Human ecology
Mathematics education
Psychology of learning mathematics
Convergence and Divergence
Definitions:
- Divergent thinking is the ability to find as many
possible answers to a particular problem.
- Convergent thinking is the ability to find the best
single answer to a problem
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
- 3-4 divergers per converger:
arts subjects - history, English literature, modern languages.
- equal divergers and convergers:
biology, geography, economics.
- 3-4 convergers per diverger:
physical sciences - mathematics, physics, chemistry, classics(!)
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:
- Addition
- Subtraction
- Multiplication
- Division
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)
- Extreme divergers: 7
- Mild divergers: 15
- All-rounders: 17
- Mild convergers: 3
- Extreme convergers: 2
Modern languages
- Extreme divergers: 3
- Mild divergers: 18
- All-rounders: 26
- Mild convergers: 7
- Extreme convergers: 0
Mixed courses
- Extreme divergers: 4
- Mild divergers: 1
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 0
Classics
- Extreme divergers: 1
- Mild divergers: 2
- All-rounders: 3
- Mild convergers: 7
- Extreme convergers: 3
Physical science
- Extreme divergers: 3
- Mild divergers: 12
- All-rounders: 33
- Mild convergers: 37
- Extreme convergers: 19
Biology
- Extreme divergers: 1
- Mild divergers: 4
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 3
"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