The emergence of the analytic-structural way of thinking in linear algebra as a blended space

Abstract

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall linear algebra topics she had learned the previous year. Following the theory of conceptual blending, the presented case study is used as a model for the description of the emergence of the analytic-structural mode. It shows how the evolution of the used signs and their relationships suggests that the analytic-structural mode emerges as a blend between the other two ways of thinking.