Towards a Pedagogical Theory of Learning

Abstract

This chapter describes the early stages of developing a theory of learning, which offers an alternative perspective to those currently underpinning teaching and learning. It is not specific to higher education; indeed, it has been developed mainly from work at school level. However, the ideas are sufficiently general to apply to teaching and learning at university level, and there are already some examples of research in universities based on the theory. As it is still being developed, the status of ‘theory’ has yet to be attained: what is offered is better thought of as a ‘framework,’ a way of thinking about learning within educational contexts. Its importance lies in directing the teacher’s attention to the specific  object of learning —the actual content of what the student is expected to learn. The theory also suggests in general terms what is needed to make learning possible, and so is a pedagogical theory which has generally been referred to as variation theory , for reasons which will become clear.

Appendix: Reinterpreting Approaches to Learning

The main focus of this chapter has been steps towards a pedagogical theory of learning primarily from the perspective of teaching. But this research builds on earlier studies of qualitative differences in learning at university level. In this appendix an attempt will be made to briefly illustrate that the variation framework outlined so far is also applicable to such differences (cf. also Marton 2015).

Deep and Varied Approach to Learning

Marton and Säljö (1976) made a distinction between two ways of going about learning, the deep approach and the surface approach . The former refers to the learner focusing on the text being read (“the sign”), the latter refers to the learner focusing on the meaning of the text (“the signified”). The distinction was based on the learners’ own accounts of how they went about learning, i.e., how they experienced their own attempts to learn. In one case they seemed to direct their efforts to be able to retell the text, in the other to tell what the text was about, in their own words. Those adopting a surface approach did not seem to search for the meaning of the text actively when reading, while those adopting a deep approach did so. The meaning dimension of variation was not opened up in the former case, but was so in the latter. When answering the question what the text was about, those adopting a surface approach tried to stick to the text as closely as possible, i.e., keeping it as invariant as they could, while those adopting a deep approach opened up the dimension of wording, but keeping the meaning found invariant. The distinction between the two approaches to learning can thus be depicted in terms of differences between two patterns of experienced variation and invariance . Silén (2000) investigated medical students’ ways of learning in the context of a problem-based learning program, from the point of view of the students’ responsibility for, and independence in, their own learning. She concludes:

Challenging one’s own perspective, looking for alternative explanations, comparing different ways of seeing the same thing, searching for novel angles and trying out understanding and doing things in different ways, are acts that the students take the initiative to themselves. This implies that this is an important and fundamental constituent part of learning. It is interesting that in the present context (the students own responsibility for their learning), seeking variation becomes to a great extent something that the students have to do (p. 265, translation mine).

This study was followed up a few years later, in the same context, with the same kind of students, by Fyrenius et al. (2007). In this case, 16 medical students were interviewed about their understanding of certain physiological phenomena and about their approach to the learning about those phenomena. In 10 of the 16 cases, the researchers found that the students strived for changes in perspectives and for deliberately creating situations or actions rich in variation (p. 156). This is often expressed metaphorically: talking about turning around, twisting, looking at the object of knowledge from different perspectives (In the transcripts below, S11 indicates Student #11, S20–97 Student #20 of the 1997 class, and so on).

(S11) It [the tutorial] contributes to what you should use the knowledge for, it is like the clinical, ‘why is that treatment better than this one? Why doesn’t it work? The same kind but it ought to work’… then you have more, like, applied it, even more like twisted and turned it, and applied it more and dissected it even more, so to say … (p. 157).

In the next quote, we can see the same “turning and twisting” metaphor in the context of “repetition with variation”:

(S12) If you work through one thought several times so that you sort of get familiar with it in a way, it sort of, that you can twist and turn it in various ways and then it sticks better (p. 157).

The need for coming up with different options (or opening up a dimension of variation) was expressed by another student in the following way:

(S7) [facts] are tested against other facts and there’s questioning work in progress all the time, how can this potentially be related to this? And then maybe you come up with some alternatives, some of which are more likely than others, some feel as they have potential (p. 157).

The above quote from S12 resembles a way of going about learning found among Chinese students. They combine learning for understanding and learning for remembering (variation and repetition). They are reading different accounts of the same thing and they read the same account several times, but different ways.

Comparing studies of high school students with their own study of university students, Marton et al. (2005) argue that while understanding and memorization are not differentiated in young high-school students’ accounts, they are frequently separated and even contrasted by older high-school students, to be brought together in a complementary relationship by many university students. Twenty students from various fields of study, at an elite Chinese university, were followed during the first one and half year. Many of them referred to the importance of variation in gaining understanding, and to an increasing extent to the central role of differences.

Some students pointed to the pattern of variation and invariance called generalization. The focused aspect of the object of learning is invariant, while other aspects vary:

Extracting what is general from different cases (S20–97).

You and the thing are in the same world. It has already been in your mind. I might not be able to speak it out, but if I encounter this word, a picture will appear in my mind and I know the general idea (S3–99).

… you know something about what you have learned, extend this knowing and draw inferences about other cases from one instance (S6–97).

… getting deeper and deeper, from the superficial to the essence (S7–99).

… you cannot stay on the surface of what you learn. You should mix in your own ideas while you learn it. So you can further digest what you learned … to have your own idea after you learned it (S5-97).

Other students referred to the pattern of variation and invariance called contrast. The focused aspect of the object of learning varies, while other aspects are invariant:

… to change to another point of view, or another side, and try to think from that person’s point of view (S6–99).

You will approach it from different angles, and then go deeper into it, and at last draw a conclusion (S14–99).

I will first grasp its intention and extension, then grasp its characterization, find the difference between it and other things.

The difference is of great importance …

Through comparison, for example when I get a concept, I will first read through it to find its general idea and its key points, then compare the key points with the difference between this concept and others (S20–99).

For example, I need to understand three kinds of knowledge, A, B, C. A is the learned knowledge while B and C are the unknown knowledge. Then I will use A to analyze B. After understanding B and comparing A and B, I have got knowledge AB. Then I can use AB to analyze C and thus get the knowledge ABC. In this continuous process, there is neither a clear end, nor the clear starting point. Understanding and memorization are mixed and this enlarges our knowledge (S20–99).

Try to think from other people’s perspectives (S8–97).

… knowledge becomes deeper. … If I want to understand something, at first I should generate interest in it. Then I will seek for its features and why it has such features that makes it different from others (S18–99).

(If you want to understand something, what would you do?) I will first think, look up references, and then discuss with classmates, comparing mine with their opinions … (S15–99).

(Marton et al. 2005, p. 310)

Experienced patterns of variation and invariance in learning illuminates what a deep approach to learning is like.

In order to develop a powerful way of seeing something, the learner must decompose the object of learning and bring it together again. Such decomposition happens in two ways: through delimiting parts and wholes, on the one hand, and through the discernment of critical aspects, on the other hand. Towards such an end, the learner has to create the necessary patterns of variation and invariance . This is deep approach to learning in terms of the Theory of Variation .

Surface and Less Varied Approach to Learning

What is then the alternative to deep approach , in such terms? Marton et al. (2005) found three students in the beginning of the study, one of them also at the end representing such an alternative. The most common answer to questions about his way of studying was ‘I will read it over and over again’ (S12–99). When he was asked about if he had a particular method of preparing for argumentative (as opposed to short answer) questions, he said:

I will memorize the key points, such as those beginning with “First,” “Second,” and discussion and exposition.

(Do you think that you have some special methods to memorize things?)

No. I only read them many times.

(For example, if you read something three times, is it the same every time? Does the meaning change?)

The same. I just repeat it until I can memorize it.

(No difference?)

No. (S12–99) (Marton et al. 2005, p. 300).

The repetitive (invariant) way of handling the learning task can also be illustrated by some interview excerpts from Boulton-Lewis and his colleague’s (2004) study how a group of Australian students with comparatively weak academic background, tried to cope with the demands of the university;

I: So what actually does study mean to you?

S: Probably just actually learning the material. Actually sitting there and for an exam … if I have to study for an exam I’ll be copying out the sheet and rereading it over and over, you know, start doing that a week before the exam or something so I can be familiar on that.

I: So after you rewrite what you are actually studying, what’s the process after that?

S: I find the easiest way for me to do it is probably writing it out again and reading it to myself and then reading it, reading it, reading it (S1–97).

I: Did you try and memorize them?

S: Yes. I wrote them over and over again on a piece of paper, the science word for it and the meaning for it. I used to write out a whole sheet before I’d get it in my head. I used to try that method before as well, just getting there and saying the bold words and the definition and read it over, I used to do both, like read the other ones and the ones I don’t get through I write over and over until I get it (S2–97).

I: How do you actually memorize it?

S: Read it over and over, then I come back and then I cover it up and I see if I remember it then I’ll have a look at it, if I’m right I’ll keep going but if I’m not I’ll read it again and again and again until I get it (S10–97) (Boulton-Lewis et al. 2004).

These quotes illustrate Brousseau’s (1997) thesis about the paradoxical nature of the “didactic contract,” from the learner’s perspective: by trying hard to fulfill the didactic contract, in the sense of becoming able to answer the teacher’s questions, the students make it impossible for themselves to fulfill the didactic contract, in the sense of making the ideas taught or read about, their own.