• 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 thinking!

• 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.

"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.