Abstract:

In this paper, we describe research that combined quantitative and qualitative methods in order to investigate how students' mathematical explanations change over time and to identify factors underlying any changes. The quantitative methods used included tracing trends in hierarchically ordered categorical data, and multi-level analyses of student scores to identify significant predictors of students' progress. Qualitative methods used included interviews with selected students in schools identified from the multi-level modelling as those in which students performed significantly better than would be predicted. By reference to these analyses as applied to one geometrical item, the paper points to how the mixing of methods shed light on trends in patterns of student response as well as on unexpected results, and led to reflexive testing of some initial assumptions about the development of mathematical reasoning.

Document Type: Research article

DOI: 10.1080/13645570500154899