Review of literature
The dialogue between biology and mathematics,
Divergent thinking is the ability to find multiple answers to a particular problem. Divergent thinking can be contrasted with convergent thinking - the ability to find the best single answer to a problem (Guilford). In the sixties, Liam Hudson carried out tests the related the convergent and divergent abilities of sixth-form boys against the subejcts that they choose to study (Hudson 1966). Orton quotes these results in his exploration of theories of mathematical learning:
|"Between three and four divergers go into arts subjects like history, English literature and modern languages for every one that goes into physical science. And vice-versa, between three and four convergers do mathematics, physics and chemistry for every one that goes into the arts." Hudson (1966, pp.56-57) quoted in Orton (1992, p.112)|
Orton also says that "only a minority of students coped equally well with convergent and divergent items" (ibid. p.113). However, the terms used by Hudson may be misleading. On the one hand, Hudson uses convergent and divergent tests to signify I.Q. tests and open-ended tests. On the other hand he uses converger and diverger to signify those boys who do better in one style of test that they do in the other style.
|"The converger is the boys who is substantially better at the intelligence test than he is at the open-ended tests; the diverger is the reverse. In addition are the all-rounders , the boys who are more or less equally good (or bad) on both types of test." (Hudson, 1966, p.55)|
We are looking here at two different ways of talking about the data. Firstly there is the method that samples convergers and finds that more convergers study science than arts. Secondly there is the method that looks at a subject and finds the distribution of convergers, all-rounders and divergers particular to that subject. Hudson was looking for a way to predict which pupils would study arts or science. Orton is looking for explanations of why "some pupils achieve more than others." Hudsonís data is better represented by a table: