Human ecology
Mathematics education
Psychology of learning mathematics
Notes - 19/4/00 & 27/4/00

notes 19/4/00

"Reviving items of information from memory storage in order to meet certain objectives is the basis of psychological production, either divergent or convergent." (Guilford, 1967, p.138)

One drawback of Guilford's model is that it deals with memory as a single operation. Other cognitive studies distinguish, three types of memory: sensory registers, short-term memory, and long-term memory. If divergent and convergent production involve recall of information for memory then these types of memory may influence tests of divergent and convergent thinking.

notes 27/4/00

Hudson's tests of divergent thinking are the "Use of Objects" test and the "Meanings of words" test.

Criticism of approach:
"Perhaps they (factor axes) are truly test-dependent, and not real underlying entities at all. The very fact that estimates for the number of primary abilities have ranged from Thurstones's 7 or so to Guilford's 120 or more indicates that vectors of mind may be figments of mind." Gould (1981:1996, p.339)


Both Guilford and Hudson take an objectivist approach to the problem of divergent thinking - their methodology assumes that their test subjects are unaware of what is being tested. The assumption may be that prior knowledge of the test will invalidate its results. Divergence and convergence rely on retrival of information from memory (Guilford, 1967, p.138). In the case of timed tests, prior knowledge of the questions may bring allow one greater time to retrival information and therefore invalidate the parameters of the test.

(Note: A further problem is that the hypothesis of the researcher might influence the test subjects. The test subjects may alter their reactions to agree or disagree with the researcher.)

Orton's review of divergent and convergent thinking in mathematics may treat these as fixed abilities within individual students. We can contrast this against the work of Pezzullo (1972) which suggests that genetic contributions to divergent thinking are extremely weak. This raises the possibility that divergent thinking can be improved through education. Alternatively, the recognition of divergent or convergent aspects in a particular problem may allow the student to choose appropriate methods for solving the problem.

Therefore, an educational perspective may look at the conscious acceptance of divergent and convergent methods by the practitioners of a subject.

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Created 27/4/00
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