From the TIMSS-Forum and the American Federation of Teachers ...
The following are excerpts from the American Federation of Teachers (AFT) - National Center for Educational Statistics (NCES) TIMSS conference that was held after the 8th grade results were released. It is rich in observations.
The complete transcript (25 pages) of this question and answer period following Dr. James Stigler's presentation of his Videotape Classroom Study is posted on the AFT web page http://www.aft.org/timss/index.htm .
It can now be downloaded as a doc or pdf file.
Q=Question from audience; JS=Dr. James Stigler; HS=Dr. Harold Stevenson ********* Q: My question is...First of all it looks like the NCTM standards are alive and well but in Japan. My question is since a lot of this is very highly polished but since we have open-ended or inquiry-based teaching-that's what it's called in this country--how specific are the Japanese content guidelines or whatever you were calling them for each grade level? In other words, how do they describe what the curricular goals are for the year? We feel a tendency, in part it seems to me from the AFT sense, to try to nail down content standards. Are we not specific enough? We tend to want to go from one extreme to the other. What do these guidelines look like?
JS: Sure. That's a great question-a comment and a question. The first comment was that it looks like the NCTM standards are alive and well. And I want to play out that that's not strictly true. There's actually been a lot of conversation going around the country on my e-mail about that issue. Yes, in some senses, yes, it looks like the NCTM standards because there's problem solving at the center of the lesson. There's alternative solution methods. There is discussion, explanation, justification and so on. All these things map very directly onto some of the processes described, for example, by the NCTM standards. On the other hand, they're more teacher directed than you get the sense of from the NCTM standards. These are lessons that are clearly highly controlled by the teacher. There's much more lecturing done by the teacher. And I think its very important to know that this isn't really the NCTM standards though they may be largely consistent with them. But it's really Japanese. It's a different system.
The second question is about curriculum and how specified it is and I think this is a really interesting question. But it's not how specified the curriculum is but it's the kind of things that are in the curriculum. We've done some analysis of the course of study ourselves and as Harold said earlier, it's not strictly limited. I mean there are many textbooks that could be written to conform with the standards. However, they are grade-level specific and they are math specific. So, for example, there might be a standard that says students should understand the relationship between fractions and division. That is in the fourth grade course of study. That's highly specific. However, there's something else you notice about that. It has the word "understanding" and this to me is a very large difference. --------------------------- Q: The lesson. The students, when they stood up to give their own explanations of their solutions-they seemed to be listening-even when one student got a little silly or maybe he wasn't sure he was explaining it correctly, the other students--the whole class--listened. Was that because the video was on or was that the general way?
JS: No. I think that's generally true and I think that the reason for that is because teachers work very actively, again, to not let themselves be seen as the authority in the classroom. In some of the work we've done in elementary schools I know we have videotape examples. I remember one that's so vivid to me. I think it was a problem adding fractions with different denominators and the student was putting the solution on the board and he had added the denominators. And we're not supposed to do that, right?
American teachers usually cut that right off; they say, "Remember the cardinal rule of fractions. Do not add the denominators." The Japanese teacher let the student go on for eleven minutes explaining and every now and then the teacher would say, "Well this is very complicated. Wait-Can you explain why you did that again?" And then when the student was finished the teacher never said, "That's wrong." He said, "Okay. Mmmm. That's interesting. Did anyone do it another way?" And the student sat down and another student came up who had done it correctly. The teacher never said "That's wrong" because I think teachers actively work to not be seen as the authority.
Then we went and looked at the teacher manual that went with this lesson. (Okay. This was part of the elementary study.) And right there in the teachers manual it said the most common error students will make in this lesson is they will add the denominators. And then it had a box and it said, "Caution! Do not correct this error. Students must be allowed to make this error and discover the problems that it leads them into. And even if it takes days, you must not prematurely correct this error." So this is the kind of support the teacher has going into the lesson. They know students are gonna do this and they've been informed that research has shown don't correct this too quickly because you want them to follow it out and see what are the logical consequences of that. ---------------------------------- Q: A couple of things. First of all, I got really engaged in this lesson and...I mean I feel as if I just had this same lesson myself, so it worked!
JS: You understood the explanation at the end. It was very clear, wasn't it?
Q. Yeah. Also the way he used the computer. The computer gave a certain elasticity to the figures that let him...without having to go through everything that was on the board. In the end he used that to demonstrate but he wasn't dependent throughout the whole lesson on it...and that was very interesting to me.
JS: Yes. That's usually the way we saw computers used-- as an object of discussion-do some demonstration and then have people talk about it or use it to explain a concept. We...I think they had one lesson where individual little groups of students interacted with it. --------------------------------- Q: Two comments. One, I'm struck by the difference what you just said a while ago about allowing the student to make the mistake of adding the denominators and how that contrasts with many places in the United States where we have evaluation systems of a checklist type where we evaluate teachers and if you don't give corrective feedback immediately, you know you're somehow marked down on your evaluation. So I think that's a real interesting comment. The other thing I wanted to comment on in the lesson is I was struck by, at the end when he pulled it together, the way he did it. It seems to me then that in terms of retaining that information that students would retain that concept much longer having struggled with it the way they did than if the presentation had been at the beginning, which we typically do, with practice afterwards.
JS: Yes. I think that's true. I think that struggling with the problem prepares you to hear how somebody else has solved it. And even if you didn't solve it, or even if you didn't even come close to solving it, if you made any progress at all, then you're very interested. I think that's why the kids are so interested to hear how other students solved it. They're genuinely interested to know what those other students did. The other point that you brought up reminds me of a very important--this idea-the American teachers are very uncomfortable with confusion-or errors. They're very uncomfortable. They rush over to correct it even if they really want the kids to work on it. They say this is a hard problem and as soon as the kids have trouble-- they say Uh-- let me show you how to do it. And I think American teachers want to do that because they think the students are supposed to learn how to do it and this is where they have to learn it.
Japanese teachers, you can have kids say, "Waaaah...I don't understand." They don't rush over to correct because they're not worried but -and this strikes upon something Harold said earlier. If you ask the Japanese teacher about this lesson, "Do you think all the kids in the class understand what you were teaching them?" they go "Of course not! No, they don't understand, you know, but they did make progress." That's what they're looking for is an environment in which the kids can increase their understanding. But they do not believe you get this lesson and you suddenly know. And that 's why they don't worry to go over and give corrective feedback. Now they think learning takes time. And that's really their theory of how people learn. You don't (snap fingers) learn like that, you learn by struggling and reflecting on what you've done. ____________________ Q. Your comments to the last person really pertain to my question. I found it interesting that the teacher was constantly soliciting feedback from the students. Is this okay? Do you understand this? But I didn't really see too many students who raised their hands saying no, they didn't understand. that and I wondered what happened to the students who didn't understand. Over time, I know you said learning takes time in the Japanese culture, but what happens to the students who didn't understand it. Were there other methods used before or after school and, if so, how does that compare to the United States?
JS: Well, in general...I would actually like Harold to say something about that. But the question. Students who really can't keep up, now they will have -uh- the teacher will work with them individually after school. They're never pulled out of regular class. Their parents might be advised to hire them a tutor. That's another possibility. But they're never held back. Contrary to President Clinton's recommendation, they're always promoted to the next grade level. And I'd like Harold then to say more about how kids who get really far behind are handled. Do you have anything to say about that?
HS: Yes. Well, they don't expect the children are all going to be kept up. Whether in elementary school they have these techniques, the famed juku where kids go and get help from organized classes in these special after school groups-and I emphasize special-I think the teachers take a great deal of time in reviewing with these kids. But by the time they're through with elementary school and entering junior high school they're already beginning to see the development of different pathways. So that if they go into a vocational school, it's going to be quite a different process. So it isn't something that continues throughout all their education. The worst problem then is in the elementary school.
There are a couple of other things I want to say and I think then to reemphasize what Jim said, I think the confidence of these teachers is fantastic. That they really know their subject and they really know how to teach it, so they really are confident. Another thing I'd emphasize is don't think of this as just a Japanese mode of teaching. It is an East Asian mode of teaching. Well, it isn't that they spontaneously do this in every situation, but in this one classroom I saw this one teacher had on her clipboard a set of notes. What they were, were boxes up here indicating the kinds of mistakes that children commonly make in that problem and then down below were suggestions as to how to handle them. The point is it is so highly articulated, so well developed, it's unbelievable... ... The last point is not only do high school teachers have a major in mathematics, but elementary schoolteachers also have a specialty in some subject whether it's mathematics or gym. ____________________ Q: Would we see something similar or very different to this if in fact the lesson we were watching were in literature or social studies, because math does lend itself a little bit more than some other curriculum areas do to this type of instruction?
HS: Science is a little different because in science you have to have laboratory equipment and that's one of the problems they have. But I can tell you very briefly about teaching reading and teaching social studies. In social studies for example, I visited a class when they were learning about Iceland. And it was the same kind of thing. That is the teacher wasn't standing up there telling them all the derivatives of the questions that might be raised about Iceland. But by the time they ended the lesson which lasted three days, they had created the geography of Iceland, the products of Iceland and Iceland and so on and so on. The main thing I think... is the goal is not to transmit information from this authority figure of the teacher to the child. The goal is to elicit reactions from the child, which the teacher can then integrate and it's a production. The successful lesson is not one that everybody has come up with the same predetermined correct answer but it is one in which the children have really thought about Iceland and what it is like to live there and most likely they've thought about the volcanoes and so on. ___________________
Q: I have a couple of tentative observations. I'd be interested in your comments on them. First, the stgructure of the math lesson seemed to me to be very much like the structure of lessons given by really terrific English teachers that I had and that I've observed. It's tantamount to... The difference is that initially there's a shared task. So you'd have an English teacher saying, "Why was Hamlet unable to act?" That's the posing of the problem. The kids have read the text and they all contribute to that. They all have different ideas and there's sort of an interplay. It's not just a matter of opinion. Again, using my own observations. And then at the end the teacher sort of adds something to it but using various things that the students have used. I've also observed that in really good history classes that you know I had- and just in observing - and so I'm curious about your observation because these were American teachers, but in a very different humanities area.
Then the other observation that I have is--well we really saw that it was mostly one student going up to the board and sort of working with the problem and the student was struggling a little bit. And no one was jeering at the student whereas observations again, my own observations from my own experience just being in schools where students don't necessarily volunteer to come to the board, and even for some who do, there's generally a tremendous fear of humiliation. And there seemed to be no fear of humiliation here either from the teacher or commonly here from other students. So I'm curious about what you think about these observations.
JS: I think your observations about English classes are very interesting and I think that a lot of the way American teachers teach math is all tied up with their whole theory of what mathematics is. And I think that they see mathematics- Americans perceive mathematics as a collection of procedures you're just supposed to learn how to execute. And Japanese teachers don't see mathematics that way. They see it as a series of ideas that are all interconnected and you're trying to understand how they're interconnected. So I think that American English teachers probably see literature more like that or like a series of ideas that are interconnected and you're trying to understand how they're interconnected. That's what it means to understand a plot. That's a very good observation... ___________________ Q: I was wondering whether part of your study was interviewing the teachers to see how reflective they were about their teaching and whether there was any difference in terms of how much they thought about their teaching or how they could describe their goals? And related to that is a question about whether this difference in teaching style arises out of a different cultural context or whether there's a different research base. For example, there are some high achieving countries in Central and Eastern Europe which have some very different ways...
JS: Yes. ... I think we're discovering something very interesting about teachers. That is, I think Japanese teachers have a very different way of thinking about "the lesson" than American teachers. I'd describe it this way.
American teachers, I think, tend to think in terms of features. They have a list of things that are good and a list of things that are bad. And these are things they might learn in graduate school. And who knows what they actually do, but they go: that's hands-on, that's good; Oh, that's not hands-on, that's bad; or, that's not a real world problem, that's bad. The teacher's talking too much, that's bad; the teacher's not moving fast enough, that's not good. Or, the teacher's moving too slow...whatever. Whereas Japanese teachers have a more, a much more theoretical approach to the lesson. They go: That's interesting. I think he explained that too quickly; he should have waited longer because-Japanese teachers say "because" more-because students needed more time to think about that before they were provided an explanation. If I were teaching, I think I would have saved that 'til the next day. I wouldn't have brought it up at the end of this lesson. __________________________ Q: I think there's an amazing difference between the two classrooms. In the Japanese classroom, even I learned some math. In the American lesson, there was something about the pace and a lack of focus. I felt a lot of pressure and it wasn't interesting. I really did learn something, I really did learn something in the Japanese lesson - I'm talking me, personally. My comment is in American schools we have a variety of teaching styles. And I know we have teachers out there who do exactly what the Japanese math teachers do. And it seems that the difference might be that we have the variety of teaching styles and perhaps the variety doesn't exist in the Japanese schools because there is a buy in, a commitment, perhaps, to a particular teaching style. I just want to know...
JS: You know what? I used to believe exactly that before I started this study. And I now really I no longer believe it. I don't think there's very much variability. And I think this is very typical. The other lesson I have on this videotape is also very typical, but they're kind of different. So in a sense you're right. There's another style of lesson. We don't have time to watch it now, but the other style of lesson is basically almost all seatwork with the teacher going around and every now and then stopping to do explanations. But between these two lessons, this is really very typical. Now we only have a small sample, but we have a national sample. _______________________________ Q. Did you perceive any difference between the way Asian societies view the goals of education and the way western societies view the goals of education?
HS: The goal of education.is...well, if you ask different people you get different things. One guy, we asked one administrator in a Japanese school and he said that the goal of education in Japan is to reduce individual differences. I thought that was interesting. Another goal of education is to develop good human beings. So there's a great emphasis upon the development of positive moral values. They teach moral education-"Let's be kind," not religious and not political-but positive values. So I think those are the kinds of emphases you get.
I want to say one thing, though, that Jim hasn't mentioned. That is, what you see here is very typical. It isn't just that he has his hundred subjects. I mean if you were to read the 200-some observations that we have -but written, not filmed-- you will find few exceptions from that. And also we've done in the past a study of kids in China, Japan, Taiwan, and the U.S. which involved hundreds of children in first grade and fifth grade, and again, it's very coherent with what you're seeing here. So it isn't just... you're not just seeing something that is derived from this particular sample. It's derived from a lot of data which is very consistent. And I think that's very important. And I think that this theory about the theory of teaching that you start with a problem, you demonstrate alternative solutions, you evaluate the degree to which those solutions are effective and, that is the kind of script that you get over and over and over again. But the way that is executed is very, very different among different teachers.
My example, my metaphor or whatever it is, for something like this is someone playing a violin sonata. You recognize it as a violin...as a particular composer's piece but you have many interpretations of it. And you certainly didn't expect that that person would have made up this sonata. Another thing that hasn't been brought out yet is the expectation that every lesson shall be novel and unique to that teacher. That is not possible. You just can't do that. I think their point is that every lesson should be an interesting representation of the content, which they want to get across. _________________________ JS: ... Actually, I don't think it's very meaningful to say, to talk about is this or is this not a traditional lesson or is this or is it not a reform lesson? One of the things I've learned is that because our discussions of teaching take place outside of any context of examples we come up with these caricatures of different styles of teaching that don't really exist and we sharpen the differences between them and it becomes politicized-like in California right now. People will argue and have emotional debates over how you should teach and the alternatives that they stake out don't really relate to any way anybody really teaches. It becomes a forum in which you can have ideological debates. It becomes a liberal and conservative issue. It's amazing to think that the method you use for teaching math can be liberal or conservative. I think this is a huge problem. You've got to stop looking at teaching outside the context of examples. Let's look at examples and let's say what exactly is it about this that you'd like to see changed? And that's how we come to understand what good teaching is. We haven't had this conversation in this country. ________________________ HS: I want to say one thing, though, about how do they buy in? I think this is really important. We think of ourselves as a democratic, representative country. We think of ourselves a little bit differently in education, I think. If you ask what is the relationship between the teachers and the principal and teachers among teachers in these three countries. The principal in Japan, as I said is this elderly man. I've never seen a woman (this was challenged from the floor by a Japanese guest). Anyhow the relationship-- so that what happens is-as a teacher in a Japanese school, you are a member of your grade level committee. All first grade teachers will get together. You may be a member of a subject committee. And all math teachers get together. You may be a member of another committee that has to do with improving the counseling of students. Another committee, one will do the execution of athletics day. So that the school is all divided up into multitudinous committees. They're the ones who come up with the ideas. They're the ones who come up with the governance of the school. The principal is the executor of the things which have been developed by these committees. So he is not their boss. He is simply the person who does what the teachers in the school want to have executed. _________________________ Q. ...The other thing that I would like to say is that every single time I begin a seminar in THINKING MATHEMATICS, I always get the same question. Well, yeah. But what about the test at the end of the year. These tests that they have to take really I think inhibit in a sense some of the changes that we want to see...
JS: ...I have an undergraduate student who actually did a little analysis of how many of our lessons there were where the word test was actually mentioned. I don't remember how many but I know it was a huge percentage of our lessons where they actually talk about tests. You know they'd say like this is going to be on the test, or anybody who gets all of these right doesn't have to take the test or whatever. They'd talk about the test. Yes...and the kids ask about the tests and we never heard them mention-ever-the word test in the Japanese classroom. In Japan, the test isn't what this teacher's doing, what they're working on in this classroom. And again we know this is a society where they're all very focused on the test. But it's not the test that this teacher's going to be focusing on. They're trying to learn mathematics. I'm sure that next year they'll talk about the test. Or maybe they'll only talk about that in their atmosphere. ________________ SF: ...we're so smart at AFT. I was reminded by Eugenia that we gave them the AFT QuEST AWARD in 1995 because we predicted how important the work that they were doing would be and I want them to know that we appreciate it today. Thank you very, very much.
Other questions concern teacher evaluation, teacher preparation, study groups and professional development, and differing expectations. The issue of humiliation is also addressed.