*Roberta M. Eisenberg is chair of the UFT Math Teachers Committee. *

As controversies rage about the best way to teach math and whether students should be allowed to use calculators — incidentally, the State Education Department on Dec. 1 declared that calculators will now be considered teaching materials, like textbooks, and schools must provide them to students — the real question is why children in this country are not better at learning math. Is it the curriculum? Is it the equipment? Is it the tests? And, haven’t we heard all this before?

In 1957, the Russians sent up Sputnik, stealing a march in the space race, and the United States decided that something had to be done, in a hurry, about math and science instruction in this country. Thus were born National Science Foundation grants to teachers of math and science so that they might get master’s degrees in their subjects rather than in education. A generation of teachers excitedly brought their advanced knowledge back to their classrooms.

Also in the early ’60s, the so-called New Math was influencing curricula across the country. The result was an emphasis on concepts to the detriment of the basics. Naturally, there was an eventual backlash when parents could no longer understand their children’s homework.

By the ’70s, teachers in middle and high schools were noticing that students were getting weaker on their recall of times tables and other basics. This could not then be blamed on calculators because there were no calculators yet in general use.

In the ’90s there was growing concern that lack of math skills by American kids would reduce us to a third-world economy. A few weeks ago, an article in The New York Times said essentially the same thing. In “As Math Scores Lag, a New Push for the Basics” (Nov. 14), Tamar Lewin stated, “For the second time in a generation, education officials are rethinking the teaching of math in American schools.”

This was not the second time nor was it only in one generation. Changing the curriculum has been going on for at least 150 years. At one time, the math skills needed by the citizenry were mainly arithmetic and practical geometry. Carpenters knew about rectangles and squares in order to produce cabinets with right angles in the right places. Very few people went to college, and therefore very few needed to know algebra and more advanced math.

It is instructive — and funny — to read some of the old tirades against slide rules and typewriters. They were blamed for students’ loss of ability to do times tables, and it was even claimed that students would no longer be able to write legibly.

Every advance in technology has brought about changes in curriculum. The State of New York has been very slow in permitting and then requiring calculators on high school Regents exams — finally allowing basic calculators. In 1989, graphing calculators began to appear. As teachers got excited by the new technology and began to change the way mathematics is taught, they also began to push the SED to require these calculators on math exams. Finally, for the past few years, they have been allowed on the Math A and required on the Math B Regents.

Now New York math standards are changing again in reaction to outcries from parents and teachers after disastrous results on the Math A Regents a few years ago. Math A and B are being replaced after a short-lived, unsuccessful life. No one knows what the new Regents in algebra, geometry and intermediate algebra and trigonometry will look like.

So why have student skills gradually deteriorated over the decades?

Is it the fault of the curriculum? There is no national curriculum in any subject. In New York State, since the introduction of Math A and B, we have the completely illogical situation of standards and assessments without any curriculum. The UFT and NYSUT have followed the AFT’s call for a grade-by-grade curriculum. Teachers need to know exactly what to teach and in how much depth. Students and parents must know what is required on each assessment (as exams are now called).

Is it the fault of calculators and other technology? Students learn much more exciting mathematics and can literally see things with graphing calculators that were never really seen before, not even by authors of calculus textbooks. The types of questions asked have necessarily changed as the technology has improved. In fact, with a graphing calculator — and simpler calculators at lower levels — the math that students do is much harder than without them.

So why are students not learning math and comparing unfavorably with students in other countries on international tests? Around 1990, Al Shanker cited a statistic that was shocking to hear but realistic upon reflection. He said, “Sixty-five percent of high school students in our country never do any homework. Never do any.”

Parents and the public don’t expect excellence to occur, nor even passable skills, in sports and music without lots of practice and repetition. How can they expect less from academic subjects?

Related to this is a public belief that it’s OK not to be able to do math. Parents often tell their kids that they themselves could “never do math” either. As Nicholas D. Kristof stated in a Times Op-Ed piece (“Watching the Jobs Go By,” Feb. 11, 2004), “The broader problem is not just in schools but society as a whole: There’s a tendency in U.S. intellectual circles to value the humanities but not the sciences. Anyone who doesn’t nod sagely at the mention of Plato’s cave is dismissed as barely civilized, while it’s no blemish to be ignorant of statistics, probability and genetics.”

He concluded, “In 1957, the Soviet launching of Sputnik frightened America into substantially improving math and science education. I’m hoping that the loss of jobs in medicine and computers to India and elsewhere will again jolt us into bolstering our own teaching of math and science.”

The hard part is not the teaching but the changing of attitudes in a country.

## 6 Comments:

1

School Information System· Dec 12, 2006 at 7:43 am

Math failures – haven’t we heard this before?…Roberta M. Eisenberg:As controversies rage about the best way to teach math and whether students should be allowed to use calculators — incidentally, the State Education Department on Dec. 1 declared that calculators will now be considered teaching m…

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Jackie Bennett· Dec 14, 2006 at 7:33 am

Thanks for addressing an issue in that is of concern to virtually every elementary teach I meet, and every math teacher on the secondary level. The question of why our students can’t do math absolutely needs to be asked, and you seem to give two tentative answers of your own, with which I agree with.

First, you say, “Parents and the public don’t expect excellence to occur, nor even passable skills, in sports and music without lots of practice and repetition. How can they expect less from academic subjects?”

I agree. And it seems that every rank-and-file teacher I talk to agrees with you too. In fact, when it comes to Math, they have agreed for years. And for years they have been yelling about the need for students to master the basics – from times tables to basic math algorithms – but have been derided as old-fashioned. They were forced – as they have been forced in other subjects – to teach against what they knew would be best. On the elementary level it was a different math concept everyday – five miles wide and one inch deep. In high school, every math teach I knew was skeptical about the change from the algebra-geometry-trig sequence. No one listened, and now – after ten bad years – it’s coming back.

Since no one but we teachers seem to care what teachers say – I offer you as support an article published in American Educator in Spring 2006 by Daniel Willingham, titled, How Knowledge Helps. Willingham, who is a professor of cognitive psychology, explains how important it is for students to acquire background knowledge, and shows how this applies to math as well.( http://www.nychold.com/talk-ocken-051002.doc) I am probably about to distort and simplify what Willingham says, and I suggest all our members read the article. But put simply,Willingham explains how working memory can only juggle a limited amount of discreet bits of information. To juggle more, it has to rely on chunking. Random letters, for example, are hard to remember and take up a lot of space in our short term memories; but NCLB takes up less because our familiarity/recall allows us to see them as a single unit. Willingham offers a better example.

“Consider, for example, the plight of the algebra student who has not mastered the distributive property. Every time he faces a problem with a(b + c), he must stop and plug in easy numbers to figure out whether he should write a(b) + c or a + b(c) or a(b) + a(c). The best possible outcome is that he will eventually finish the problem—but he will have taken much longer than the students who know the distributive property well (and, therefore, have chunked it as just one step in solving the problem). The more likely outcome is that his working memory will become overwhelmed and he either won’t finish the problem or he’ll get it wrong.”

So, mastery of basics has the blessings of the teachers, the cognitive scientists – and finally the National Council of the Teachers of Mathematics, whose fuzzy notions about math have driven education here in NY, much to the dismay of classroom teachers. This Fall NCTM finally reversed itself (something it won’t admit), and perhaps now math teachers can all get some relief.

I agree also with your second point: there is no curriculum. As you point out, and as the UFT and AFT have pointed out, there is no clear idea of what children should know, and when they should know it. Our voices have been in line with some of NY’s top educators, which of course have been ignored. For example, Stanley Ocken of CUNY delivered a paper in October of 2005 entitled, Mathematics Education Reform: Toward a Coherent K-12 Curriculum. ( http://www.aft.org/pubs-reports/american_educator/issues/spring06/willingham.htm) In it, he pointed out that under Harold Levy, the Board of Education and CUNY convened a Math Commission charged with setting directions for NYC K-12 math education, which resulted in the Goldstein Report. Ockem tells us:

“A principal recommendation of the resulting Goldstein Report was to focus on K-16 education in New York as a “seamless system,” with co-ordination between CUNY mathematics departments and K-12 educators. The word “seamless” was used to indicate proper alignment of mathematics requirements from elementary school through college. That was a great idea. Had it been implemented, following the California model, we could by now have been well on the way to establishing a K-16 mathematics curriculum that is both seamless and coherent……Unfortunately, that goal seems rather distant.”

Ocken goes on to tell us how he and other CUNY and NYU math scholars were shut out of the discussions about Math once Klein took over. In fact, they even sent a letter of warning about the programs Klein was adopted, but as Ocken says, “That letter never received the courtesy of a reply.” Instead Klein relied on the NCTM standards that came up short on basic math skills, in favor of concepts.

So, it is not for lack of voices that math has suffered in this country, and especially in New York. It’s for lack of ears.

3

jd2718· Dec 17, 2006 at 2:31 pm

Thanks for writing this, Bobbi.

It is the attitude in this country that is a problem, but not the only problem.

We can look far back, and things before were not rosy either. How many students used to really “get” algebra? 60%? Geometry? 30%?

So we made lots of changes to help reach the kids who weren’t getting math, and made things worse for the kids who were. I am as nervous about the new regents as you are, but I am glad that at least the names of the exams now make sense. We need to take some steps backwards, and that is one.

At the same time, there is still the problem of reaching the kids who never got math. Just because A and B were complete disasters does not remove our obligation to teach as much math as students are able to learn, and to keep trying to increase the amount they are able to learn.

Jonathan

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jd2718· Dec 17, 2006 at 3:02 pm

Over six years ago the Bronx Superintendant told us that every high school in the Bronx would change their math programs to IMP or Math Connections (two constructivist programs). Math teachers griped, and the UFT stepped up.

Our District Rep at the time, Dave Schulman, organized a committee of us to file a district-wide request for professional conciliation under Article 24 of our contract.

About two dozen teachers met on and off over the course of a year to prepare. There were maybe five or six core teachers, and I was one of them.

We did good work. We had our hearing with the Supe and his deputy present. And we won.

Why mention this now? Because along the way our core group became very familiar with other, national aspects of the Math Wars. And part of that education was being exposed to what I would characterize as extremists: those who were using mathematics as a political battleground. As a group, we were not comfortable with either side.

Here’s part of what I wrote to Dave, on the evening before our hearing:

“Let’s start with the “Math Wars.” It makes me damned nervous to be on the same side as what I would call right-wing kooks. It started as a California thing: “Back to basics” vs. “Constructivists” along roughly the same fault lines as the anti-Bilingual and the anti-Affirmative Action fights there. … I like to think of us as taking the reasonable center against the Ed nuts on one side, but then holding it against hte back to basics cretins who will certainly be emboldened enough to start making real noise…”(June 14, 2001)NYCHOLD is very much part of that back-to-basics extreme. And as far as the CUNY math chairs being excluded, and mind you, I like these guys, but they do not even have a consistent curriculum campus to campus. They were right that Diana Lam and Joel Klein’s decisions stunk, but they did not have a better proposal, and do not; they are not pedagogues. It is easier to be a critic, which is a suitable role for them, than to actually make the curricular decisions.

Jonathan

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Jackie Bennett· Dec 18, 2006 at 9:40 pm

I agree with you Jonathan- extremes on either side are bound to fail. And if you think Math is politically fueled — well, you should see reading. At least the content in math classes is not politically charged, but in English it is(even at the elementary level), and I think the wars there are even fiercer than they are in Math.

I think teachers tend to know how to avoid the extremes and the politics — their focus is on real teaching, not theory. That’s the problem with the Kleinists. They say their programs are balanced, but the teachers I speak to (and my own experience as a high school English teacher) tell me they are not. Teachers find themselves compelled to enact someone else’s theoretical and political agenda, in programs that lean too heavily to constructivism in math and whole language in English. In reading, writing, and math in the elementary schools either you teach the Klein way, or, well, you teach the Klein way. Curriculum is de-emphasized, and pedagogy is not permitted to grow intrinsically from the content .Then in high school we are left to pick up the pieces.

You were lucky to be able to have that kind of collaboration in your district, and that sounds like the heart and soul of what unions and DR’s ought to do with their members. Six years ago sounds pre Klein. Was it?

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jd2718· Dec 19, 2006 at 3:30 pm

6 years ago was indeed Pre-Klein. And all of our effort (tremendous, and successful) was wiped out two years later by the Lam-adoptions…

However, the sense of control and professional input that we gained was immense, even if the results were bureaucratically over-ridden later on.

And I have heard a bit about reading. It is often the same people arguing whole language vs phonics as argue traditional vs. constructivist math.

Jonathan