This paper discusses a framework for analyzing the dependence on mathematical theory in test items, that is, a framework for discussing to what extent knowledge of mathematical theory is helpful for the student in solving the item. The framework can be applied to any test in which some knowledge of mathematical theory may be useful, both within mathematics itself and in other subjects. The relevance of the framework is related to the important distinction between language and content in mathematical theory.
We used groups of scorers categorizing test items from TIMSS grade 8, PISA, and TIMSS Advanced. Differences in results across countries and groups of countries are analyzed.
Our results indicate, among other things, that the dependence on mathematical theory in the set of TIMSS Advanced 2015 physics test items is greater than in the set of PISA 2012 mathematics test items. Concerning relations to item difficulty, we find interesting differences in average p-values between the sets of item groups defined by our framework concerning participating countries and geographically defined groups of countries.
The results indicate deep differences in mathematics teaching traditions and curricula in different regions of the world. Documenting such differences may help different educational systems learn from each other, and as such is relevant for all forms of educational research.
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