Analyzing the use of history in mathematics education: issues and challenges around Balacheff’s cKȼ model

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff’s cKȼ model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the first part of this paper, Balacheff’s cKȼ model (conceptions, knowledge, ȼoncepts) is shortly presented, and in the second part, the relationship between the epistemological background of the model and the use of the history of mathematics is explored in order to show a possible suitableness. The third part addresses an example of a school activity (about ancient Indian geometry) in which the model is applied and the historical issues clarified. Questioning the role of problems both in the cKȼ model and in the use of history, the last part shows how a study at the students’ conception level enlightens the way in which historical elements can interact with contemporary mathematical learning.