Mathematical Thinking: Short Circuits Between the Mathematicians’ Work and Educational Theories

Abstract

To better prepare students for society, mathematical thinking has become a key goal of mathematics education, but it is unknown how educational theories on mathematical thinking relate to the thinking and working of mathematicians. The aim of this study is to align the thinking and working of mathematical researchers and theories on mathematical thinking, in order to clarify mathematical thinking as it might be addressed in mathematics education. Ten in-depth semi-structured interviews were conducted with mathematicians from Utrecht University and analyzed based on themes from educational literature on mathematical thinking. As a result, the following aspects of mathematical thinking were identified as most important: posing the right problem before solving it, creativity, and reasoning with examples and visualizations rather than proof language. Furthermore, discussions of educational models on abstraction, problem solving and modelling revealed that problems are rarely solved in a linear way and that mathematicians only generalize when it has a purpose. It is concluded that mathematicians’ thinking and working align to some extent with educational theories on mathematical thinking, but not entirely with one single theory. The results of this study give rise to ideas to improve the implementation of mathematical thinking in education: spend more time on thinking processes in the early phase of conceptual development and put more emphasis on mathematical ideas, rather than on formal notation.