William Chinn Interview, Part 3 of 3

Roberts: This is a continuation of the interview with Bill Chinn. This is tape number 2, side A. You were talking about a book by Newman.

Chinn: Newman and Kasner, called Mathematics and the Imagination, [E. Kasner and J. Newman, Mathematics and the Imagination (New York: Simon and Schuster, 1940)] and that one, I first read in the army. Because they were paperback kind of things, and it was fascinating.

It talked about the idea of topology. That's what got me fired up, and I asked around at that time at UC and they did not offer any course there. Then along comes this fellow and I took his class and I got fascinated by it. Then after a while we happened to belong to the same group of people with the New Mathematics Library.

He was one of the people there, and we became very good friends at that time. Then we bounced ideas between each other. He says he has a start on something that he would like to try out. I said okay, we can experiment and see what happens.

Let's both go back and forth and see what kind of ideas will come out. And so we started out and eventually we started on the questions. He says I would like to put out a book showing the idea of what topology involves. So we talked about the question in what direction should we go?

Should we start from where the student is and try to change his viewpoint slowly and do it that way. We did start that way, and after two years, he says no, that won't do. It is better to start completely to orient them to topological thinking, in fact.

So we went through the whole thing already. We started the titles and so forth, and then the second attempt we did not abandon the titles at all, it's just we put in the flavor of topology immediately from the start. Chapter by chapter we were doing the same things but from a different viewpoint.

And that was what came about and we finished the work after four years. All because the first two years was to experiment in one way, and we were not very happy about it. Especially Steenrod who knows what he wants.

By the time we got through with this we were hoping some of these ideas would creep into the idea of calculus, how to approach calculus the same way. It never got caught very quickly, but one of these days I hope it will be done.

One of the things that was stopping that idea was that there were too many high schools starting calculus A and calculus B on their own, and they, of course, start with the idea of calculus the very same way that their teachers started it.

In fact the teachers stick around, and even if the teachers wanted to change the ideas got frozen in the lower grade. Because that's the only kind of thinking of approaching limits that the students have, and because of that the ideas never got full blown to go into topological thinking. Eventually I hope one of these days it will be the other way around. But it will take a long time. All because of habits.

Roberts: Did you have any interaction with critics of the New Math? Did you ever encounter parents that were complaining about it?

Chinn: No. In fact, when I was, when we were doing these kinds of things, we would get requests from parent groups and so forth and so on. So Ed Begle would send me around to different places to give talks about the thing and to demonstrate, using students to demonstrate how they respond.

When they saw their own children responding in the right fashion and so forth, it got them excited enough to say that this is okay, it's not something so far fetched. Because when they did not know about it, then they worry. Until they see that their own children can respond in the correct way. Then they feel not so apprehensive about the thing.

Roberts: So you felt you were able to calm the anxieties of the parents?

Chinn: Yeah. There were times when they were pretty worried about it, and they expressed it.

Roberts: How about the teachers, were they worried about this new material?

Chinn: No. That's why we worked closely with teachers. And my experience with the writers also helped me to explain certain things to teachers so that they understand what we were trying to do.

Roberts: Now there were a few mathematicians that were very critical of the new math.

Chinn: Of course, like Morris Kline.

Roberts: I wanted to ask you about Morris Kline. Did you know him personally at all?

Chinn: No. I don't, I just see his criticisms, and we said, Well we did really not try that way. That's because he refused to see other people's viewpoints, I think. He was too much a physicist. Because he is into physics too. But of course I was into physics also, but I did not react that way.

Roberts: One of the things he said, and maybe some of the other critics also said, was that the new math curriculum initiatives were rushed into the classrooms too quickly, without enough testing. Do you have any reactions at all?

Chinn: No. Of course, as coordinator I do read their things, but it's simply that my job was so definite about looking at, getting reactions from the students and so on, that I was not separating the writing from that kind of activity. And as long as it seemed to be reasonable, then I have no problems with those writings.

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

Chinn: I think he was very very concerned. He's a man who would pace up and down the hallway. You always feel his presence there. But you know that he is concerned when somebody criticizes it. We try to do what we could. We had frequent meetings every now and then, to make sure we are on the right track.

Roberts: Now, we've mentioned Max Beberman as another innovator in this period. There were others. I was wondering if you were at all acquainted with their work. Bob Davis?

Chinn: Yes. He was with us for a while, and then he spun off and started his own thing. Obviously his things and our things were pretty close together, because he worked with us and he got the same ideas and he thought that it was reasonable.

Roberts: How about Paul Rosenbloom?

Chinn: Yeah, he's in the Chicago area.

Roberts: He was in Minnesota.

Chinn: Pretty close. I don't hear too much about him. I have heard his name. Who else?

Roberts: Those are the names I can think of at the moment.

Chinn: If it comes back, you know.

Roberts: So what is your retrospective assessment of the new math and of SMSG in particular?

Chinn: Well I thought they were reasonable. It's just that by this time the ideas have crept in and people don't realize it because it is part of the standard curriculum by this time. You see it when you go through some of the courses and so forth. But it is there.

You don't mention that it is there because as long as it is there harmlessly, people will not get so excited that they say Wow, we'd better throw this out. Because as long as it gets the kids to start thinking about things, it's a good idea to leave it alone.

Roberts: There are several notions that were popular with the New Math, and with SMSG in particular. One is the emphasis on sets and set notation. Morris Kline I think thought that was a little bit over done.

Chinn: The idea of course is that way it keeps people, they concentrate on different things. That you can have this one as a set of certain things and another one a set of some other, constituting different things.

And you can talk in terms of sets of things, and no matter what you visualize, you can still apply mathematics to it this way. It does get talked about. I know there are a lot of criticisms about the vocabulary. But if you use another word, then it will be that word that would be getting into the picture anyway.

Roberts: So you continue to feel that set is a fundamental notion?

Chinn: Good enough to work with.

Roberts: Another concept, the distinction between numbers and numerals.

Chinn: That is mainly to differentiate that one is the name for something, whereas the other one is the idea. A number is abstract by itself.

Roberts: Some critics thought that was over done.

Chinn: It could be, depending on who's doing it.

Roberts: Of course another is the emphasis on axioms of algebraic structures. Commutative, associative law. . .

Chinn: Of course, that comes directly from the theoretical idea of mathematics. That each one has its own set of discipline. In order to focus it, the teachers onto the things, you use those kinds of a vocabulary. Sometimes they get overblown because you stick to it all the time. So they can be overused.

Roberts: Now mathematics education can be justified in lots of ways. In your view, how much mathematics should the average person learn?

Chinn: What do you mean?

Roberts: How much mathematics should a person learn?

Chinn: Well of course as I mentioned to you, we were raised as children that mathematics is an important subject. And we don't see any difference as to why we should think that it is not so.

Roberts: But should everyone take mathematics up to a certain level, in your opinion?

Chinn: I would think so. I think if possible you can continue on. You can see, certainly people can think in terms of mathematics, in different levels, as far as you wish to push it.

Roberts: Do you think of mathematics as...

Chinn: A discipline.

Roberts: Some people would think of mathematics as mainly something that has a usefulness in solving problems.

Chinn: Yes, of course, that was the ultimate defense of use of mathematics. Is that it extends from what we think is important, but it helps with our counting and you can of course try to crystallize it, but when you do too much crystallizing then you lose your foot and it becomes a little more abstract than you want. Once that is carried to extremes, then you lose the idea of it being useful.

Roberts: Now sometimes it's claimed that technological progress requires that more people learn more mathematics. But on the other hand it seems that some technology is designed to reduce the need for technical knowledge by people.

For instance, the calculator removes the need for people to know certain algorithms. How do you feel about that? Is it still necessary for students to learn the long division algorithm, for instance, if they can have a calculator that can do it for them.

Chinn: The trouble is of course that after a while using calculators, when the calculator malfunctions you will not recognize it unless you are aware of it. So that is important that they do not become over-dependent on calculators. At the same time that is a tool, you would certainly be silly not to use it. So you have to balance on both issues.

Roberts: Have you been following the latest round of reform in mathematics education, the NCTM Standards? Have you heard anything about this?

Chinn: I've read about them, but I've never seen what the difference is, so I haven't been thinking about it.

Roberts: You don't feel that you're qualified.

Chinn: I suppose that's because I'm retired. If I were still in the business, I might really feel about it.

Roberts: You don't feel qualified to pronounce judgment on what's going on in mathematics education today.

Chinn: Not much, because I haven't been with it.

Roberts: Are you much interested in, you mentioned reading that Newman and Kasner book, which is somewhat a popular account. Have you read other popular books of math?

Chinn: Not the same way. They have a very good way of doing things. And it makes everything exciting, and everything comes out, I feel. And in fact, there was something, I forgot what it was, something that I wrote and it went through to some publishers and they happened to have a daughter of one of those two people on the staff.

And she read it and she said, This has the touch of daddy's book. And I didn't realize it, because it'll trap you, so you absorb it without knowing. It was nice to know the girl recognized something like that, because she thinks of it from a different angle.

She can see that this guy has been influenced by my father's book. Which is a strange thing to make a remark. But then the publisher relayed me that story, and I said I never realized that that happened. But you can't say that it won't once you realize that is done.

Roberts: Do you see a role in education for popular mathematics books?

Chinn: Sometimes you wonder if a person sets out to be popular, whether he fails it because he thinks he's doing something and he's trying to be very popular and so forth and he fails because he tries to find a prescription.

I think things like that have to come from within yourself, you can't force it. You have to have it already stored in your knowledge and it come flowing to you unconsciously.

Roberts: So would it make any sense, for instance, to use a book like Mathematics and Imagination as a text in a course?

Chinn: I would think they are still as attractive that way. I'm quite sure the book is still very well used around.

Roberts: Are you much interested in recreational mathematics? Work of Martin Gardner, for instance?

Chinn: I don't know. Not much.

Roberts: Puzzles and games and so forth.

Chinn: Of course you yourself do that every now and then. Just like playing with, well nowadays, my work with puzzles has centered around these jumbles, in the newspapers you know. Between myself and my sister-in-law in Sacramento we try to play and give each other the answer right away.

We both get up early in the morning anyway. Unfortunately, sometimes my paper gets late, quite often. But we play around, you can do the same kind of things with mathematics. Just like working with crossword puzzles and so on.

Roberts: Martin Gardner has advocated using puzzles to get kids interested in mathematics. Does that seem like a reasonable approach to you or not?

Chinn: You have to really select things. Just as, for example, every now and then you want to try something new. For example, there was a time I had everybody come to teachers exposed sometimes to classes that are students trying to, you know, like dumbbell classes or something.

You try different things to interest them. One time I tried to just talk about the problem, and then after that to talk about another problem, similar kinds of things and so on, until it gets to formulate by itself what you are going to do to solve the problem.

It worked out a little bit. They didn't know how to take you at first, and then after a while, when you do not provide them with the answers and so forth and how to do it, some of them would stop doing it. And that's what you want to do, to lull them into that situation, and let them do some thinking for themselves. But you cannot always guarantee that you will succeed.

Roberts: Have you done much reading of the history of mathematics?

Chinn: You can't help it when you're talking about mathematics. Sometimes you do try to bring in some histories. You know for example who does what when and so forth.

Roberts: So that can be a help in education, interest students to bring this material in?

Chinn: Not enough to bring them in as special topics. Now and then, you do present them with the stories as to who started this and so forth and so on, and they light up a little bit. But not everything can be frozen like that.

Roberts: How would you describe your own teaching style? Did it change over time?

Chinn: Sometimes you want to try something new. I do try that, but I eventually go back to what I think was the tried and true way. You run out of ideas, I guess.

Roberts: Mrs. Begle mentioned, she thought you still had a lot of material here related to SMSG.

Chinn: I do have some longitudinal studies books down below. Maybe I can dig them up and give them to you, because they are still there. Let me see how much of it I have downstairs when we are done.

Roberts: Well, I think I am just about at an end here, unless there's anything else.

Chinn: You have quite a thorough list of things. It brings out kind of different kinds of things. You must have to think about all these kinds of things from different angles to try to fill in the story.

Roberts: That is what I was trying to do.

Chinn: That must be interesting when you finally get it.

Roberts: Is there anything else you'd like to add?

Chinn: I'll try to find, give you the names of the people who were instrumental in the, not the topology,

Roberts: Those UCLA people who gave you the letters?

Chinn: Yes, I think that is downstairs.