absorb and practice new math skills. As the grades have progressed, she has found that new material gets piled on from week to week, and day to day, and that sometimes there is very little time to get confident with one kind of exercise or concept before moving on to the next. She also said she found teaching styles very variable from year to year. Interestingly, she was not too enamoured of calculators, complaining that on occasions too much time can be spent plugging things into calculators when she'd like to do more pencil and paper practice, or cover the concepts. Well, that's just one kid's thoughts anyway....

[Lindsay Beyerstein]

I think drill is underrated in high school math. Kids who want to go on in the sciences need speed and accuracy to excel in first-year science classes. The fact that you "get" the concept of fractions and decimals and basic operations there on simply isn't enough. You won't ace your Chem 101 midterm unless you can manipulate those algebraic symbols as deftly as and confidently as nouns and verbs in sentences.

[Firebug]

Alon: Then how do you explain the huge number of unemployed over-40 techies? Did they somehow lose their ability to do advanced math over the years? Don't feed me that line of bullshit. Corporations go for cost, not quality. Until US corporations are keelhauled, there will be no point in most people learning advanced math.

[Alon Levy]

Did they somehow lose their ability to do advanced math over the years?

No, but Indian and Chinese immigrants are just better at it than they are. I know that aptitude for theoretical math decreases with age, but I don't know if that's also true about engineering.

[jose]

I think drill is underrated in high school math

I think that you have the right idea about not only stressing concepts but also stressing repetition, but I think that there is a potential to lose the concept and just learn the process. As a TA for undergraduate engineering classes, I find that the emphasis is always on learning the steps to do something, and not on understanding why. I think at all levels the connection between concepts and solution methodology is very lacking. Students just want to plug numbers into a mysterious formula, and no one cares where it came from or why they are using it.

As for the unemployed engineers over 40, the traditional reasoning is that when people get older they lose their ability for innovation. There may be some truth to that, but I think that the main reason is like Firebug said, senior employees cost more, and quantity is infinately valued over quality.

[Jeff Rubard]

The idea that the short-term success of Indian and Chinese immigrants can learn us good about broad-spectrum math education in the US is straight from the Ronald Reagan school of idealist garbage. Those people are not typical results of an exotic foreign method for internalizing math fundamentals which we have become too soft for the likes of, but exceptional (and exceptionally privileged) imitators of the American method, as attested to by the numerous Indian reviewers of (garden-variety US) math and computer science textbooks on Amazon. They represent the ne plus ultra of American pedagogical ways, not an exception to them; they were already singing along with Mitch Kapor.

Furthermore, when we consider less-than-ultimate results, I suspect that American results are not entirely grim. It seems quite possible that a study would show more average Americans are familiar with the rudiments of set theory (thanks to the New Math which was maligned in the previous iteration of this debate) than elsewhere in the world, and such skills are real mathematical knowlede, useful or not. And when we reach those whose math skills fall below average levels, only a true grit-addled go-getter could fail to see that the main problems with learning math supervene on the problem of being young in the US: the milieu is nasty and brutish as well as short, and generally aptitude for theoretical math increases with caloric intake.

[1984 Was Not a Shopping List]

>Until US corporations are keelhauled

Cruel as it would be if taken literally--and please, don't take it literally--that's a funny image if taken literally. Andrew Fastow, or your favorite CEO, lashed to the keel and going under, in his or her business suit.

[Alon Levy]

generally aptitude for theoretical math increases with caloric intake.

If I'd known that in time, I'd never have even applied to grad school (for the benefit of people who haven't seen me in person: my caloric intake is less than 2,000/day).

[Lindsay Beyerstein]

I'm very pleased to find there's so much interest in math teaching! I'll keep that in mind for future posts.

(OT @Alon: Do you deliberately restrict your caloric intake, or is that just how it works out?)

[cooper]

It was a two-hour late start in school today, so I asked my 15 year-old daughter her thoughts on math instruction at school. She felt that it was pretty good in elementary school, when they had plenty of time during the day to absorb and practice new math skills. As the grades have progressed, she has found that new material gets piled on from week to week, and day to day, and that sometimes there is very little time to get confident with one kind of exercise or concept before moving on to the next.

Welcome to the real world of applied physics/math.

Frankly, we need more of this, not less.

[cooper]

I think drill is underrated in high school math. Kids who want to go on in the sciences need speed and accuracy to excel in first-year science classes. The fact that you "get" the concept of fractions and decimals and basic operations there on simply isn't enough. You won't ace your Chem 101 midterm unless you can manipulate those algebraic symbols as deftly as and confidently as nouns and verbs in sentences.

I think you are misrepresenting this. You will "ace" Chem 101 or E-Mag or Parti Dy if you know how to do it on your HP48 or TI 8X, not if you know how to do it on paper.

This is the problem with "math" We teach paper technique to the exception of useful math survey.

[Jeff Rubard]

If I'd known that in time, I'd never have even applied to grad school (for the benefit of people who haven't seen me in person: my caloric intake is less than 2,000/day).

If only you had been around 60 years ago: you could have shown Gerhard Gentzen how it was done. Seriously, this is the George Gilder subtype of Reaganite idealism: surely it is about as well understood as can be that physical distress from deprivation, such as the American underclass experiences on a daily basis, is a bar to normal functioning in all areas, and tossing off a tea anecdote isn't going to change that. "Mind over matter" only works for those lacking neither: substantive public policy analysis demands seriousness, not dis-ingenuity.