I
On Learning and Language
1
The Space of Learning
Ference Marton
Ulla Runesson
Amy B. M. Tsui
School is an institution with which all citizens in the industrial world have extensive familiarity, and one that frequently attracts considerable public and political attention. The discussions about school can be heated and the opinions polemic: âWe should have less whole-class teaching,â âWe should have more project work,â âWe should have more peer learning,â âWe should have more problem-based learning,â âBy the year 2006, at least 20% of all learning in our school should be information technology (IT) supported,â âStudents should have more homework,â âStudents should have less homework,â âWe should do away with age grouping,â âWe should reintroduce age grouping,â âWe should have streaming,â and so on.
All these opinions about what should be done assume, of course, that doing this or doing that is better than doing something else. But if we ask the question, âBetter for what?â the answer is likely to be, âBetter for learning, of course.â âBut for the learning of what?â âFor the learning of everything?â These are the questions that must be addressed.
The point is that it is highly unlikely that there is any one particular way of arranging for learning that is conducive to all kinds of learning. In order to find effective ways of arranging for learning, researchers need to first address what it is that should be learned in each case, and find the different conditions that are conducive to different kinds of learning.
It is only when we have a fair understanding of what learners are expected to learn in particular situations, what they actually learn in those situations, and why they learn something in one situation but not in another, that pedagogy becomes a reasonably rational set of human activities. It is the aim of this book to provide such an understanding.
When people argue for a particular way of arranging for learning, or for a particular teaching method, such as working in groups or the use of pedagogical drama, they should make it clear what the particular arrangement, or the particular method, is good for and why. Pedagogical acts should take as their point of departure the capabilities they are supposed to contribute to developing. The point of schooling is not that students should or should not be grouped together in certain ways under certain conditionsâsuch as being divided up according to age, ability level, or gender. Neither is the point that teachers should do certain things in certain ways, or that certain content should be covered. The point is that the students should develop certain capabilities.1
THE OBJECT OF LEARNING
Learning is always the acquired knowledge of something. And we should always keep in mind what that âsomethingâ is, that is, we should be clear about the object of learning.
In this book, the object of learning is a capability, and any capability has a general and a specific aspect. The general aspect has to do with the nature of the capability, such as remembering, discerning, interpreting, grasping, or viewing, that is, the acts of learning carried out. The specific aspect has to do with the thing or subject on which these acts are carried out, such as formulas, engineering problems, simultaneous equations, World War II, or Franz Kafkaâs literary heritage. In other words, the general aspect refers to acts (the indirect object of learning), whereas the specific aspect refers to what is acted upon (the direct object of learning). The learnersâ focus is normally on what they are trying to learn (the direct object of learning), whereas the teacherâs focus should be on both; not only on that which the learners are trying to learn, but also on the way in which the learners are trying to master what they are trying to learn. We might assume therefore, that teachers are trying to work toward an object of learning. This object may be more or less conscious for the teacher and it may be more or less elaborated. But, whatever the circumstances, what teachers are striving for is the intended object of learning, an object of the teacherâs awareness, that might change dynamically during the course of learning. This is the object of learning as seen from the teacherâs perspective, and as such is depicted in this book as being evidenced by what the teacher does and says.
What is of importance for the students, however, is not so much how the teachej intends the object of learning to come to the fore, but how the teacher structures the conditions of learning so that it is possible for the object of learning to come to the fore of the learnersâ awareness. What the students encounter is the enacted object of learning, and it defines what it is possible to learn in the actual setting, from the point of view of the specific object of learning. There are obviously certain necessary conditions for learning one thing or another. The enacted object of learning is the researcherâs description of whether, to what extent, and in what forms the necessary conditions of a particular object of learning appear in a certain setting. The enacted object of learning is described from the point of view of a certain research interest and a particular theoretical perspective.
What is of decisive importance for the students, is what actually comes to the fore of their attention, that is, what aspects of the situation they discern and focus on. In the best case, they focus on the critical aspects of the object of learning, and by doing so they learn what the teacher intended. But they may also fail to discern and focus on some of the critical aspects, or they may discern and focus on other aspects. What they actually learn is the lived object of learning, the object of learning as seen from the learnerâs point of view, that is, the outcome or result of learning.
The Origin of Powerful Ways of Acting
Learning is the process of becoming capable of doing something (âdoingâ in the wide sense) as a result of having had certain experiences (of doing something or of something happening). Developing a learnerâs capability of handling novel situations in powerful ways is considered to be one of the most important educational aims. In order to address how this can be done, we have to reflect on the nature of powerful ways of acting, that is, ways of engaging in acts instrumental to achieving oneâs goals efficiently. Acting in powerful ways means, therefore, doing different things to achieve different aims, and doing different things in different situations. The powerfulness of oneâs acts is relative to oneâs aims and the situations.
Let us first consider the situations. As rational beings, we always try to act in accordance with any given situation, that is, the situation as we perceive it. What knowledge we might try to exploit depends on how we make sense of the situation. Our previous experiences affect the way in which we perceive the situation, but the way in which we perceive the situation also affects what experiences we see as relevant in that particular situation. We are trying to act in powerful ways, that is, we are trying to achieve our aims, not in relation to the situation in an objective sense, but in relation to the situation as we see it. Powerful ways of acting spring from powerful ways of seeing.
Let us take an example. Someone is standing in a lake with the water up to his knees and aiming at a fish in the water with a harpoon. He might aim at the fish where it appears to be, that is, where he actually sees it, or at a slightly adjusted angle, that is, where he thinks it should actually be if he takes the refraction of the light into consideration. These two different ways of acting are based on two different ways of understanding the situation and the latter is more powerful than the former. Let us take another example. Let us imagine that a sales tax of 10% is introduced in Hong Kong. One car dealer selling expensive cars simply increases the prices by 10%, while another adds only 5% on to the previous prices. The first car dealer assumes (wrongly) that sales tax must be added to the previous price and the buyer must always pay for it. However, the second one predicts (rightly) that demand will be adversely affected by the price increase and realizes that even if 10% of the net price has to be given to the tax authorities, a part of this sum has to be absorbed by the seller. (A similar example is elaborated in chap. 8). Again, there are two different ways of understanding the same situation and hence two ways of acting, one of which is more powerful than the other.
Let us look at some other examples that illustrate the thesis that powerful ways of acting derive from powerful ways of seeing. Let us take a very simple one to begin with. A word problem was given to some 7-year-old children. The problem is as follows: âI didnât have much money this morning when I went to school. Bob gave back 4 kronor that he had borrowed from me last week, and with that I could buy a green chocolate bar for 7 kronor. How much money did I have this morning when I came to school?â
Some of the children knew the answer almost instantly, whereas others struggled in vain. Was there anything that the former could do that the latter could not? Actually none of the children had ever seen a problem like this, nor did they remember any addition tables. Those who did not do too well saw the problem as one of addition; the child had some kronor to begin with and then he got 4 more, which made 7 altogether. But what then caused these children difficulty was the question: How can you add when you donât know what to add to? The children who did not find the problem difficult at all said something like this to themselves: âI can say that he had 7 kronor altogether and I know that he got 4 kronor from Bob. So I have to take away 4 kronor from 7 kronor.â They continued, âOne goes away: 6. Two goes away: 5. Three goes away: 4. And four goes away: 3. So he had 3 kronor this morning.â Others might have said, âI have to look for the other part. I have to find out how many kronor I have to add to the 4 kronor I got from Bob, to get 7 kronor altogether. So the answer is 3.â These children started with what they had got, which was 4, then they counted three units, 5, 6, 7, and visualized the âthreenessâ of those three units. Or others perhaps simply knew that 7 can, among other things, be broken down into 4 and 3. The children who could come up with the answer easily did not see the problem as an addition/subtraction problem but as a partâwhole problem: the whole and one of the parts are given, the whole is 7 and the given part is 4; the missing part must then be 3. So the difference between the children who handled the problem easily and the others who did not was not so much what they did, but rather what they saw, that is, how they understood the problem. The children who could solve the problem saw it in terms of parts and whole, and therefore could solve it easily, whereas the children who could not solve the problem saw it in terms of the arithmetic operation, that is, addition, and therefore had difficulties solving it. The point here is that, in many cases, seeing simple arithmetic problems in terms of partâwhole relations is a more powerful way of seeing them than seeing them in terms of arithmetic operations (Neuman, 1987) as already shown. The partâwhole way of seeing works very well for any of the problems in which two parts are given and you have to find the whole, or when the whole and one of the parts are given and you have to look for the other part. For example,
a + b = _
a â b = _
_ + b = c
a + _ = c
_ â b = c
a â _ = c
Seeing the problem as a partâwhole relation enables the child to act in a powerful way, in the sense of having a capability to deal with different problems.
Another well-known and more complex example of how âthe capability of seeingâ is of decisive importance, is de Grootâs (1965) work on expertise in chess playing. âWhat is it that chess masters are especially good at?â de Groot asked, eager to find out whether it is true, as many people believe, that what chess masters are good at is being able to mentally visualize and try out a number of alternatives actions (and their consequences) in great depth.
However, this did not in fact turn out to be the case. The chess masters did not try more alternative courses of action than other players, or follow them up for longer. But the courses of action they considered were mostly more powerful ways of handling the situations than other courses of action would have been. So, what was it that enabled the chess masters to find more powerful ways of handling the situations? The most striking fact was that chess masters seemed to see the chessboard differently to other people:
We know that increasing experience and knowledge in a specific field (chess, for instance) has the effect that things (properties, etc.) which, at earlier stages, had to be abstracted, or even inferred are apt to be immediately perceived at later stages. To a rather large extent, abstraction is replaced by perception, but we do not know much about how this works, nor where the borderline lies. As an effect of this replacement, a so-called âgivenâ problem situation is not really given since it is seen differently by an expert than it is perceived by an inexperienced person, (de Groot, 1965, pp. 33â34)
Although de Groot also found that chess masters were much better at remembering positions on the board than novices, this was only true when the arrangements represented meaningful patterns, and was not the case when the arrangements were random configurations. In the latter case, the chess mastersâ memories were not significantly better than that of other people.
These findings were replicated by Chase and Simon (1973) who by examining the ways in which chess masters reconstructed configurations that they had briefly seen, and the errors that they made in doing so, arrived at the interpretation that chess masters can remember a great number of patterns of about eight pieces, and that they interpret every configuration on the board in terms of at most seven or eight such patterns. These patterns form a kind of gigantic alphabet comprising up to 10,000 letters, each one corresponding to a certain pattern (cited in Bereiter & Scardamelia, 1993).
The main difference between chess masters and less experienced players, according to this line of reasoning, has to do with the differences in ways of seeing the chessboard, and differences in ways of seeing various configurations as meaningful patterns. It is the chess masterâs way of seeing that enables the player to engage in powerful ways of acting. And there are other similar findings on the nature of expertise. Glaser and Chi (1988) showed that experts and novices differ as to the problems they see as similar and those problems they see as different. Physicists are able, for instance, to see that the problems of river currents, and the problems of headwinds and tailwinds in airplanes involve similar mathematical and physical aspects, such as relative velocities (Bransford, Brown, & Cocking, 2000). Similar findings originate from such diverse fields as electronic circuitry (Egan & Schwartz, 1979), radiology (Lesgold, 1988), computer programming (Ehrlich & Soloway, 1984) and teaching (Sabers, Cushing, & Berliner, 1991).
Relating these cases, Bransford et al. (2000) stated that expertise in a domain is characterized by sensitivity to patterns of meaningful information that might not be available to others dealing with the same problems within the same domains. In this book, we would like to assert that various degrees of expertise, that is, the capability of acting in powerful ways within a certain domain, is reflected in the various ways of seeing, that is, in the various meanings seen in a particular scenario or problem.
Thus it can be seen that people act not in relation to situations as such, but in relation to situations as they perceive, experience, and understand them. One of the most frequently recurring findings from our own research, as well as from othersâ research, is that whatever situation people encounter, they see it, experience it, and understand it in a limited number of qualitatively different ways (see Marton & Booth, 1997). In r...