Mathematics education

Psychology of learning mathematics

Notes

Stephen Jay Gould (1981:1996) "The mismeasure of man (revised ed.)"

Ch.6 The real error of Cyril Burt

Factor analysis and the reification of intelligence Spearman - Burt.

Correlation is not proof of a causal link.

Correlation matrices.

Principle component analysis - (vs. Qmethod?) as a method of simplifying the correlation matrix. Are you looking for one factor or many.

Error of reification

Principle component analysis is not the only way to simplify. Rotation can produce two-factor or many factor methods.

"Automatic reification is invalid for two major reasons... no set of factors has any claim to exclusive concordance with the real world. Any matrix of positive correlation coefficients can be factored, as Spearman did, into g [a major factor] and a set of subsidiary factors or, as Thurstone did, into a set of "simple structure" factors that usually lack a single dominant direction. Since either solution resolves the same amount of information, they are equivalent in mathematical terms. .. How can we claim that one, or either, is a mirror of reality?

Second, any single set of factors can be interpreted in a variety of ways. Spearman read his strong g as evidence for a single reality underlying all cognative mental activity. ... Thompson, using the same data, inferred that the brain has hardly any specialized structure at all."

Gould (1996, p.299)

Burt's extensions of Spearman's work. 'inverted' Q-mode - vs. Stephenson extended Spearman's two

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Created 2/10/00

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