Conference Material

Maryellen Harmon: How do you do that?

Alfred Manaster: Working as a community together was another one.

Maryellen Harmon: I guess there were some ideas that struck me, perhaps, as being key, and others as being, flowing from them, just like the people at one table said, you need to get the key idea and then it moves by a nice transition from one place to another. There were two things that struck me as being really key, and one of them, I think, is the notion that there has to be that content control. I forget which table said that, but you have to know not just what you're going to teach today, but what happened in previous grades, what happened last week, what built up to it, and still more, where it's going. What are the problems in tenth grade, because of some foundation that didn't happen in third grade. It's a very interesting question, anyhow, it's a question that I think we should look at.

Alfred Manaster: And I think it's related to one of the big differences between the U.S. and most other countries. Most other countries do have a national curriculum that's carefully laid out, so a teacher teaching third grade knows what's needed to be known in terms of where thing are, have come from and where they're going, but that teacher doesn't have to solve all those problems by himself or herself. Here, in California there are five hundred school districts with five hundred different curricula. Multiply that, not by fifty but by something close to fifty, there's a lot of room for chaos, but more to the point in terms of teaching it seems to me, if we as a community provide teachers with a well laid out curriculum that gives them the opportunity to really practice their craft, which is to say, to work together, as some of you mentioned, to build lessons, to reflect on them, without having to worry about where does this fit in the curriculum. Let someone else do that. Give them a coherent vision, this is what the curriculum about, this is why proving is important in mathematics, this is why designing experiments is just as important as carrying them out in science, but then let the teachers work on the really hard part, another hard part, both parts are hard, of how do we, with our students in our classes, encourage our students, give them the respect that they deserve, and at the same time be guiding them through this curriculum which does have many endpoints and get them to it.

Maryellen Harmon: You know Al, there's something here, I did hear some of this somewhere, but I want to come back on it. I think that there's a change in philosophy that's needed, I don't think this has a quick fix. I think that we need to think differently, teachers need but I need and you need to think differently about the teaching/learning process, that the learner (I work a lot with teachers, they're my learners) is just as competent as I am. I may know a little more about this and they may know a little more about that, and somehow we have to come into mutuality, but the learner is competent, so we don't have to do what I sometimes have heard in workshops, "Oh you can't ask the teachers to do that, they won't do it, they don't know how to do it, they don't want to do it, duh-dah." I need to believe in them. Just as I think the teachers need to believe in the student's potential.

Alfred Manaster: But there's a risk.

Maryellen Harmon: Where's the risk?

Alfred Manaster: You have to be careful, because that can be overplayed. You can take those words way too far and say, as I think Joyce likes to worry about, we want students to discover on their own the principal of conservation of energy.

Maryellen Harmon: But you can't.

Alfred Manaster: Yes.

Maryellen Harmon: You can't do that, and that's why the teacher has to have that content knowledge, to know how to get from where the student is to where they need to get. And, not be afraid to lecture. You know, we've got a lot of politically correct stuff, kids have to work in groups, even if working in groups is chaos because you're up at the board lecturing.

Alfred Manaster: [laughs.]

Maryellen Harmon: Or kids have to discover, but they get to a point where they can't discover anymore. Somebody's got to say "You're almost there. This is what the scientists think today. This is how we make sense of it." That sense-making kids can't always do for themselves. But they need to struggle. Just like we all needed to struggle. You struggled with the problem of how are we going to get professional development to work, to get where we want to be. And temporarily, having seen that tape, temporarily now we can forget the Japanese versus U.S. thing. Just forget it. Because they've got their culture, we've got our culture, they've got their problems (don't think they don't), we have our problems, but we have to deal with the teachers we have, and they need affirmation. You're running a workshop. There comes a key point in that workshop where you say "Right on. You made a good point. Let me take it a little further."

Alfred Manaster: One of the comments that came from one of the tables this morning, the Japanese script is not the only way, by any means. And I can understand why that comment was made, because I think it sounded like I was saying "Here is an example of what I obviously consider and my colleagues consider a very powerful lesson, here is a script of how many lessons like this are taught," that doesn't mean, we don't have time to do everything, right, as you well know, in fact we don't have time to do hardly anything, but this is one model, it's a model I think is very powerful, it doesn't always apply, but, it does apply, I think, a lot of times. I also wanted to say in terms of science again, I see this as guided inquiry. That is an example of guided inquiry in a lot of ways, and that the students are trying to figure things out on their own. I wanted to bring up one more point; it seems increasingly clear to me there are many communities involved in this activity, one of them which some of us would like to see more involved is the research mathematicians and research scientists, and one of the questions is "How do you pull those kinds of people into these kinds of activities?" My experience has been, it's really helpful if you have something concrete to talk about. Doesn't really matter what it is, it should be something of mutual interest, something where the scientific researcher feels that there's something to contribute, but also something where the education community feels that what's being contributed is relevant, important, can be valued. One way to do this, which we're starting to do in California, which I find quite exciting, is to look at video tapes of U.S. classes and what we've been doing is having tables made, and then getting mathematicians to look at those tables, to focus on the content, and then go back to the teachers, even, which is really fun, I have to say, from personal experience, and talk to the teachers about the lessons and watch them recraft their lessons. So, you can bring people like me in to do this very limited kind of activity, which provides a little bit of help. Those teachers need a lot of other support, they also need to be risk-takers, but when it happens, I can tell you it's really exciting.

Maryellen Harmon: That word "risk" is a word that went around a lot, it's a word that I feel very strongly about, and I'd like to tell you an anecdote about a man at Harvard that I know, but that's an aside for the second, because it isn't just that the kids are at risk, it's that the teacher is at risk. The teacher has, for a long time, if an experienced teacher, worked in a certain way and it has worked reasonably well, and it has gotten good test scores on a certain kind of test. And there's always a dissatisfaction, but it has worked. Now you're asking the teacher, not totally to abandon that, but to make a hundred-and-eighty degree turn and try to do something in a very different way. And what do they do? Just what kids do. They go too far, they think inquiry means they've got to discover Newton's Laws and Einstein's as well, or they're afraid to go at all for fear of what the kids'll do, so they have to be allowed to make those mistakes and the professional development scheme has to be big enough, long enough to provide some correctives, to bring out, "No-no, that's going a little too far, the kids can't discover everything," or whatever. And it seems to me that that's important. I want to tell you about this man at Harvard because I was so struck by it. This is an experienced professor in political science at Harvard, and he suddenly got the light, you know, revelation from on high, that the way to teach his classes was not to stand up and lecture to them, although he was very knowledgeable, but to engage them, because they were people coming in from business, coming in from education, coming in from medicine, from all sorts of places, to engage them and build, what he wanted to get them to learn, don't forget that, he had some plans, to build that out of their experience and expertise which was rich in areas where his wasn't. He took a high risk decision, and beginning one September about five years ago, he said "No more do I lecture, I'm going to do this or bust." His colleagues thought he was nuts, the people that he talked to and described what he was doing thought he had gone right out of his tree, but he did it, and it now is very successful. But it took him four of those five years to iron out the bugs. That's my parting shot.

Alfred Manaster: And that really does have to be a parting shot because we're out of time. I think we both learned a lot. I learned that Maryellen and I can have a useful conversation for five hours yesterday, we're not going to do that with you today, I promise, and we turn it back to Diane.

Maryellen Harmon: Thank you very much.

Diane Spresser: And this is the last opportunity that Alfred will have with us in a formal role as a leader for sessions at this meeting. He'll be with us through much of the rest of the day, but then he has to leave for other commitments. So, given that this is the last time that there's a formal such opportunity, Alfred, I'd like to just sort of mention that last evening, after the session and I went home, tired as I was as I'm sure all of you were, I was reflecting a bit on why I felt so uplifted after that session. And in fact I took a few moments and jotted a few things down, even last evening, because I thought about the session that you, Maryellen, Susan, and others had planned last evening, and how well it was designed around significant and engaging content. That the session was coherent with a lot of strong connections across its' various components. There was a supportive use of technology. The content of the session lent itself to a variety of observations by participants. And I found that as I wrote out the various things that I thought marked that session, that I was in fact writing many of the things that came out of the observations that the panel made, after we had engaged in those activities. In particular, the leadership had such a deep understanding of the important ideas to be developed. And because of this, a kind of confidence that enabled participants to go down different avenues of thought, and so, Alfred, we thank you for having made this a priority on your list to come and spend time with us, we thank you for the expertise and the experience that you bring to this as a mathematician, as an educator, and through your deep involvement for TIMSS, but most of all, perhaps the ultimate reason for saying thank you is the modeling that you did last evening for the best of the Japanese lessons. So please join me in expressing our appreciation to Alfred.

[Applause.]

Alfred Manaster: I just have to say thank you very much to Diane and to all of you, and also, another thing that was modeled very much last night was, yes I was the presenter, but I was only part of the creator. This was a team effort, and the hours that were spent with Maryellen and Susan and others before were all part of this, so it wasn't just me standing up and doing by a long shot, it was a very much a planned activity, trust me. Thank you all very much.