Psychology of learning mathematics
Notes - 25/3/00
Divergence and mathematics: Orton's questions
- If most mathematics students are predominantly convergent
thinkers, does this imply that few specialist mathematicians are
capable of creativity or inventiveness?
- It cannot be the case that no mathematics students are genuinely
creative, but Hudson's results might be taken to suggest that the only creative mathematics students are the minority who are either
divergent thinkers or who are equally at home with both kinds of
- Further, does the predominantly convergent nature of the
thinking of the majority of mathematics sixth-form students imply
that this will remain the case throughout life, or is their hope for
us all? Divergent / convergent thinking is not genetic.
- Does the typical school mathematics education produce the
convergent thinkers which we find in the sixth form or is it the
case that the pupils are already predisposed towards convergent and
our mathematics curriculum does little to counteract it?
- Are students attracted to mathematics because it appears that
only convergent thinking is required?
- If we attempt radical changes to the mathematics curriculum so
that it becomes much more based on open-ended situations will we
deter some students where preference is for convergent studies?
- What should be doing, as mathematics teachers, to cater for both
convergence and divergence in the preferences of our pupils?
How do the differences in divergent / convergent thinking in
biology and mathematics affect:
- 1. the types of mathematics used / useful to biology.
- 2. the mathematics education of biologists.
Methodology: critical theory.
"Recall that a critical theory strives to interpret the condition of
a group of sufferers, make plain to them the cause of their
suffering, and by sketching a course of relief, demonstrate that
their situation is not immutable. Any such theory is validated by
reflective acceptance and ensuing action on the part of its
audience. In its standard presentations, then, a critical theory
has three aspects: one interpretive, one quasi-causal, one
emnacipatory. Whereas Q Methology Q is largely silent on questions
of causality, let me suggest that it can generate major
contributions to both the interpretive and emancipatory moments of a
critical theory. " (my emphasis)
(Dryzek, J.S., 1990, "Discursive
Democracy: Politics, Policy, and Political Science")
Advantages of Q methodology:
- [focuses on] individuals measuring rather than being measured.
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