September 18, 2006

Cats and Dogs Getting Along

Today's NY Times editorial, Teaching Math, Singapore Style, is a rare bird. I don't completely disagree with all of it. Clearly, it deserves a full analysis.
The countries that outperform the United States in math and science education have some things in common. They set national priorities for what public school children should learn and when. They also spend a lot of energy ensuring that every school has a high-quality curriculum that is harnessed to clearly articulated national goals. This country, by contrast, has a wildly uneven system of standards and tests that varies from place to place. We are also notoriously susceptible to educational fads.

Is there any problem that the NYT editors don't think can be solved by nationalizing it? If there is, I haven't seen it. We call that "wildly uneven system of standards and tests that varies from place to place" federalism and it's proven to be, by far, a more successful system than centralized top-down systems beloved by NYT types.

While it is true that "[w]e are also notoriously susceptible to educational fads" it is only because we are burdened with idiotic educators. Who do you think will be influencing those national standards? Groups like the National Council of Teachers of Mathematics (NCTM), of course. Their grimy paws will be all over any standards. Set the wayback machine to 1989:

One of the most infamous fads took root in the late 1980’s, when many schools moved away from traditional mathematics instruction, which required drills and problem solving. The new system, sometimes derided as “fuzzy math,’’ allowed children to wander through problems in a random way without ever learning basic multiplication or division. As a result, mastery of high-level math and science was unlikely. The new math curriculum was a mile wide and an inch deep, as the saying goes, touching on dozens of topics each year.

Many people trace this unfortunate development to a 1989 report by an influential group, the National Council of Teachers of Mathematics.

Now imagine if that "unfortunate development" were enshrined into national law. It only took nearly a generation of mathematically crippled kids for the NCTM to come to their senses. And, even then, if you listen to their current rhetoric, they're still claiming nothing has changed.

School districts read its recommendations as a call to reject rote learning. Last week the council reversed itself, laying out new recommendations that will focus on a few basic skills at each grade level.

That's because that's exactly what their recommendations said. By the way, what the NCTM calls "rote learning" is anything but. A lesson they still haven't taken to heart yet.

Under the new (old) plan, students will once again move through the basics — addition, subtraction, multiplication, division and so on — building the skills that are meant to prepare them for algebra by seventh grade. This new approach is being seen as an attempt to emulate countries like Singapore, which ranks at the top internationally in math.

All these references to Singapore are encouraging, given this country’s longstanding resistance to the idea of importing superior teaching strategies from abroad. But a few things need to happen before this approach can succeed.

Quite a few things, in fact. Almost all the textbooks have to be rewritten for starters. Then teachers will have to learn how to use those rewritten textbooks properly, something that Ed schools have failed to do. And, then:

First of all, the United States will need to abandon its destructive practice of having so many math and science courses taught by people who have not majored in the subjects — or even studied them seriously.

And, then:

We also need to fix the current patchwork system of standards and measurement for academic achievement, and make sure that students everywhere have access to both high-quality teachers and high-quality math and science curriculums that aspire to clearly articulated goals.

So, they got half of it right. That's good for the NYT.

Until we bite the bullet on those basic, critical reforms, we will continue to lose ground to the countries with which we must compete in the global information economy.

Close enough.


rightwingprof said...

Okay, it's been over three decades since I was in high school, but one thing I am curious about is when, and why, did the curriculum move back? In my high school (grades 9-12), the college prep math track was Algebra I, Geometry, Algebra II/, Introductory Calculus, with trig spread across the junior and senior years. I suppose a lot of what we did in junior high could be called algebra, at least pre-algebra math.

I was, btw, the last class in our high school who were able to take two years of Latin (they were just phasing Latin out nationally).

Anonymous said...

"Almost all the textbooks have to be rewritten for starters"

No, they don't. In industry this is called a "buy versus build" decision. We *could* just start purchasing textbooks from Singapore. I bet we could get quite a discount, too, given the volumes.

We won't, of course ...

-Mark Roulo

KDeRosa said...

Unfortunately, our math teachers don't know enough math to teach out of the Singapore math books.

There's always Saxon and Connecting Math Concepts. But the chance of either of those two curricula catching on is also slim, though they are both certainly aligned with the NCTM's new focal points.

rightwingprof said...

Why rewrite the textbooks? We have perfect fine textbooks -- they've only been out of print for years. There's nothing to update -- 2 is 2, whether it's 1976 or 2006.

KDeRosa said...

when, and why, did the curriculum move back

I believe the answer is the early 90s in response to the NCTM's original math standards. Though certainly trouble was afoot before that.

I went to a Catholic high school in the early 80s which offered two years of Latin and a year of Greek. Latin was clerly on the wane, though; only six students were in my Latin II class. I transferred in my mid-Junior year to another Catholic high school that did not offer Latin -- so I only wound up with a year and a quarter under my belt.

rory said...

I think I am going to scan a few pages of my kids 3rd grade math text books next time they bring them home. Its all bright and cheeful... has lots of fun little facts... and not bogged down with all those bothersome numbers and problems.

One question. I was under the impression that Singapore math was mostly concentrated at the elementary and middle school levels? At least in elementary school, surely even the typical liberal arts degree teacher should be able to teach the level of math required at this age. Middle schools and high schools would be the ones that would really need the qualified teachers. Unfortunately, teachers are paid well compared to college graduates with liberal arts degrees, but are poorly paid compared to graduates with engineering, science and math degrees. There needs to be more flexibility to pay people comparative with their skills, instead of the one pay scale fits all. I would love to be a math teacher, but the average starting salary here for a new teacher with a math degree is around $30,000. If I was willing to accept that amount of money, I might as well just get a degree in basket weaving.

KDeRosa said...

The problem with the traditional textbooks is that too many students were not mastering math. Sure, they were great for that top 20% of the class. That group learns using pretty much anything. The bar is set low.

I think, however, that these traditional books were not written with the average math student in mind, not to mention the lower performers. These kids need the concepts broken down a bit more finely and they need much more practice than the traditional textbooks provide before they will understand and retain the material.

We've learned a lot since the old traditional textbooks were in common usage. Singapore Math, Saxon, and CMC all represent improvements on traditional math.

KDeRosa said...

Do you know the math curriculum they use, Rory?

Singapore's math curriculum is called Primary Math and goes from grades K to 6. Every student regardless of ability goes through the same sequence. Then it's off to algebra at which time the kids get tracked. Nonetheless, they all learn algebra, some just go a bit deeper than others.

Here are the placement exams. They are no walk in the park.

You really shouldn't need a math degree to teach elementary math. But when schools fail to teach math properly at the K-12 level anyone without a math degree tends not to know enough math to be able to teach basic math effectively.

Anonymous said...

The Chinese teachers certainly don't have math degrees.

But I admit I was shocked to find that college algebra was not required to get a teaching degree. That seems pretty basic. Even if you're a third grade teacher, you need to know where they're headed.


allen said...

I'm a computer jock and the first phrase that comes to mind when I see the discussion about math books is "open source!"

Are there any open source textbooks? I know you could do as little as scan in a textbook that's out of copyright (what is it now? fifty years or something?) and not be too far of the mark. Still, I'd like to think that we've learned something about how to structure textbooks in the last fifty or sixty years and could do better then those textbook authors. Not that the knowledge is valued by the buyers of textbooks but that's a separate issue.

rory said...
This comment has been removed by a blog administrator.
allen said...

I guess I should have googled before posting:

Sean's Applied Math Book

Sun's McNealy Leads Non-Profit Open-Source Drive

Do Open-Source Books Work?

The search string I used was "open source math textbook" and holy-canolli, there's a bunch of textbook projects, both open source and interestingly, free but not open sourced.

Just to see how much it might cost to get a dead-tree version of an open source textbook into my hands, I got a printing estimate from Kinko's for this textbook of American history. 158 pages, black and white on 20lb paper, comb binding. $16.63.

If you want color the price is astronomical, $144.53, but as the technology advances and competition works its magic, that should come down.

rory said...

My book is Mathematics: The Path To Math Success!

A review of the 2nd grade version is over at

Overall Evaluation [3.4]

Students using this program have a reasonable chance of moderate achievement levels. On the other hand, this program is not seen as supporting high achievement levels. It is possible that a skillful teacher could overcome some of the limitations of this program and use it more effectively. The heavy reliance on models and the potential confusion in the treatment of perimeter are examples of areas where an effective teacher could improve upon the student learning supported by this program.

KDeRosa said...

I could be worse I suppose.

The best way to deal with a crappy program like that is to preteach your kids basics so they can use the dopey problem solving exercises as additioanl practice instead of for "discovering" math.

Catherine Johnson said...

Have you read KNOWLEDGE DEFICIT yet?

I'm persuaded we need national curriculum standards. Hirsch says all you need is 40% to 60% of the school day devoted to everybody learning the same core stuff. (I think he starts at 40%.)

The problem for American students is huge mobility, including schools with greater than 100% student population mobility per year.

I don't see it happening federally, but I can imagine it happening via NCTM & the like - via NGOs that appoint themselves guardian of the standards.

I keep hoping Courant will produce a set of grade by grade standards.

KDeRosa said...

No, I haven't. Is there anything more in it than what's avaialble inother paper's he's written?