Mathematics education

Psychology of learning mathematics

Notes on tests - 14/2/00

**Significance of tests.**

Minimum of four intervals

- High maths, high divergent production (DP)
- Low maths, high DP
- High maths, low DP
- Low maths, low DP

- High/low maths: achieved A level / achieved GCSE?
- High/low DP: 50/50 cut of test results? What is distribution of test results?

Divide people into groups of high maths and low maths

**Null hypothesis: in each maths group there should be equal numbers of high
DP and low DP people.**

Notes 28/2/00

**Hypothetical example**

If the test involved 30 people, 10 of which were in the high maths group, what distributions would show 5% and 1% significant deviation from the null hypothesis?

Using Fisher exact 2x2 test and from the above possibilities:

The hypothesis we want to test is that high DP people are less likely to be high maths people. The above conditions would produce

- High maths
- Number of high DP = n
- Number of low DP = (10 - n)

- Low maths
- Number of high DP = (15 - n)
- Number of low DP = 15 - (10 - n) = n + 5

The most extreme case of our hypothesis would be that n=0.

From the Fisher test, the probability of this case occuring by chance is:

p(n=0) = .0099%

The next probabilities are:

p(n=1) = .25%

p(n=2) = 2.2%

p(n=3) = 9.7%

The cumulative probabilities are:

p(n<1) = .0099%

p(n<2) = .25%

p(n<3) = 2.5%

p(n<4) = 12%

From these figures we can see that our 5% and 1% significance cases occur when n=2 and n=1 respectively.

The two goals of the project are:

- 1. A pilot study to see whether Hudson's results are still generally applicable as a measure of the difference between the subjects of biology and mathematics.
- 2. Identification of individual students that may have problems with certain aspects of mathematics.

- If I can get 60 pupils, Goal 1. might be achievable.
- For less than 30 pupils, it might be better to concentrate on goal 2. Changes to the tests might involve longer tests to about ten people.

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Created 20/2/00 from PLM - Notes - 14/2/00

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