Henry Pollak Interview, Part 3 of 4

Pollak: Now I think it's true that a number of the mathematicians started out in this mainly as a way of making some nice money in the summer. But, they got hooked.

They found that it really was an interesting and challenging problem to try to think about school mathematics. In the long range effect, the twelfth grade team as I recall in the first summer included Mary Dolciani and Ed Beckenbach and Bill Wooton.

They turned out to be the core of the Dolciani series of high school mathematics books, which at its height had 80% of the market and was extremely profitable and very good. So, SMSG trained those people, I think, or helped to train them in the writing of mathematics. So, that was another kind of effect.

There were some very, very good people on SMSG. We had very interesting times arguing about these issues, which are not easy. They are intellectually just as difficult as research issues in mathematics, but they're different.

Roberts: What is your assessment of the general relations between research mathematicians and school teachers on the project?

Pollak: I'm sure it varies from grade to grade. In the ninth grade writing team, of which as I said, Henry Swain was chairman, our rule was that the teachers had absolute veto power over what went into the course.

For example, I can remember writing a piece of a chapter that I got right the first time. I can also remember one that I had to rewrite eight times before the teachers finally said okay, the voltage will now do. So, this was essential.

People like Rickart and myself would have a late evening conversation saying, hey, wouldn't it be fun to be able to do the following, and we'd talk about it, see how important it was, and then the next morning we'd call on Martha Hildebrandt, and say, you know, we'd like to do the following. We'd explain to her what it was and why.

Then we learned to shut up, which is very difficult for me. Martha would sit there with her eyes closed, her lips moving rapidly, and what she was doing was pretending she had a class in front of her and that she was teaching this.

This would go on for some minutes, and she'd open her eyes and say, Pollak, it won't work. [chuckles] Then she'd tell me why, where she got hung up in trying to teach this, and then Rickart and I would go away and try again.

So, that was a very important part that, as I say, as far as that team is concerned and probably some of the others, and I'm not privy to their inner workings, the teachers had an absolute veto power. Really, I don't think anything went into SMSG that some teachers hadn't tried somewhere along the way and found worthwhile.

It was a codification and a unification of the structuring of things. We understood, for the first time, what first year algebra really was all about. But, it was really a joint work between the two.

Roberts: Did your position as a nonacademic mathematician give you any special advantages or disadvantages in dealing with SMSG colleagues?

Pollak: Gee, I don't know. I was sort of a freak, and that's okay. I don't think I was really considered very different from any of the other research mathematicians that were there. I think the participation in this did have interesting effects on people.

I think, and maybe this is not the sort of anecdote I ought to tell, but I can remember Chuck Rickart telling me that he, as at that time head of the math department at Yale, after that first summer, for example, wrote a letter back to a high school congratulating them on what wonderful preparation they had done of a student who had just come to Yale, and it wouldn't have occurred to him before that summer to write such a letter; at least, that's my opinion. I shouldn't speak for him.

So, there were things like that that happened, a very important mutual appreciation of problems. I think in all fairness that the connection between school and college mathematics, the communication, the understanding of each other's problems, and the willingness to work together to solve them, was better then than it has been at any time since.

Not that College Board does [not do] a wonderful job on this, but it doesn't now have the large number of people involved and really thinking about the problems that we had at that time.

Pollak: What was the attitude of your professional colleagues at Bell Labs towards your work with SMSG?

Pollak: I think the way that Bell Labs ran in my time is that you tried to hire the best people that it could find, and then let them do what they think is right.

It is certainly rare in my own managerial career that I would ever say to anybody, No, you may not do that because either you trust their judgment or you don't. If you trust their judgment you let them do what they want to do, and if you don't trust their judgment you don't tell them no, you get rid of them.

Yes, I asked permission from the vice-president for research at the time when I got my invitation, and he said sure. I certainly was promoted once or twice after I had gotten involved in this, so if somebody was trying to give me a message to quit they didn't do it very successfully.

I think generally the position at Bell Labs always was, hey, how important is it that a person does what he or she does? You don't define that very narrowly. How much difference does it make?

Well, difference to whom, the company, the country, the subject? There was no rule that said it had to be one of those. So, I was never discouraged in any way from doing this.

Roberts: Would mathematics education benefit from more involvement by people from industry?

Pollak: I think that certainly that's what's been happening. I probably helped to set the pattern for this among many other people. I do remember that way back when when Carroll Newsom was not in academia, when he was editor of the Monthly of the MAA, when he would naturally have become president of MAA, it didn't happen because he was not in academia.

I think I was the first nonacademic president of the MAA. Yes, there's more and more involvement.

It's very important because the teachers of mathematics and mathematicians more broadly than that like to know, among other things, why their stuff is useful as to what it's good for. Suddenly their students want to know, and therefore, some of the teachers want to know.

That's one of the great strengths I have in teaching now at Teacher's College. Along with being a major source of distraction, I will talk about why something is important.

Sometimes when somebody asks me, sometimes even without that, which means that I'm not going to finish the syllabus. Well, tough. So, yes, I think that sort of involvement is a very important and useful thing.

Roberts: What is your assessment of Begle's leadership of SMSG?

Pollak: I thought it was very good. I wasn't in a judging position. Eventually I became chairman of the advisory board towards the end of the whole project, but I think he was quite astute and quite able to handle the kind of criticism which anybody is going to get when they try to change something.

Roberts: How well did you know Morris Kline?

Pollak: I knew Morris Kline, not well. My impression of Morris Kline is probably very unfair, but I'll give it to you as I had it at the time.

When you talked to Morris Kline in private and in person, he was a very reasonable man and very much willing to talk about the issues and the difficulties and so on.

Give him an audience and he became a demagogue. He looked for wonderful phrases to make fun of things and to denigrate them.

He didn't, for example, ever say in public that he had tried himself to write a school curriculum and experimented with it; it didn't work; people didn't know that. Yet I believe that to have been the case.

An anecdote which is totally unfair but years later, sometime in the seventies I think, we were on a visiting committee to the math department at Montclair State University or College at that time in New Jersey. I was chairman of the committee.

We had our differences of opinion about what direction things might go. I actually, I don't know whether it was an accident or not, but we had to keep the meeting going into the evening at which point Kline wore out.

He was older than I. I recognize this because people do it to me now. [Roberts chuckles]. But, at the time we got through what we wanted by just his wearing out.

Roberts: What was your understanding of Kline's criticism of the new math and of SMSG in particular?

Pollak: I thought that it, in part, was a misunderstanding of what was being done. I think that when mathematicians speak with each other they are usually much closer together than the public utterances and the prints and the polarizations of the positions would lead you to believe, and I certainly found that, as I said, in private in dealing with Morris.

The impression that he conveyed is that the usefulness of mathematics, the applications, the relationship to other disciplines was being totally ignored by SMSG, that all of this was much too pure.

I felt at the time, and still feel to some extent that part of this was too narrow an understanding of what applications of mathematics actually are. Kline was in a population of mathematical physicists at Courant.

And the fact that discrete mathematics and instructional mathematics and modern algebra kinds of things had lots of significant applications was something that I don't think he or many of the colleagues at Courant would have taken seriously.

They just instinctively know that mathematical physics is just an order of magnitude more important than all other applications of mathematics combined.

We did a lot of systems mathematics in Bell Labs, and they complained bitterly about what they called set theory which was really set notation and had set ideas.

That had many important applications. All our switching theory depended on this, and so I felt that they weren't crediting the applicability of mathematics outside of physics to the extent that they should. That's changed a lot.

Nowadays, it's very fashionable to talk about the unexpected applications of number theory. At that time I was able to show people a couple of unexpected applications of number theory, but nothing like cryptography.

They would have thought that was an idle amusement and that obviously number theory was not useful for anything. So, my feeling was that they didn't understand quite the breadth of applications of mathematics.

Roberts: Do you recall this 1962 open letter [Lipman Bers et al., "On the Mathematics Curriculum of the High School," Mathematics Teacher 55 (1962): 191-195]

Pollak: Yes.

Roberts: on math education which you signed?

Pollak: Yes, and the reason I signed it is what I just said, that I felt that, in fact, SMSG had satisfied the principles which that letter was espousing, that is that applicable mathematics was being taught. I know that is not what most of the people who signed it thought, but I don't think I was the only one who thought that, so that's really where that came from.

I remember that Joe Landon, who was one of the leaders of that, Professor at the University of Illinois, he and I talked about it, and he said I understand what you're saying, but really you shouldn't have signed it if that's the way you feel, but I felt that, in fact, SMSG was carrying out the principles which were in that letter, and that's why I signed it.

Roberts: In retrospect, do you think Kline played a positive or negative role in the New Math debate SMSG?

Pollak: I think at the time I thought of him as a nuisance. I thought one of the things... keep looking at it in a much longer range point of view, SMSG began a second round of materials which nobody remembers.

There was a letter which Ed Begle published in Science Magazine and a couple of other places, calling upon people to come and help in creating a curriculum that had much more connection with the world than the first round of SMSG was reputed to have. That work went on in the spring of 1966.

Work began in the summer of '66 on such a curriculum, and if you look at those materials - I don't know whether you have or whether anybody ever does, they completely disappeared from human consciousness almost, but those materials had the first explicit instruction at the junior high school level on mathematical modeling explaining what modeling is all about, using the term, I think, for the first time in any curriculum materials or very close to it.

It was a very interesting and very modern development, way ahead of its time, this second round. And, as I say, it disappeared from consciousness. There were materials written for seven, eight, and I think also nine.

It had the effect of bringing this about, and twenty years later people began, for the first time, to think seriously about teaching some modeling, of seriously seeing how and why mathematics connects with different aspects of the rest of the world.

Now that stuff fits in just fine. So, it was way ahead of its time. I think Kline helped to bring it about and provided a history for modeling that we might not have had otherwise, even though I think very few people know about it.

As far as how valuable was this, it seems to me that the alternatives which you have asked about are too simple. (Note: Pollak was here referring to a written list of alternative assessments of SMSG suggested by Roberts. This was included among the questions sent to Pollak prior to the interview.)

What I think we learned more from SMSG, and learning again at this point, is that nothing is as important as teacher education.

I think that that is the number one issue. I think we learned that in SMSG with a vengeance over the whole period and when SMSG was by no means the only project in it.

We didn't learn our lesson from it and we're having the same trouble all over again. If you have teachers that really know and understand their mathematics, I think that many different curricula will work.

The extremes that people cite, the ones that the critics make fun of, the crazy things that sometimes get said, come from a lack of knowledge and understanding and confidence in the subject.

As far as I'm concerned, high school SMSG, secondary school was a great success, and elementary school was a failure. Now, why do I think secondary was a great success, and how do I prove it?

It was a success because there was a concerted, serious effort to work with teachers. We had in the middle sixties approximately ten to the fifth high school teachers in mathematics in this country, just about 100,000; it may be 150,000 now, but that's about what it was.

A majority of them went to an institute, at least once in that period; I think the total number of people that went to an institute was somewhere in the neighborhood of 60,000 and there may have been some repeaters among those.

So, something a little bit over a half of all high school teachers had a chance to find out what are you doing and why and how do you teach it and what have you got in mind? We had, and still do, a little over ten to the sixth elementary teachers, and people threw up their hands.

They said, look, we can't possibly reach a million elementary teachers so let's put all this good stuff in the teachers' commentary. This was incredibly naïve. I certainly didn't know at the time, but I know now that elementary teachers don't have time to read the teachers' commentary, so whom are you kidding?

So, what happened is that the material intended to be taught in a very different way, with very different purposes from standard elementary school math was taught in the same old way and they made hash of it. We made a tremendous mistake in not insisting on teacher education for the elementary teachers.

When the computer came along in the seventies and first people seriously thought about computers in teaching or calculators in teaching in elementary school, NCTM made a serious effort to try to reach teachers.

Many other kinds of things happened, but we're in great danger of the same problem again of taking materials which are different in their intent to some extent, different in their pedagogy from what people are used to, and having teachers without sufficient preparation try to handle them and come up with, not only a fair number of examples of nonsense, which opponents very naturally pick on, but in cases of real failure to teach what and in what way was really intended.

I hope that this doesn't happen on a large scale, but I firmly believe that any of the curricula that people are talking about now and any of the curricula in the sixties would have been and would be a notable success with enough well-prepared teachers, well-prepared in the mathematics and in pedagogy, or the alternate forms of pedagogy that we've got. Without that they're not going to do very well.

The trouble is, of course, that probably the traditional curricula would do very well with sufficiently well-prepared teachers also. You wouldn't have the drill and kill that people talk about. You wouldn't just have a sage on the stage as people like to use the phrase.

But, there is a point to trying to change because the usefulness of mathematics and the relationship to the technology and mathematics itself have all changed very seriously in the last ten or fifteen years, and that deserves to be reflected in the school.

So, you really do have to change content and pedagogy to some extent, and with enough good teachers you'll be able to do it.

So, there is a point because you need the availability of the things. As I said, when I went to school there was no such thing as probability and statistics and discrete mathematics and optimization and computers or anything.

Those are all terribly important nowadays, and the materials which don't say anything about these, the materials which are still on the narrow track with only calculus as a destination, are wrong, in my opinion, for the totality of the population.

We have changed in our point of view since SMSG. We're trying to get better mathematics, not to thirty percent, but to close to one hundred percent of the student body, which means that you have to try to work into the motivation of kids, whom the beauty and the structure of the subject just aren't going to motivate.

Roberts: Do you think this is a good thing that we're expanding to teach more students?

Pollak: Yes, I do because I think it is fundamentally important in a democracy to give everyone the opportunity to learn to use mathematics. I think the nature of the society is going in that direction, and I know how much fun it is to teach the mathematics you love to people who also love it. Boy, you can have a good time. But you have a responsibility to teach everybody.

If you break kids up into sections, if you do that too soon I think you're making a mistake. That's a terribly difficult issue that gets argued about at great length, and again the key ingredient of the solution is really good teachers.

Roberts: Just a more specific question here now - I note that you served on a panel on programmed learning. What was your involvement with this?

Pollak: One of the experiments that SMSG did was to see how well you could teach good mathematics, in this case the first course in algebra in a programmed way. Well, there are two different kinds of programs.

There's a constructed response kind of program and my recollection is that there was multiple choice and there was constructed response and we simply wanted to know scientifically how well these things could do.

So the attempt was made to see how that would work, and that was my involvement in it. I don't know that there's much more to say about it than that. Again, there are anecdotes about how it worked, but go ahead.

Roberts: Did you personally come to any conclusions about the value of programmed learning?

Pollak: I think, again, it's workable but no panacea for anything. I remember one group that particularly strongly claimed what a wonderful thing it was and had the data to show it until we realized that they only tested the students who got to a certain level at a certain time, and all the ones who hadn't gotten that far weren't in the data which is a bit of a bias in how you report the results. So I don't have any strong feelings one way or the other.

Roberts: I note that you served on the Cambridge Conference on Mathematics Education of 1963. What are your recollections of this conference and what is your assessment of its influence?

Pollak: My recollection of the conference, even at the time, is that I thought it was, at least in part, an act of hubris It was abstract or research mathematicians being as researchy as they could be. There probably was much too much influence of the highest level of freshman course at Princeton at the time. That may be unfair.

But, they deliberately excluded people who knew anything about math education in the Cambridge Conference and said look, what would we as mathematicians really like to see happening?

It did have one interesting effect. There were some experiments done. Andy Gleason went into elementary classrooms and tried some of the things that were said. Other people went and tried things.

There was an experimental two years of kindergarten and three at elementary school developed by Mismason?? School in Princeton in which they decided to essentially teach variables and negative numbers to five-year-olds with great success.

It worked beautifully. That was an attempt to implement some of the ideas in the Cambridge Conference. So, there were some interesting things that came out of it, again long since forgotten by people. But, I think we learned a lot.

Roberts: I guess I'm getting to the point where I had some questions that, in reading over, seem rather vague

Pollak: and we may have covered them earlier.

Roberts: Yes, I think possibly we have. Why should anyone listen to a mathematician on education reform?

Pollak: That's a good question. I think there's a serious difficulty there. I think that there are some people who