Human ecology
Mathematics education
Psychology of learning mathematics

Convergence and Divergence

Definitions: These definitions where introduced by Guilford in the nineteen fifties as part of his 'structure of intellect' model. Guilford was unhappy with the one or two factor models of intelligence that where advocated by Pearson, Spearman, Birt, etc. There had been attempts to contrast intelligence (as measured by I.Q. tests) with "creativity", however Guildford found that these terms were unsatifactory. Guilford constructed a multi-factor model of intellect from factors that emerged from intelligence tests and theoretical discussions of intelligence. This model replaced the terms "IQ intelligence" and "Creativity" with the terms "convergent production" and "divergent production", respectively.
Convergent / divergent thinking - (Orton, 1992, pp.110-113) - (Hudson, 1966)

Convergence and Divergence

Most people are either divergers or convergers, a few are both.

From Hudson?? (1966) quoted in Orton (1992, pp.112-113)

Examples of convergence and divergence in mathematics
After reading Liebeck (1984)

Possible examples of divergence:

Possible examples of convergence:
Notes 16/2/00

The sixth form subjects chosen by convergers and divergers (n = 267). (Hudson, 1966, p.180)

History (note 19/2/00: 5% difference from null hypothesis - Kolmogorov - Smirnov test on this distribution of pupils)

Modern languages Mixed courses Classics Physical science Biology "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. As a matter of convenience, I define 30 per cent of my usual schoolboy sample as convergers, 30 per cent as divergers, and leave the remaining 40 per cent in the middle as all-rounders." (Hudson, 1966, p.55)


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Created 17/1/00
Last modified 7/4/00