In the last lecture, we looked at a number of examples of students ideas in science and mathematics. In this lecture, I'd like to explore what is the nature of students ideas? How can we understand students ideas? One question that I think is important to think about to begin with is, can't we just tell them that they're mistaken? I think it's important to think about a couple of different telling that we've talked about before. One is factual errors. So if a student says that the tilt of the Earth is 15 degrees, we could simply correct them and say well no, it's actually 23 degrees. So they had a factual error. "Oh, okay I will now remember that is 23 degrees." Usually problem solved. On the other hand, if there are conceptual issues, this is a much deeper concern. So if a student was talking about how the tilt of the Earth affects the seasons in something of a misconceived way, it's a little more difficult to just tell them the right answer and expect that to make a difference. Some of the reason for that, Stella Vosniadou will talk about, and she'll talk about how this issue of children's ideas is as much deeper than we might think. I think the most important thing that I would like to communicate is that children are exposed to science ideas. They need to greatly adjust what they already know in order to be able to understand this new information. The new information is many times very different from their experience. For example, take the explanation of the day-night cycle. Our experiences is that the sun goes behind mountains, or behind the sea, or it goes somewhere behind the clouds, and it gets dark, and the moon appears in the sky. Now, this experience is very different from what children are taught when they go to school and they learn about the day, night cycle. Professor Vosniadou goes on a little bit later to talk about how we often underestimate the conceptual change that children need to make in order to understand these ideas. If you think of the Earth as stable thing on stable ground on which we live as a sphere that moves around and turns around, these are extremely counter-intuitive ideas. But the scientific explanation has become so much part of our culture that as teachers or as adults, we don't think of how counter-intuitive these ideas might be for a child who has not been exposed to these ideas before. So we greatly underestimate the change that needs to happen in their conceptual systems in order to be able to understand these ideas Let's think about the nature of students ideas in the context that we've already thought about ourselves, that of what do you think causes the seasons? Now, one way of thinking about this often incorrect answer that students give, the seasons are caused by the distance from the sun. This is simply an incorrect statement or piece of knowledge in the mind. A different way of thinking about this is that students construct this answer drawing on intuitive and taught ideas. So for example, students know that it's hotter the closer to a heat source. That's an intuitive, the closer the stronger the further the weaker. That's an intuitive idea. They've been taught that the Earth's orbit is elliptical and so combining these ideas, they can come up with the very reasonable idea that the Earth must be closer to the sun in the summer and further from the sun in the winter. As another example from Professor Vosniadou's work, the earth is like a fishbowl, an idea that we looked at couple of lectures ago. Again, is this an incorrect statement in the mind? In fact, Professor Vosniadou talks about this as constructing an answer, drawing on intuitive and taught ideas to construct what she calls the synthetic model. So where I live is flat, that's an observable. There's a definite down direction which she calls an intuitive- presupposition. I see the sky above me like a dome. Again, that's an observable. Things are as they appear to be, what she would call an epistemological presupposition. The earth is a ball, this is a taught idea. So combining all of these, we come to the amazing insight that my son came to that we must live inside of the ball-shaped earth or a sky dome above us. So what we can see is that much of students ideas are beneath the surface. So similar to an iceberg, the answers that they express, the answers that they give, hide this whole complex of intuitive sense-making beneath the surface. As with an iceberg, where I think about 90 percent of the iceberg is below the surface, a large percentage of students ideas are intuitive below the surface difficult to observe both for themselves and for teachers. These intuitions underlying students expressions, sometimes they're called intuitive primitives such as closer is stronger, a greater force leads to a greater result, or intuitive presuppositions, the term that Stella Vosniadou uses. I've used the terms core intuitions and implicit models. Here is again Professor Vosniadou talking about this up-down presupposition. One presupposition is for example, the idea that things are organized in terms of up-down. The organization of space in terms of the directions of up-down is something that is very basic to our cognitive system because this is a world that we are exposing. So it's very hard for children to understand anything that violates this notion. Here's another presupposition that Professor Vosniadou talks about that she calls epistemological. That is, how do we know what we know, and this is the presupposition that things are as they appear to be. Another presupposition which is more epistemological is that things are as they appear to be. So if you see something, if you see the sun going down, the sun goes down. It's very difficult to understand. That things may appear to be in a certain way but in reality they are different. This is a very difficult notion to understand and often even many adults have not understood that. I think it's very important for schooling to give the education that helps children consider their epistemological beliefs. Thinks that what we're seeing is is real may not be what appears to us to be real, and that our understanding of the world is actually an interpretation. So we can see from these examples that students ideas are usually rooted in intuitive presuppositions, primitives, core intuitions, implicit models. A number of other terms have been used to talk about a very deep seated grounding of students ideas. I think another question to ask is, are students ideas static or dynamic? Do they, as with an iceberg which is a kind of a static thing? Or are students ideas more dynamic, more organic if you will, ever changing? I'd like to look at an example that might imply that the ladder is in fact the case. This is an interview that I did with a high-school students about electricity. She had not had physics before. So we were playing with batteries and bulbs, and we observed that the bulb would light under this configuration. So the tip of the bulb is touching the positive end of the battery and the side of the bulb is connected to the negative end of the battery through a copper wire. So I asked her, would this configuration turn on? She said, "I don't think it would turn on." Gave some good reasons for that that particularly, that the tip of the bulb needs to be touching the battery in order for the bulb to light. So we try this and in fact it does work, the bulb does light in this configuration. So she was very surprised, and I want you to notice the timestamp. I'll call this zero. So the time when she initially saw this surprising results and came to realize that that particular configuration would light. Actually, 41 seconds later, she again spontaneously mentions that configuration is lighting. A bit of time passes and less than two minutes later, she says, "No, that was what we were going to try, I would say that it wouldn't turn on because the tip is not touching the battery." Now here she had a very surprising revelation that this in fact did light. She mentioned it later spontaneously as lighting and less than a couple minutes later, it's like she'd never had that experience before. Her ideas, her intuitive ideas seem to be dynamically reforming into the expressed idea that the bulb will not light. So this I would call it a conceptual attractor that the tip is incredibly important and is what ignites the bulb if you will need to be in direct contact with the battery seemed to be more powerful even than her direct experience, and it seemed to reorganize her expressed ideas. I'd like to look at this idea of an attractor in this particular context. This is a simulation of a rabbits and grass. So you can see that here we have, we start out with about nine rabbits and a number of patches of grass. The rabbits will be moving around and they'll be eating the grass and if they eat enough grass, they'll be able to reproduce. So obviously, if they eat a patch of grass, that patch of grass will disappear. So the population of rabbits and grass will vary. Let's see what happens when we run it. So we can see that the population of grass shoots up because there aren't many rabbits. But then the population of rabbit shoots up because there's lots of grass. We can see that the population of rabbits seems to reach a steady-state around 240 rabbits. The population of patches of grass seems to reach a steady state of around 40 patches of grass. So I think the question is, what if we started off with a much larger number of rabbits, what would happen? I would think that we would end up with a much larger number of rabbits, but let's see what happens. So as we run this, we see that again looking at the population of rabbits is again around 240 rabbits and the population of a patches of grass is around 40. So this seems to be an attractive, a place where the dynamics of the system is attracted to. So again, similar to a conceptual attractor, this is a dynamic attractor for this ecosystem. So it seems like almost regardless of how the system starts, it will eventually come to this steady-state. So reflecting back on the nature of students ideas. I think we've seen that much of students ideas are beneath the surface. They are intuitive and unconscious, are similar to the image of the iceberg. There are also organic and dynamic rather than mechanistic and static. So they can dynamically form, dynamically reform as we saw with Tanya and her ideas about the battery and the wire. We see that there are primitives or presuppositions that can pull thinking back to intuitive conceptual attractors. So students ideas are largely intuitive, they are dynamic, they can form and reform. So it's something of a moving target if you will, which obviously makes it difficult for instruction. So thinking about implications for intuitively grounded ideas, telling is typically ineffective. I think a very powerful demonstration of that was with Tanya, when she had this very powerful experience of the bulb lighting in that configuration and less than two minutes later, she had forgotten about that. Her dynamic ideas seem to reorganize to again bring the idea that the tip is very important to the four. So we need to help students express their ideas. We need to help them critique and modify these ideas. We also need to help them draw on intuitive anchoring ideas, ideas that are also intuitive but that can help to ground more sophisticated canonical ideas in science and mathematics. In the next lecture, I'd like to focus on the second point that we need to help students express their ideas and ask, how can we go about doing that. One of the most powerful ways of doing that is to ask them and then to listen to what they say.
