Human ecology
Mathematics education
Psychology of learning mathematics
Project Draft
Draft 18/5/00 - Methodology


Objective testing in Guilford and Hudson. Top

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 et.al. (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. In this case a Q-methodology test may be an appropriate statistical tool.


Critical theory and Q-methodology - 22/5/00 Top

The conscious (or reflective) acceptance of ideas by an audience is part of the (practice) of critical theory (Dryzek, 1990, p.185). Critical theory has had an impact of education research, mainly in field of curriculum studies (Cohen et al., 2000). Cohen et al. note that there is no empirical support for critical theory, but that it is used in the field of action research (ibid, pp.). Action research deals mainly with qualitative methods, and might provide an alternative perspective to the objective quantitative methods of Guilford and Hudson. However it may also be possible to use a quantitative measure of subjectivity. One such measure is Q-methodolgy. Dryzek suggests that Q-methodology may be a useful tool for critical theory (Dryzek, 1990, pp.173-189).

Q-methodology was invented by the physist and psychologist William Stephenson in the nineteen thirties. Q-methodology provides a qualitative measure of subjectivity. Following Brown (1991), I will briefly outline the main steps involved in Q-methodology:


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"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. (Possibly not)


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Created 22/5/00
Last modified 23/5/00