### Teachers’ mathematical knowledge for teaching in relation to the inclusion of history of mathematics in teaching

Bjørn Smestad, Uffe Thomas Jankvist and Kathleen Clark

#### Abstract

This article discusses how the inclusion of history of mathematics in mathematics education draws heavily on a teacher’s mathematical knowledge for teaching, in particular horizon content knowledge, in the context of curricular changes. We discuss the role of history of mathematics in school curricula, its inclusion in textbooks and its consequences for the mathematical knowledge needed for teaching. We address the matter from three national settings (Denmark, Norway and the United States). These settings exemplify how, in particular, teachers’ horizon content knowledge needs to be broader than what is necessary for only the current curriculum.

#### Bjørn Smestad

Bjørn Smestad is an associate professor of mathematics education at Oslo and Akershus University College of Applied Sciences, Department of Primary and Secondary Teacher Education. His main research interests are the role of history of mathematics in teaching and teacher education, ICT in teaching mathematics and school placement as part of teacher education.

#### Uffe Thomas Jankvist

Uffe Thomas Jankvist is an associate professor of mathematics education at Aarhus University, Department of Education, Campus Emdrup, Denmark. His research interests include the use of history of mathematics, applications of mathematics, and philosophy of mathematics in mathematics education, both from a theoretical and an empirical point of view, including also students’ beliefs about and images of mathematics as a (scientific) discipline, as well as interdisciplinary teaching and learning. Also, he is involved in educating Danish ”maths counsellors” for upper secondary school at Roskilde University.

#### Kathleen Clark

Kathleen Clark is an associate professor in the College of Education at Florida State University. Her primary research interests lie in two fields, mathematics education and history of mathematics. In the former, her research investigates ways in which prospective and in-service mathematics teachers use history of mathematics in teaching and the ways in which the study of history of mathematics impacts mathematical knowledge for teaching. In the latter, her historical research is focused on 17th and 18th century mathematics, with a particular emphasis on the early development of logarithms.