Mathematics education

Psychology of learning mathematics

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

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(!)

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:

- Partition
- Factorisation

- 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

- Extreme divergers: 3
- Mild divergers: 18
- All-rounders: 26
- Mild convergers: 7
- Extreme convergers: 0

- Extreme divergers: 4
- Mild divergers: 1
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 0

- Extreme divergers: 1
- Mild divergers: 2
- All-rounders: 3
- Mild convergers: 7
- Extreme convergers: 3

- Extreme divergers: 3
- Mild divergers: 12
- All-rounders: 33
- Mild convergers: 37
- Extreme convergers: 19

- Extreme divergers: 1
- Mild divergers: 4
- All-rounders: 14
- Mild convergers: 4
- Extreme convergers: 3

Links at this site...

- Guilford's 'structure of intellect' model
- References and further reading.
- PLM - Notes - 4/1/00
- PLM - Notes - 8/1/00
- PLM - Notes - 16/1/00
- Features of concept maps
- PLM - Notes - 1/2/00
- The Marriage of Object and Subject: Notes - 2-3/4/00

Links at other sites...

Created 17/1/00

Last modified 7/4/00