Sunday, October 22, 2006


A most interesting interchange


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September 14, 2006
9:00 a.m.
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Broad Institute
7 Cambridge Center
Cambridge, Massachusetts
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MR. GARFUNKEL: Good morning. My name is Sol Garfunkel. I'm the Executive Director of the Consortium for Mathematics and its Applications. I have a doctorate in mathematics from the University of Wisconsin. And I have been a principle investigator on one or more National Science Foundation projects and in mathematics education continuously since 1976.

Basically, my comment to this panel is don't do this, don't write the report that we all expect to come out of this Panel, because I think it will set back mathematics education for a number of years. Don't write a report that says there is a lot we don't know, or a seemingly reasonable report that says there is a lot we don't know about mathematics education. There is a lot of research that needs to be done. It should be funded by the Department of Education. And until that research is complete, we should stop innovation in curriculum development, except if we adopt something like the Singapore Program, and that we should cut off funding for that curriculum development, we should cut off funding for the National Science Foundation. I suspect that that's what this report will eventually say and it's a terrible mistake. I think people forget, purposely possibly, why the standards were written in 1989 by a much more courageous National Council of Teachers of Mathematics. They were written because we were here. The problems were there, we recognized them and things were not working. And to be honest,there was a remarkable consensus about that. Everyone came up and said the kinds of things you are hearing today, students don't learn, teachers don't know any mathematics, nothing good is happening. By the way, nothing good is happening at the low end and the high end and we've got to do something about it. The NCTM Commission issued standards with their own funding. It was a very brave act. What the standards said and what I think gets lost, by the way, is that those standards were supported by every major mathematics organization at the time, including the American Mathematic Society (AMS) and the Mathematical Association of America (MAA). And what those standards said was we need to innovate, and we need to look at content, pedagogy, applications, and technology. We have to think hard about the choices we've made and the choices we might make.

Yes, they made some suggestions about ways to go, but the point was dissatisfaction with where we were and a desire to try some new things. The National Science Foundation supported a lot of grants, a lot of work of innovators, of content developers, not, and I say this at every possible opportunity, not with the sense that we've got to replace where we were. We've got to take the pre 1989 materials, throw it out and replace it with these new curriculum just to see whether we could, on a day to day basis, make the vision of NCTM extend, that we could actually create materials that embodied that vision, those ideals, and to experiment with them, to innovate, to try things, to see what worked, to give researchers a body of material that they could work with to see in fact whether this was going to do any good.

And I think what's happened is that there is evidence, a significant amount of evidence, that some of those innovations, some of the changes that we've made in content, some of the changes that we've made in applications, in pedagogy and technology have done some good. Look at the ARC Center report. Look at Joe Boehler's research. I'm not saying it says take this curriculum and replace it with that one, but it does say that there is a place for that innovation.

What this panel should not do is, in their report, cut off that funding, cut off that generation of people who have started doing this work, who you will need when it comes time to do the kind of actual changes, homemade, not imported, real change, with real innovation, with the American mathematics educators who have been working on this problem for 20, 30, 40 years. And that's all I have to say.

MR. FAULKNER: Questions or comments from the panel? MR. SIEGLER: Why is it relevant if a program was developed in the United States or in Singapore?

MR. GARFUNKEL: Well I will say the relevance is there are two kinds of --. By the way, the people in Singapore, I go there, I talk to them. They come here to look for innovation. They come here to look for creativity. They argue that their students can do lots of very nice and manipulative technical things that we test for, but they can't create. They are not the students who come to MIT. They are the students who do well on these exams, fine. But I'm worried about that pipeline as much as anybody else here and unless we have that innovation, unless we have that creativity, unless we build in the things that Americans are actually good at, then we are just doomed to having kids who do well on tests. Fine, if we want kids who do well on tests but can't compete in the society. People from Singapore come here to learn how we get creativity.

MR. WU: Sol, there are just a few points of factual error. One is that AMS, yes, approved of the NCTM standards in 1989, but the fact had been documented that it was approved with actually no reading of the standards, that's number one.
Number two, about Joe Boehler's research, it's in great
dispute, and there are scholarly concerns about the quality and the methodology. Number three, about Singapore, indeed Japanese educators and Singapore educators came here to look for answers. They looked for answers and in the case of Japanese educators. They took a lot of information back, and I believe that three or four years ago they have since made a U-turn and decided that it couldn't be done, so I think I should stop here.

MR. SCHMID: I mean of course there is a frequent complaint that somehow the East Asian countries emphasize calculation at the expense of mathematical thinking. You should be very careful when you say that Singapore children don't get mathematical understanding and then they have no ability to excel, let's say, at a higher level.
First of all, Singapore of course is rather small, so if you talk about the number of people who do various things, we have to be careful in making such comparisons. Take South Korea, South Korea has a curriculum that in many ways has similar characteristics to the Singapore curriculum. Of
course it isn't written in English, it is therefore not as well known as the Singapore curriculum. At Harvard, we see a very large number of graduate students from South Korea, who have gone through a curricula of that sort, who are certainly capable of functioning at the highest level. What you said about the Singapore curriculum is a slur.

MR. GARFUNKEL: My point is that the answer is not to simply import a curriculum because you find it to your liking. We have in mathematics education in the United States, we are quite capable
of taking the best of those other curricula and the best of what's done here. You wouldn't do it with other things. You only do it here because this curriculum happens to be to your liking. I will say that you should not cut off the research and the development of materials that are going on by homemade people just because one curriculum happens 14
to appeal. It's a mistake.

MR. SCHMID: This committee cannot cut off funding for curricular innovation in the United
States and even if we could, we would not ask for that, that is not the point. It is, as you say, one needs to be guided also by international comparisons, that is one reason for focusing, let's say, on the Singapore curriculum, to see what is good there and that that be properly appreciated. It does not mean that there has to be a wholesale importation of
foreign curricula.

MR. GARFUNKEL: But you don't focus on
the Dutch curriculum, for example.

MR. FAULKNER: Let me go to Tom. I think we are not going to get to everyone who is signed up if we aren't crisp with our comments

MR. LOVELESS: Just one quick question. I assume you heard the testimony of Holly Horrigan just before you. As someone who supports these new curricula, how would you respond to her, as a parent, with her concerns?

MR. GARFUNKEL: I want to be careful about this. What I am supporting is not any one curriculum, what I am supporting, what I am supporting are the ideas behind a number of those curricula. There were horror stories in 1989. You think you couldn't come up with a parent in 1988 who said that their kids, who were very bright at home, weren't doing well at school, hated math, aren't going into math. Read those reports, read those articles, we could easily, of course that's going to happen with any experimentation, we don't have the right, the one curriculum. But if you look at data over large numbers of students, take the ARC Center report, for instance, you do see positive effects. I think a horror story here, a horror story there, it's just anecdotal. It doesn't do any good, it doesn't tell
you what the policy should be.

MR. FAULKNER: Thank you, Dr. Garfunkel, I appreciate your being here.

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