Three past mathematicians’ views on history in mathematics teaching and learning: Poincaré, Klein, and Freudenthal

Abstract

In the HPM (History and Pedagogy of Mathematics) literature, the three mathematicians Henri Poincaré (1854–1912), Felix Klein (1849–1925), and Hans Freudenthal (1905–1990) are often mentioned in relation to having opinions about the role of the history of mathematics in the teaching and learning of mathematics. Such mentioning often appears without any further account of their viewpoints. In the paper, we seek to dig more deeply, asking the questions of what these three mathematicians’ views on history in mathematics education were, how they themselves expressed these, and what the similarities and differences might be. Our departure point was the known texts by the three mathematicians in which they touch upon aspects of the history of mathematics in relation to teaching and learning, or mathematics education in general. When possible, these written works were accompanied by secondary accounts. Finally, we draw perspectives concerning the issue of how the views of these three mathematicians may or may not align with some of the trends in modern day HPM research.