From Empirical to Structural Reasoning in Mathematics
Dietmar Küchemann, Celia Hoyles · 2010
This chapter describes patterns in high-attaining students&s; 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&s; 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&s; 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;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.