Interview: Roy Pea
Excerpts from an interview with Roy Pea, Director of the Stanford Center for Innovations in Learning, Stanford University
Discussion of "Building on What We Know – Cognitive Processing"
Cognitive processing refers to what the mind is doing as it listens, as it comprehends, as it produces symbol systems of all kinds, whether it is language, whether it is visualizations of different kinds of knowledge. And the term processing is used by analogy to the computer which processes information, does various transformations of it to get to results. And a lot of the work in cognitive science sought to understand how the mind worked by building computer models of how the mind worked. And they made some pretty good progress in creating programs that could play chess rather well and solve algebraic equations and things of that nature. Whether they've in fact provided an account of how the mind works, is quite up for grabs. But the term cognitive processing has stuck as a way for thinking about the reasoning and thinking that goes on and how it is that the structures and processes of the mind work to reason, to remember, to retrieve information when it's appropriate, to transfer it to a new situation, to form concepts, and do many of the things that are integral to the learning enterprise. And so cognitive processing is an important thing to think about and learn about, both as a teacher, but also as a learner. I mean, it's important to emphasize that young kids have pretty developed theories of cognitive processing themselves. People that have studied even elementary school children's understanding of memory, of language, of reasoning, they're quite reflective about these things. They recognize that when they're tired or distracted, they don't do as well, they don't remember as much. So they're attentive to cognitive processing. What teachers can help bring to the equation from the learning sciences is much more attention to teasing out what their learners are thinking and believing by having them represent that knowledge in conversations, in pictures and in other modalities.
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How we process information is so variably influenced, it's a miracle that we do as good a job as we do. We can be influenced by the energy we have at a particular time of day, hunger, things that are very common sense. Things that are less common sense, that teachers can do something about, involve how are students already thinking about the subject matter, that they're doing some cognitive processing about. And for that, it turns out that the research tells us we don't listen enough to how our students think. We don't give them an opportunity to voice their beliefs, to draw pictures, to tell them what they think about and what they see. And many adults are surprised when you actually start to interrogate a child in the most positive sense, to understand how they think and believe, to find that their thoughts are very curious and unusual constructs. They might believe that a cloud really is alive, like a person, as a Piaget taught us years ago. Or that a moving tree is a living thing like a person. And these beliefs that they have are important to understand for us to go building on in instruction. So, prior conceptions, some call them misconceptions, we prefer to call them prior conceptions, are one very significant influence, that work in the learning sciences has helped reveal over the last number of years and that I think teaching can really pay attention to.
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One of the highlights, and again work in the learning sciences, look at representations. Both mental representations – how is it, is it in images or words or in other symbol systems that students are thinking. So this we talk about as mental representation. But every bit as important are external representations, inscriptions. When someone writes something down, a written language, a picture, a diagram of how things work with little arrows for flows and so forth, processes of some kind or other, and, it can be of considerable aid for the teacher to understand how the learner's thinking and to help advance that learner's thinking to use these multiple representational forms. And they have different trade-offs. And this is part of what a learner needs to know. A graph may be wonderful for looking at a slope, but not so good for other purposes. So, each of the representations that we use for reasoning and for asking questions, has trade-offs affiliated with it. There are certain things that it's good at and other things that it misses and, and part of what we need to help learners do is to understand the strengths of those representations, and when they're appropriately used.
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Visualizations are, as Rudolph Arnheim tells us in his famous book Visual Thinking, one of the more interesting inventions of human kind. Of course written language is a form of visualization, but usually we're talking about many other things and they range from pictures of actual, unique situations to diagrams that represent a huge class of situations. They also include maps, concept maps where one can do concept mapping of the relations between concepts and something new that one is learning. And one of the things that visualizations do is they use vision to think. And so, that's one of the strategies that humans have acquired to overcome their cognitive processing limitations. They can only keep so much in memory at once. The magical number is seven plus or minus two. And so they write things down in the world to serve in some sense as cognitive aids for their thinking. So as we go writing or drawing a diagram we can start to look at part/whole relationships in a way that's very hard if we have to hold it all in memory. So a diagram can in a single glance, show the relation between the parts of the machine to the machine itself. McAuley's wonderful book, How Things Work is one good example of this and in the computer world, more and more effort is going into creating visualization systems that can help students understand very complicated global phenomena like, issues in the environment, global warming, and changes of that kind.
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Visualizations can help students depicting their thinking about a situation which might include the provision of an explanation. This is how it works because. And what visualizations can do is off-load from a pretty limited memory, not just in kids, but in adults, some of the work. That is to say you can draw in a picture something that you then no longer have to remember as you go building a complex story. So, I could create a diagram that describes my day and all the things that I do in it and what I need to do as part of a plan. We do that all the time – it's called a to-do list. So the to-do list ends up being a visual organizer that helps solve a number of problems of memory and thinking. And the same thing that makes a to-do list useful for an adult, makes concept maps and other kinds of visualizations useful for kids. It becomes a cognitive tool for reasoning and for explaining and for communicating.
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Well, many of the same strengths that make visualizations useful for reasoning and thinking are available as tools for the teacher, as well. The rub there, or the catch, is that if the teacher only uses these powerful visualizations to tell knowledge to students, they're not going to get the opportunity to give students the power of these same tools. So, I did some research work in a number of, well-known high school classrooms some years ago on how geometrical optics is taught in physics. And this is an 18th century science – it's nothing new, but it involves how does light interact with matter, like a lens or a mirror, to form images. People have experiences of this every day. And, diagrams are used to teach this subject matter. But in these classrooms where students did very well on tests, very famous schools actually, when they were asked to reason aloud at a chalkboard later, and by drawing a picture, they were very poor and didn't reveal much understanding. And the simple reason was that they had memorized the formulas. They had memorized the diagrams they had seen the teacher put on the board, instead of having some facility with using this powerful visualization tool themselves. So if teachers only use visualizations in a lecture mode and don't give the students an opportunity to construct visualizations, they're missing a crucial learning and teaching opportunity.
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So, visualizations provide a new window into thinking beyond hearing students talk. So a student who might be less verbally oriented, may be quite willing to draw a picture of how they're thinking about things and to even label its parts in a way that can then become what we would call a conversational prop for a learning conversation – something that can be pointed at, refined, talked about in a learning community in which all of the kids in the classroom are creating visualizations. And part of what's really interesting when a teacher does this, in virtually any subject matter – it can be math, science or humanities, social science, social studies, language arts – is that you find real differences in the diagrams and the pictures that kids create. And part of that is due to their having different beliefs. Some of it is due to their having idiosyncratic conventions for representing the knowledge in, some form of a visual representation. So this gives you opportunities as a teacher for doing several things at once. One is to introduce more canonical or typical forms of representing those ideas visually. Another is, learning about potential problematic conceptions in the way that the child is thinking as revealed through those pictures. And the third opportunity is that it provides their peers with a model for both appropriate ways of thinking in the domain and problematic ones. So it has many, many opportunities in making thinking visible.
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The differences between novices and experts in any of the fields in which cognitive scientists have studied them, from chess to writing to mechanics to bartenders, all of these different areas are ones in which experts tend to among other things that differentiate them from novices, see the world differently. They see patterns in situations that are typical problems in the area. So if you're a chess master, a classic finding that has chess experts versus novices, look very quickly at chess boards that are flashed with pieces that are in legal positions, that is ones that could've actually happened in the game, and you find, not surprisingly, that experts remember far more than novices do because they can see what the meaning of the different chess pieces in that position is, what possible states of play they could represent because they've had huge experience, usually over 50,000 hours to become a chess expert. But if you, interestingly enough, just scramble up the pieces and show the novices and experts those same boards, there's no difference between an expert and a novice. So it's not that experts have bigger memories. The novices do. But they've come to chunk the world differently and what they see. The same thing works for an expert teacher versus a novice teacher. When they look in a classroom in the to and fro of 25 to 30 kids all vying for attention and, in the context of some complex piece of teaching, novice and expert teachers see very different things. They see different opportunities. They see different problems arising. Like a chess player, they're running ahead what are different scenarios. If I do this thing with that child's question, what will happen to this other group? And so part of what it means to bring the child novice to being more of an expert in relation to, say mathematical problem solving, involves looking at what are the aspects of skills and concepts that an expert has and how can we help scaffold or support the learner to go building those. And so some of the things that differentiate mathematics experts from novices are, among other things, their facility with lots of representational systems. They don't only use equations. They will write. They will draw diagrams. They will use computer programs. They will create graphs of different kinds for looking at functions. They will even do data tables, again, depending on what their purpose is. And so they have a meta-representational capacity. That is, they know what representational systems there are and what they're good for and pick them. They also manage their mental work. They have a metacognitive capacity to think about the time that's allotted, think about what they know and don't know and focus their attention so if they go pursuing a process for a particular point in time, they don't run it into the ground and run out of time. They'll go to a certain point, see that it's not gonna work, and shift course. And so, these are only some of the properties that differentiate novices from experts. But, part of the process of helping students become more expert involve modeling the kind of thinking that a more mature problems solver in the domain does, giving students opportunities to pursue that same kind of thinking aloud with support from the teacher and the distributed experts in the classroom, because some of the kids may know more than that particular child. And to, over time, fade that kind of support, having seen what expert problem solving looks like, and supported the student in trying to perform at a higher level and then, withdraw the support and see to what extent they can move themselves along an expertise continuum. This is, of course, at a level of abstraction, but I'm sure you'll be playing that out in the series in the concrete examples.
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There are various visualization techniques that are used heuristically. Now this is a word that is kind of, to mean rules of thumb. Things that may be useful, not necessarily guaranteeing a result which an algorithm does. So, heuristically, a matrix, or a table is often really good at brainstorming, and highlighting gaps in one's thinking. So, if you'd like to take an example, you might have the faculty who teach your math courses, as rows, and the different topics that are covered in the curricula being the columns, and you might find from a process of curriculum mapping that low and behold, there are some missing topics that you should have been treating in the curriculum that you didn't. This ends up being a useful value of the matrix for faculty work. Well it's not surprising that it could be useful for kids as well. And, so in their case, you might want to, be using matrices for planning different kinds of story outcomes in a story writing task, or, science problem solving as well.
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[looking at the segment in "Building on What We Know – Cognitive Processing" that features Sandie Gilliam]
Part of what this teacher does that's extremely useful is setting the problem solving context in a motivational one of human narrative and drama. And that helps, attracts students' attention, probably relates to situations they could imagine themselves in, as opposed to being simple, dry, decontexturalized formula. She then gives them the opportunity for reasoning quantitatively about their use of supplies during their trip, water in particular. And so they then have the opportunity to talk about what the shape of a graph would look like for water availability at different times in the trip – when they were trying to conserve and a period where they don't know they're going to get water, when they refill and so forth. And these issues of rate of change of a quantity are important not just for mathematics, but in physics and in a whole host of other subject areas. So, engaging students' sense making around a narrative that then provides a kind of a smart tool, a graph, for helping reasoning with, is really a powerful strategy for bringing mathematical meaning into students' reasoning and experience, even in what, in this case could easily be a social studies problem where no mathematics might normally be done. So, she's doing a lot of work here weaving together some historical work, so the students' making sense of situation and mathematical representations.
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[looking at the segment in "Building on What We Know – Cognitive Processing" that features Fe MacLean]
So in Fe's class, she has the students classify animals, with cards that represent those animals because she's really interested in how these students think about the animals and on the basis of what features do they categorize them into groups. To hook back to our novice/expert distinction, a lot of the methodology there for distinguishing novices from experts has them sorting, different problems into piles. And experts tend to look at deep similarities, between problems situations, say in physics, whereas novices tend to categorize based on surface features of the similarity of, for example, the diagrams and the problems. Are there things going downhill in both problems? Whereas at a deep structural level in terms of Newton's Laws, that might not be, those things might not be similar. So in this case she's trying to tease out what are the student's categories? And then she does some work tapping the distributed expertise of the group around what are the features for thinking about these concepts? Why are these different, species in one category rather than another? And she starts to get out what are the properties, that for these kids help define those categories. A very different approach would've been to just tell them the answer. What are the categories as we scientists have defined them, which doesn't give the students an opportunity to, on the one hand do their own thinking about it, nor does it give the teacher an opportunity to learn what they're already thinking. And, of course, it doesn't mean that their results will be error-free. They may have concepts that need some work. But the point is, she's engaged their thinking in a way that if she'd only told them the answers, she would've engaged only their memory in a way that after the course is over and their tests are done, they are most likely to go back thinking the same way that they did before. So, the opportunity of bringing out students' concepts and then building them in a conversation in the moment, is the powerful idea in this scenario.
