Abstract
The analysis of some of the problems associated with teaching mathematics to science students provided in this thesis is a philosophical one, and as such claims to clarify rather than solve these problems. An important aspect of the thesis is the criticisms it offers of the philosophical and methodological assumptions underlying research within educational technology. In particular, the attempt to state the end point of educational processes in terms of precise statements of behaviour has been criticised, not by suggesting that there are other, non-observable (i. e. mental) outcomes, but by demonstrating that the intended behaviours cannot be stated in advance. This criticism has been based on Wittgenstein's analysis of understanding, which Wittgenstein calls a 'grammatical' analysis since, crudely, it consists of looking at how words are used. The purpose of the analysis, in this thesis, has been to show that educational technologists, in looking for behaviour corresponding to understanding, have misunderstood the use of the word 'understanding'. The context for the discussion of understanding has been provided by Kuhn's view of the nature of science and the analysis has been linked With Wittgenstein's criticism of the traditional notion of a concept since this has a bearing on assumptions made about what is learnt in the mathematics class and taken over into the science class. This analysis if accepted, demonstrates that in order to study the problems associated with mathematics for science courses, one cannot specify, in behavioural terms, what the student must transfer. Instead, and this is the main conclusion of the thesis, one must look at the criteria for understanding used in the two subjects.