Mathematics education

Psychology of learning mathematics

notes 19/1/00

Views of mathematics questionaire (Ernest, 2000, p.98)

- Maths consists of a set of fixed, everlasting truths.
- There are many ways of solving any problem in maths.
- The is always a rule to follow in solving maths problems.
- Some maths problems have many answers, some have none.
- Learning maths is mainly remembering facts and rules.
- Maths is basically doing sums.
- Puzzles and investigations are not proper maths.
- Maths is always changing and growing.
- The procedures and methods in maths guarantee right answers.
- There is only one correct way of solving any maths problem.
- A person should not mind risking a mistake when trying to solve a maths problem.
- Maths is always exact and certain.
- Knowing how to solve a problem is even more important than getting the right answer in maths.
- Exploring number patterns is not real maths.

Dualist 1,3,5,6,7,9,10,12,14 SA=1 SD=5

non-Dualist 2,4,8,11,13 SD=1 SA=5

+ Convergent / Divergent test.

notes 20/1/00

Divergent tests in psychology.

check Gross. - Guilford (Gould)

Lindsey - check NDDH library - psychology?

Get a copy of Hudson at Exeter.

"[Kouba and McDonald] found that unlike adults, children do not view mathematics to be a well defined subject matter. With regard to the results with primary school students they said that the students largely identified mathematics with counting and number operation work. They also regard it as an exclusive domain, school based and isolated from other areas of study. In addition "For them, the domain of mathematics, while being narrow, is also not constant. Rather it is upwardly shifting. To many children when something becomes easy, it is no longer mathematics." (Kouba and McDonald 1987, p.107)" Ernest (2000, p.100)

notes 22/1/00

Guildford (1959)

"Make up as many equations as you can which follow from

B - C = D

and

Z = A + D"

Orton (1992, p.112)

(This is an example of a symbolic/divergent/implications item. ibid. p.118)

Guilford's 'structure of intellect' model.

Content

- Figural
- Symbolic
- Semantic
- (Behavioural, Gross 1992)

- Cognition
- Memory
- Convergent thinking
- Divergent thinking
- Evalution

- Units
- Classes
- Relations
- Systems
- Tranformations
- Implications

Note - Orton levels out the behavioral aspect of content. This aspect is included by Gross (1992) and Gould (1981:1994). Therefore, were Orton says Guilford's scheme identifies 90 abilities, Gross and Gould give him 120 abilities. Orton also says that Guilford identified these abilities by factor analysis, whereas Gould(?) says that this is a theoretical catagorisation.

(Note - classification. For my purposes, this theoretical / empirical distinction is less important than the evidence that convergence / divergence tests separate biology and mathematics.)

**Draft - Abstract**

Throughout this century mathematics and biology have provided useful
insights into each other's work. However, this dialogue may be weakened by
false preceptions of each other's field. Several universities give courses
in mathematical to their biology students, but how successful are these
courses? How well do they meet the needs of these students?

(I need some proper words to describe work and field)

Mathematics and biology can be distinguished by analysis of convergent and divergent thinking amongst students. Biology students have equal numbers of convergent and divergent thinkers. In mathematics convergent thinkers out-number divergent thinkers by three or four to one.

This could imply a few possibilities

- 1. Convergent thinkers are better at mathematics than divergent thinkers.
- 2. Convergent thinkers are better at mathematics than biology.
- 3. The practice of mathematics contains both convergent and divergent operations, but that convergent operations are more common.

The distinction between convergent and divergent thinking seems to be similar to the distinction between dualist and non-dualist philosophies of mathematics. If divergent thinkers think that mathematics is largely dualist would this affect their attitutes to, and ability at, mathematics?

The test would then involve these sections:

- Level of academic attainment at mathematics.
- A convergent / divergent test.
- A dualist / non-dualist views on mathmatics test. (As in Ernest, 2000, p.98)

- Contact biology dept.
- What areas they would like to investigate.
- What students are available.
- Numbers needed for statistics to be valid?

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Created 22/1/00

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