In the last lecture, we looked at some of our own ideas to try to get an inside look at this idea of an idea. In this lecture, I'd like to look at student ideas, examples of student ideas. To do this, I've enlisted the help of some expert interviewees, who will be joining us periodically throughout the remaining modules. I'd like to introduce three of them, Stella Vosniadou is an educational psychologist, and a leading expert on students conceptions and conceptual change. James Minstrell is a former high school physics teacher of 30 years, and he's now a researcher focused on students ideas and instruction, and Carol Smith is another eminent educational psychologists and expert on students conceptions and conceptual change. We'll be seeing some of their comments throughout the remaining lectures. This is actually work taken from one of Stella Vosniadou's papers, and in this paper, she presents this as an example of something that surprised her. This is an interview with a student who, she called Matthew, and it's an interview about what the Earth is like. She was going into the interview thinking that perhaps Matthew might think of the earth as flat, which he had encountered before, and so she was asking questions to explore this idea. So she was exploring particularly the idea of an edge, or an end to the earth. So Matthew starts off by saying, "If we walked for a very long time, we might end up at the end of the earth." "Would you ever reach the end of the earth?" "I don't think so." A little bit later, "Could you fall off the edge of the earth?" "No, because if we were outside of the earth, we could probably fall off. But if we're inside the earth, we couldn't fall off." A little bit later, "Would you ever reached the edge of the earth?" "If I had a rocket I could." "Is there an edge to the earth?" "Yes." So these are some puzzling responses. She goes on to have further interactions, and let's look at the final interaction. "So is there an edge to the earth?" "Yes." "Can we walk over to the edge, and just stand there and look?" "Well, we can walk to a dead end." Now I've often shared this interview segment with students, and teachers, and a very common response is well Matthew was just confused. Sometimes he says there's an edge or an end, sometimes he says there isn't. He talks about inside the earth, he just seems confused. Stella Vosniadou decided to explore his ideas further by asking him to take a ball of clay, and with the ball of clay, he showed her what he thought the Earth looks like. And this is a drawing representing the clay model that he drew or that he constructed, which shows that the earth was, he thought of the Earth as being like a fishbowl, if you will. That's spherical, but you live on the inside, and there is an edge to the earth as you can see it's the top edge of the fishbowl, and that's too high, so you would have to take a rocket to get to the edge, if you wanted to get to the edge. If you walked over, kept walking and walking you would come to a dead end, etc. So if you go back and look at the interview with this model in mind, his ideas make perfect sense. So this is an example where a student seem to be confused, but in actuality had a fairly well-formed idea that he was trying to articulate. Here Dr. Vosniadou talks about this particular idea. So other ways to misinterpret this information, is that they think that the earth is a sphere, but people live at the bottom of the earth, and the top of the earth is the sky, that covers the earth like a dome. A number of years ago, one of my sons, who I think was about four at the time came to me very excited and said, "I know what the earth is like." And so I was familiar with Dr. Vosniadou's work, and so I asked him, can you show me that, can you draw that for me? And this is what he drew, and you can see that it's pretty much of a fishbowl model, where the earth is a sphere, and we live inside on the flat part, and you can see there's a little rocket ship there flying up to get to the edge of the earth. So this was very much like the interview that we just saw, and he was very excited. Here he had come to a way of making sense of both the taught idea, that the earth is a ball, but the obvious idea that the earth is flat, that there's a definite down direction, and so he had come to a way of making sense of these things that he thought he was very excited about. This is the way that Stella Vosniadou talks about, student's ideas of the earth at their constructions that try to make sense of taught ideas, as well as intuitive ideas, and bring them together into what she calls a synthetic model. Another one of the interviewees, James Minstrell was talking about this particular experiment that is very common in high school physics classes of rolling a cart along a table. The cart is being pulled by a string, and you want to examine the motion of the cart and see what happens. It's of course very common for physicists to say, let's think of an idealized situation where there is zero friction. So they were talking about this, and the students were talking about air resistance, and so James Minstrell says, "Well, let's see if we can remove all air." And let me just play that, and you can see that, they had some very interesting ideas. We were talking about, so what are the forces acting on this cart? So they brought up the idea of well there's friction acting on it. So I say well, let's suppose that we were able to set this up with no friction whatsoever, just I want to know, what's going to be like here, and what are the forces acting on it? And well, there wouldn't just be the string force, because then there'd be air resistance. So I said, "Okay. Okay. Well, let's suppose there's no air in the room then, and now what about this cart, and the forces acting on it?" And then I heard voices here and there sort of saying, "Well then, things would just drift off the table." And I was tempted to say no, no don't think like that. But I hop back instead, and said, "Okay. Say more about that." And they were talking about well like space, is a vacuum, there is no resistance there, and things, you'll see the astronauts just drifting around up there, and so if we take the air away, and there's no gravity. Okay. So that one was probably one of the biggest surprise. So this was a very surprising idea to James, and as he said rather than try to correct the students, he thought let me try to explore their ideas a little bit more, and he was rewarded with a student's expression of an idea that he has since found out is rather widespread, and so he's adapted his instruction, and he typically now asks the following question, that explores their ideas of air pressure, and gravity. So the question is, if you weigh an object, and it normally weighs ten pounds, what would it way, if it were in a vacuum? He finds that students often say it will weigh nothing or way less than it would if it was just weighed normally. So this is something that surprised him, and he has since adapted his instruction to take this idea into account. Another one of the experts Carol Smith, talks about students ideas of matter. I think most teachers recognize that the particular theory of matter is really challenging for students. So it's crazy for them to think why should a solid chair be made of tiny particles that are moving, that have a lot of empty space. But they might assume that they really have some basic ideas about what matter is, and my research suggests that there are a lot of things that are not obvious. Just give kids a clay ball, and ask if it weigh something, they'll say sure, it weigh something. Then you take off a tiny piece from that clay ball, and give it to them and say, well does this little piece from that clay ball, does it weigh a lot, a tiny bit or nothing at all? Many will say it weighs nothing at all, and if you ask them, they'll say it's too tiny to weigh anything. So this is an example of a rather surprising idea, that a little piece of clay would weigh nothing at all, and students often talk about, well, I can't feel anything, so therefore it doesn't weigh anything. This seems like it might be something that a kindergartner might think, But Carol Smith finds that this is not limited to young children. And it's not just elementary school students, I've done interviews with middle school students, where half the class sometimes decided that those things don't weigh anything at all, which can be quite surprising. So these have been some examples of students ideas in science, that are often surprising, that would clearly have important ramifications for instruction dealing with topics that involve these ideas. In the next lecture, we'll look at some ideas that students have regarding ideas in mathematics.
