chapter  10
From Empirical to Structural Reasoning in Mathematics
Tracking Changes Over Time
WithDIETMAR KÜCHEMANN, CELIA HOYLES
Pages 20

This chapter describes patterns in high-attaining students' mathematical reasoning in the domain of number/algebra and traces development over time in their use of structural reasoning. A major challenge in mathematics education is to develop students' abilities to reason mathematically, that is to make inferences and deductions from a basis of mathematical structures, rather than by arguing, for example, from perception, the assertion of authority, or, in particular, from empirical cases. The project used a combination of quantitative and qualitative methods. The quantitative methods included the identification of trends in hierarchically ordered categorical data obtained by coding students' responses to each item in each proof test, and multilevel analyses of student scores in geometry and in algebra to identify significant predictors of progress. High-attaining students in people's large random sample made progress, albeit modest, in the use of structural reasoning over the 3 years of the project suggesting a positive and cumulative outcome of teaching.