Fox News Sunday with Tony Snow (April 22, 2001)
"Not Your Parents' Math" featuring Lee Stiff, president of the NCTM, and Merryl Tisch, member of the New York State Board of Regents.
SNOW: About half the public schools in New York City are practicing a controversial teaching method called constructivist math. The method assumes that, one, children learn better from peers than children; two, retain information better if they discover it themselves; and, three, that most respond poorly to rote memorization.
Joining us to discuss the issue are proponent of the theory, Lee Stiff, president of the National Council of Teachers of Mathematics, and opponent Meryll Tisch, a member of the New York State Board of Regents.
Now, before we start. We're going to try to illustrate the difference * it's a crude illustration, but we're going to do it anyway- between the old math and the so-called new math. And we're going to use a sample question written by new math advocate professor Ruth Parker. Here it is. It's sort of a word question.
You may eat 1/4 pound of turkey each day. Your butcher gives you three equal slices weighing a total of 1/3 of a pound. So, how many slices do you eat? First the old math approach. You start by determining the weight of each slice -- 1/3 divided by three equals 1/9. Then you write an equation to figure how many slices produce a quarter pound. X times 1/9 equals 1/4. Then you multiply both sides by nine and presto, out comes the answer, 9/4 or 2 1/4 slices.
Now, in constructivist math, you start by drawing pictures of the three slices. Then you draw six more slices to produce a pound's worth of turkey. Next, you divide the picture into quadrants, each of which represents 1/4 pound's worth. Then you add the fractions from any of the quadrants, and here you see it. You've got a whole plus two halves plus 1/4 and bingo, you get the same answer.
Mr. Stiff, first let me start with the theory here. Do you really believe kids learn better from kids than teachers?
LEE STIFF, PRESIDENT, NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS: As president of the National Council of Teachers of Mathematics, we propose standard space mathematics, which is not exactly the same as what you're talking about.
So, we don't think kids learn better from kids per se. Kids learn better from using materials and talking about ideas and having teachers direct them and help them, facilitating the instruction.
SNOW: Facilitating the instruction, how does that differ from standing up and saying, "OK, here are the times tables. Memorize them"?
STIFF: Well, in the example that you just gave, it allows young people to see what the problems are all about. So by using manipulatives, we would call them, or those objects, they can actually cut and divide in ways that they can actually see what the amounts are and reason the answer.
SNOW: Ms. Tisch, what's wrong with that? MERYLL TISCH, NEW YORK STATE BOARD OF REGENTS: There is absolutely nothing wrong with what the professor is saying. But what I really am seeing across New York State is a balance. And we believe very firmly that children need to learn to walk before they can run.
SNOW: Meaning? TISCH: Meaning they need to have the basics so that discovery and inquiry, which are part of the analytical reasoning that I think the professor is alluding to, becomes a natural process.
But we have found that as students are acquiring the basics, they are more able to enter into those discovery and inquiry exercises. And without the basics, we find that they are starting with a deficit.
And might I just add, that if a deficit starts in elementary school, we know, based on data, that it is very hard to make up lost ground in middle school and high school.
SNOW: Mr. Stiff, isn't it true that in recent years there's been some rethinking of constructivism to accentuate basics, because there was some evidence that kids, in fact, they knew how to play with the manipulatives, how to divide things into piles, but when time came to multiply nine times eight, they weren't sure?
STIFF: What was said is not exactly true. We want kids to learn the basics. We want kids to be able to add, subtract, multiply and divide. We want kids to understand how that all works as well.
So in addition to just being able to put down two and carry one, we want them to understand what the one represents. And we do this in a variety of ways.
So, when we talk about standard space mathematics, when we talk about young people having the opportunity to reason and do problem solving, we want to engage them at the very beginning. Bases are needed to solve problems, but the facility of solving problems happens with doing it, not waiting to some threshold moment in time where you all of a sudden begin to solve problems.
SNOW: But is there not a point at which doing it becomes impractical when you're dealing with large sums or where you start doing more complicated mathematical operations, when you start doing integration, for instance, to sort of...
STIFF: That's the power of the approach. We begin with reasonable sums so that young people understand the relationships. And then as they encounter larger sums that you spoke of, then they're better able to understand and see through that because they've had the experience with more manageable situations.
SNOW: I don't understand that, explain. STIFF: So that in the situation that you showed in your problem to begin with, that was a very manageable situation of division and multiplying of fractions. So when it comes to a problem that involves larger numbers or more complex situation, they have something to look back on to inform them on how to handle a more complex situation.
SNOW: OK, Ms. Tisch, a lot of educators complain that you and others who are skeptical about this just don't get it. You're afraid of a new teaching method, and you want to go back to the same old stuff that you and I and, I suspect, Mr. Stiff also did when we were kids sitting in the classroom.
TISCH: I don't think we can afford to go back to the same old stuff, and clearly what we're doing in New York, which is what I'm most familiar with, is very far from the same old stuff.
In New York State, there was a two-tiered system and I think the professor knows that very, very well. We have exit exams in high school, and every child, every young adult must pass five exit exams, what we call regents exams, to get out of school.
What we were finding that there were two tiers of exams-there were the competency exams, which were the low-level exams, and then there were the regular regents exams. We have removed the low-level exams because we were hearing from everyone, particularly from the business community, that students graduating from high schools in urban settings in the United States were not qualified, either mathematically or literally in literacy skills, to take their places in the work force in this country.
There is no going back for us. Going back for us would be the worst. SNOW: OK, well, I'm not sure what you're saying, you're going back too. Do you believe that basics are being stressed too much or too little?
TISCH: I believe that what we have to do and that what we are doing, and I think our exams bear this out very well, is we are striking a balance. We are very clearly testing basic competency skills, and we are also testing higher-order analytic skills. And to say that you can have one without the other sets these kids on a path which cheats them out of their future.
STIFF: And we would agree with that. We want to provide basics and the problem-solving abilities that young people need to be successful in the work place and in their future lives.
All I ask is that you look at the facts. Look at the student performance. And in New York, in the recent exams, state and citywide standardized test, young people who've been taught using the standard space approach have done better than the students who were taught using the traditional math approach. Look at the data that recently came out from NAEP, that show that in California where a lot of this happens...
SNOW: That's the National Assessment of Educational Progress. STIFF: Yes. That the students in 28 out of the 32 states that participated did better under our program, and no one declined in performance. And in California, the fourth and eighth graders did better than you would have expected.
SNOW: There's considerable scholarly dispute, but let me ask you the question. If it's so successful, why are so many parents ticked off in New York City and California? There was a rebellion. Why are parents ticked off about it if it's so good?
STIFF: Parents are upset because, when they visit classrooms, they see activities that they're not used to. When they were students in school, they probably sat in rows neatly lined up, and the teacher just talked and talked and they used paper and pencil, and that's how they learned their mathematics.
When they see students engaged and talking with one another, when they see teachers allowing students to question and think thoroughly about the mathematics and the relationships, they wonder if the basics are going to be achieved. But the test results show that they are, their students are learning the basics.
SNOW: Ms. Tisch? TISCH: I respectfully disagree. Not with the premise of students starting to do better, because I think students are starting to do better because there is a balanced approach.
But there are a couple of things that you have to be aware of. Number one, Stuyvesant High School, which is a nationally renowned high school, has a very ethnically mixed student body, will tell you that now they must do entrance exams and placement exams for students coming in from the strict, constructivist philosophy, because they're not coming in with the basic pre-algebra skills that they need to go into the higher-level courses.
Additionally, let's be clear. There's a teaching shortage in this country. It's in math, science and foreign language in particular. And for us to think that we are going to be able to take a group of novice teachers and instruct them and their students at the same time on how to do real constructivist math, which I believe is what the professor is talking about, I think really will put the entire system at a disadvantage that will last far into the future.
SNOW: OK, we're going to have to wrap it up there. But I'm sure we've whetted everybody's appetite for further debate, and I want to thank you both for joining us. Meryll Tisch, Lee Stiff, thanks so much.
TISCH: Thank you.
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