Mathematics education

Psychology of learning mathematics

Notes

8th February 2000

Dear Sir

My name is Grant Sherman, I am Doctor of Education student with Prof. Paul Ernest in Exeter. I wonder if you could help me with a small research project?

I would like to look at the mathematical ability of biology students. Would it be possible to conduct a short test on some of the students at Exeter?

Specifically, I would like to test the negative correlation reported between mathematical ability and divergent thinking (Orton, 1992). Tests conducted by Hudson in the sixties suggest that, while there are equal numbers of divergent and convergent thinkers in biology, convergent thinkers outnumber divergent thinkers by 3-4 to 1 in mathematics (Hudson, 1966, pp. 56-57).

This is interesting to me for two reasons.

First, there is the observation raised by Ernst Mayr that the methodology of biology has strayed to far towards the methodology of physics and mathematics. Mayr suggests that biology involves pluralist solutions to problems (1997, pp. 67-68) and that biologists should learn more from the methodology of history (ibid., pp. 37-39). (Hudson says that divergent thinkers outnumber convergent thinkers by 3-4 to 1 in history).

Second, there is my personal experience of mathematics and biology. My BSc is in Astrophysics, my MSc is in Analytical Biology (mainly ecology). During the MSc we had a course in mathematical biology. It was noticeable that many people who were good at biology had difficulties with mathematics.

This research could have two practical applications to biology.

The first application investigates the constructive dialogue which has grown between biology and mathematics over the last century. This dialogue has been helpful in passing biological ideas to mathematics (neural nets, genetic algorithms, Lindenmayer systems) and in passing mathematical ideas to biology (particularly the role of population dynamics in reconciling the ideas of Darwin and Mendel). This dialogue may be weakened if biologists and mathematicians do not recognise areas of similarity or difference between their subjects. If the correlation noticed by Hudson are representative of the types of thinking required by biologist and mathematicians, then this might open new lines of dialogue between the two subjects.

The second application involves the identification of individual biologists who have difficulties with mathematics. On one hand, different teaching styles may be needed for these individuals. On the other hand different areas of mathematics may be more accessible to them. Further studies may identify specific areas of biology and mathematics that require divergent thinking.

The test would last about 1-2 hours and would need to be conducted sometime after 6th March. The report has to be completed by 2nd June. I realise the Easter holidays place a restriction on the timing of the test.

I thank you for the time you take to read this letter and I look forward to any helpful comments you can make.

Yours sincerely

Grant Sherman

References:

- Hudson, L. (1966) "Contrary imaginations" Harmondsworth, Penguin
- Mayr, E. (1997) "This is Biology", Belknap, Harvard
- Orton, Anthony (1992) "Learning Mathematics, 2nd. ed." Cassell, London

Links at this site...

- Pluralism in biology. Important quote.
- Convergence and Divergence

Links at other sites...

Created 10/2/00

Last modified