Learning as a critical encounter with the other: prospective teachers conversing with the history of mathematics

In this paper, drawing on the philosophy of dialectical materialism, we present an elaboration of two concepts that tend to remain backstage in debates in the field of history in mathematics education, namely, the concept of mathematics learning and the concept of classroom mathematics knowledge. The elaboration of these two concepts makes room to return to the longstanding question of the role of history in mathematics education. We argue that the history of mathematics in education is not a choice but a need-a central part of the process of understanding our human nature as essentially historical and cultural. We illustrate these ideas through the analysis of the encounter of a group of prospective teachers with a 14th century problem about motion. In this encounter the students engaged critically in conversations with voices of the past, while restoring the aesthetic, ethical, and historical dimensions of knowing and learning.