Topic: Mathematics Education, Held in conjunction with the annual
meeting of the National Council of Teachers of Mathematics (NCTM)
Guests: Jack Price (JP), President, NCTM
John Saxon (JS), Independent Textbook Publisher
Michael McKeown (MM), Member, Mathematically Correct
Roger Hedgecock (RH): Jack Price, the criticism seems to be that there has been a dumbing down, that the K-12 graduate does not know, by objective testing that has been done, and recent years have put, for instance, the 4th, 8th and 12th graders at dead last among the G7 nations, the industrialized nations, when the same tests are applied. In mathematics there is not really a lot of fudge room here, you either know what algebra is or you don’t know what it is. You either know what trigonometry is or you don’t know what it is. You either now that 1+1, 2+2, etc. You either know these things or you don’t. It’s not like English or composition skills or even vocabulary. This is a much more precise thing that can be measured. What are these levels of understanding of these basic mathematical approaches that have been absorbed by the students and the testing is 4th, 8th and 12th graders are dead last among the industrialized nations and your group are the teachers who have produced it. Now what are you going to say to that?
JP: What I say to that is that if you look at the subtests, that the basic skills parts of the test are really on a par with most of these nations. Where we fall down is in problem solving. What we need to recognize here is that at most 20% of the classrooms have implemented anything to do with the standards. So that what we are talking about is really a failure of the kind of mathematics that we have presently, not the failure of the mathematics that would be based on the NCTM Standards.
RH: What is it that we have now?
JP: What we have now is nostalgia math. It is the mathematics that we have always had, that is good for the most part for the relatively high socio-economic anglo male, and that we have a great deal of research that has been done showing that women, for example, and minority groups do not learn the same way. They have the capability, certainly, of learning, but they don't, the teaching strategies that you use with them are different from those that we have been able to use in the past when young people, we weren't expected to graduate a lot of people, and most of those who did graduate and go on to college were the anglo males.
RH: Michael McKeown, math is being taught for anglo males and that is why we are having a problem.
MM: Roger, I think my wife, the Phi Beta Kappa math major from UCSD would object to that, that my daughter, the leader of her school, would object to that.
JP: (Interrupting) Mike, you know that those are ....
MM: I think that this is separate but equal. This is saying, “Oh, these poor guys, they can’t do math.” I think that in fact, that it would seem to be racist that we need to think about designing a math program for an ethnic group. If I said, if somebody said, “Oh, they can’t do math,” which is almost what he is saying, that he would, that Jimmy the Greek would have been drummed out of education.
JP: That is not true, Mike. That isn’t what I said at all. What I said is that everybody can learn mathematics but they need to be taught differently from the way that the teacher is standing in front jamming it down their throats. The way that we learned it.
RH: Let me....
JP: Now don’t put it that way, you know it as well as I do.
MM: It sounds like you are saying that these groups over here, that they need it taught differently than what works for other people.
JP: Because they learn differently.
RH: Well, let me ask, No Mike, wait Mike....
MM: Are you saying that they are genetically inferior?
JP: No, and you know that’s not what I’m saying.
RH: Now Mike and Jack. Jack Price who is President of the National Council of Teachers of Mathematics and Michael McKeown, a local parent. Let me jump in with just a little example here. I want to get as concrete as possible. When I learned that 3 x 4 was 12. I did not know that when I came into that class, in second grade or whenever it was I learned that. Someone had to say to me by writing “3” and then an “x” and said “this is times and I’ll tell you what times means in a minute” and then the number “4” and then “equals.” “I’ll put two bars here and I’ll tell you what that means in a minute” and then its “12”. And then they would say something simple like “OK, here are 3 pens and if I had 4 piles of 3 pens I’m going to have 12 pens.” And finally, you know, it kind of gets in your mind and then you have it on a piece of card and you memorize it and then it comes up on a test, and you have to give the correct answer, and what it basically comes down to is you don’t know that 3 x 4 = 12 until you get your memory to say to you that every time you ask yourself, “What is 3 x 4 ?” you get the number 12 comes up in your brain. Now Jack, in what way would a woman or a minority learn that differently than I learned it?
JP: All of the research that has been done with gender differences or ethnic differences has been - - - - males for example learn better deductively in a competitive environment, when - the kind of thing that we have done in the past. Where we have found with gender differences, for example, that women have a tendency to learn better in a collaborative effort when they are doing inductive reasoning.
RH: What does that mean, inductive reasoning?
JP: Well, they are able to generalize from a number of different kinds of - - - I can’t think of the word I want, but, from a number of specific instances they can make a generalization.
RH: So in my example of learning that 3 x 4 = 12, how would males and females, based on that research, learn?
JP: Well, since you used two or three different ways to teach that, probably there wouldn’t be a problem with it. What we are saying is that you cannot give a student a bunch of these multiplication facts and just say, “OK, learn them.” What you need to do is help those children learn what it is to multiply and how they can get to it if they forget that 3 x 4 = 12.
RH: Wasn’t that the way it was always taught? I’m trying to figure out whether you are saying something in different ways that’s always been there or whether there is something new about what you are saying.
JP: What we are being accused of is that we don’t teach basic skills, are that we don’t want the basic skills taught. We do want basic skills taught. We have never stopped teaching basic skills, but what we want to do is teach the basic skills so that students understand what it is that they are doing. So that if for some reason their memory fails them they can recreate it.
RH: Michael McKeown, what’s wrong with that?
MM: I think, that as you described, it’s in fact the way that almost everyone was taught, everyone understood why 3 x 4 is 12 and I agree that I certainly want my children to understand the meaning of 3 x 4 and so we don’t disagree there. The question is “How do you consolidate that into memory so it becomes automatic?” as you talked about, and in fact whether the programs, no matter what the meaning of the NCTM Standards are, it’s the books that come from it. Whether they allow just an understanding that 3 x 4 is 12 in some way or 2 + 5 is 7, but in fact a sense of immediacy so that is right on the tip of their tongues or ready to go at a moment’s notice without having to reconstruct something as trivial as 3 x 4.
RH: In other words, if I’m interpreting that right, Jack Price, Michael McKeown says you are trying to eliminate memory.
JP: NO.
[Discussion of memory, teacher competence and the Saxon Method deleted. This is the beginning of the first call of the day]
Tulvio: Hi, I’m a retired engineer and I recently received my mathematics teaching credential from UCSD. I taught the CPM/UC Davis course I Algebra at Hoover High School. We were kind of like the beta site.
RH: What does that mean, Beta site?
Tulvio: Well, we’re one of the first schools in Southern California doing this, and so we had a lot of teachers coming in visiting our schools, our classrooms, every day, all kind of impressed because everyone seems to be having fun learning. I really did think that this new math did have its points with these students who have not succeeded with traditional math in the past.
RH: Why?
Tulvio: Well, I don’t understand that too well, OK? But the students that I got, that I was supposed to teach Algebra to, couldn’t add very well, they couldn’t subtract, they could not add a row of numbers with a decimal. They didn’t know they had to align the numbers with the decimal in a vertical line. I had those kind of problems. So ...
RH: In other words, these kids have been passed through grades when they didn’t understand the concepts they were supposed to absorb in those grades.
Tulvio: That is exactly correct. They should not have graduated from grammar school and here they were in high school. OK.
RH: Now, despite that, you think this new curriculum helped them?
Tulvio: Well, it helped them because it simplified the material, OK? It made it a fun exercise so it got their attention, it kept the kids quiet, it kept them on track, and that’s what I think everybody got excited about.
RH: Interesting, Tulvio...
Tulvio: But not withstanding this fun learning experience, I found CPM Math is relatively inefficient in teaching style. Worse, the math content is reduced way down, and the little bit that is being taught takes an inordinate amount of time to teach, and, as a result, while the pacing seemed fast for a lot of my kids, it was kind of boring for a lot, for some of my better students. So while maybe this kind of math might be appropriate for Hoover High School, I think it might be inappropriate for most students that encountered it at other schools like Torrey Pines, where I have my son.
RH: Now, Tulvio,hold on a second-Now, Jack Price, here's a teacher saying "hey, it was great, it certainly did advance people who before had evidenced no ability in mathematics, whatsoever" but it also represented- I don't want to put words in his mouth- a "dumbing down" of math knowledge that was transmitted to that class with the brighter students being bored. Is that a fair assessment?
Tulvio: I think that is a fair assessment.
RH: And Jack Price, what do you think?
JP: It’s a fair assessment of what he said. I’m not certain that it is a fair assessment of the material.
RH: Well, here is a teacher who did it.
Tulvio: Well let me also add that I taught summer school where we had both students coming from the CPM method and the traditional method, and, you know, found the students coming from the CPM method were at a tremendous loss. They were lost. Luckily, I had some background, I had the background of CPM, that I could help them, but when we tested they were always behind. Other teachers had, they had the same results. As a matter of fact, we forwarded these results to Tony Spears at the (San Diego) County Office of Education saying “Hey, you ought to be aware of this. You’ve got a big problem.”
RH: Mm. How hold right there Tulvio. It sounds like, Mike McKeown, that this teacher is validating what you have said.
MM: Yes he is. It fits with what we have heard from other teachers in other districts who’ve done side by side comparisons with classes and test.
RH: Now, our California State University Trustee, is also with us, Ralph Pisqueira. Ralph, hello..... Hello, Ralph?
Ralph Pisqueira: Yeah, Roger!
RH: There you are. Now you are sitting at the other end of the pipeline, at the California State University system. We’ve had this discussion before about the need for remedial math work on kids that come out of the K-12 supposedly in the top third of the graduating students because that’s the only pool you’ll look at to admit freshmen to your system.
Ralph Pisqueira: That’s right. In fact, in 1994 63% of the high school graduates were incapable of handling basic college algebra and were not really prepared to come in and we had to remediate them.
RH: Well, what do you think about this new math. Is this an answer or a problem?
[Comments on the quality of the telephone connection deleted]
Ralph Pisqueira: There is an interesting disconnect here that in trying to teach K-12 people, nobody bothers to go to the universities to check this out. We have a Standards Committee right now looking at how, or the kind of math that we’re going to be expecting: Algebra I and II, Geometry, Trig and Calculus for college bound students and they must demonstrate competency in that, not in theory, but competency in, as you said earlier, you know 3 x 4 is 12. I find that they don’t come to our offices, they may go to individual teachers on our campuses but they don’t come to our offices and try to promote these things because they feel that all they’ve got to do is stay in the K-12. We looked at the Whole Math concept and we’re not too excited about it, and the CPM we’re definitely not excited about.
[This was the end of the calls. The end segment of program has been deleted. This includes a statement by RH on the meaning of being educated and the value of some higher math for educated people, without regard for whether or not they will use it in the work place]