Kathleen M Clark

Kathleen M. Clark, Florida State University, Tallahassee, Florida, USA

History and pedagogy of mathematics in mathematics education: History of the field, the potential of current examples, and directions for the future

The field of history of mathematics in mathematics education – often referred to as the history and pedagogy of mathematics domain (or, HPM domain) – can be characterized by an interesting and rich past and a vibrant and promising future. In this plenary, I will describe the development of the field, and in doing so, I will highlight the ways in which research in the field of history of mathematics in mathematics education offers important connections to more mainstream aspects of research in mathematics education, with a particular emphasis on student learning. To begin, I will succinctly situate the HPM domain within mathematics education, with careful attention to the development leading up to establishing the International Study Group on the Relations between the History and Pedagogy of Mathematics in 1976. Precipitated by the creation of the HPM Group, research in the HPM domain has continued to grow in last 40-plus years, and includes all levels of learners and teachers. Part of this growth has been marked by the creation of a thematic working group on history in mathematics education, beginning with CERME 6 in 2009. Next, I will provide an overview of different approaches and frameworks that are useful in empirical research in the HPM domain. In doing so, I will highlight specific examples in which research on the use of history of mathematics contributes to the broader landscape of research in mathematics education. Recent examples include the application of Sfard’s (2008) thinking as communicating framework in research within the Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (or, TRIUMPHS) project in the United States, as well as the work of colleagues in Denmark and Brazil. These examples also address the role of history of mathematics in the learning of a wide variety of mathematical concepts, ranging from the function concept to determinants of matrices, as well as topics in analysis and abstract algebra. Furthermore, efforts to extend knowledge about beliefs research via detection and inspection of domain-specific beliefs, and the contributions of working with primary historical sources on pre- and in-service teachers’ mathematical knowledge for teaching hold great potential for both strengthening theoretical and empirical connections to research in mathematics education. Finally, after a brief analysis of ongoing discussions for calls to strengthen empirical work in the HPM domain in light of certain pitfalls and dilemmas facing the field, I will propose directions for research in the coming years, and the ways in which Thematic Working Group 12 can contribute to bridging research in this important field with the broader mathematics education research community.