Corinne Hahn

Educational Paths to Mathematics: Which Paths Forward to What Mathematics?

Most people involved in mathematics education agree that it is complex, multi-layered, dynamic, multi- and interdisciplinary. To study and to improve mathematics education on the various levels of its curricula and its practices has been a goal of the Commission Internationale pour l’Etude et l’Amelioration de l’Enseignement des Mathematiques (CIEAEM, the International Commission for Study and Improvement of Teaching Mathematics) since it was created and established in the 1950s. CIEAEM continues to investigate the actual conditions and the possibilities for the development of mathematics education. This introductory chapter provides the rational for the book by looking at historical developments in school mathematics. The structure of the sourcebook is explained at the end of the introduction.

Apprenticeship in Higher Education in France: An Experimental Device to Help Apprentices to Link Academic Knowledge and Work Experience.

The French apprenticeship system has been an object of research in France for more than 30 years now, by experts from different backgrounds. Over the past 15 years apprenticeship has grown significantly in higher education. At this level, if a greater importance is attached to theory, it becomes more difficult to connect this theory to more diversified work situations. Referring to Geay’s alternance model and to Vergnaud’s theory of conceptual fields, this article will focus on the impact of apprenticeship on the learning process. I will describe a pedagogical device I designed and implemented in a business master’s programme in order to help apprentices link their professional experience with academic knowledge taught at school. The exploratory study I conducted with 37 master-level apprentices showed that these students were driven to build generic situations out of their personal experience at work and also to interrogate these situations from the perspective of academic knowledge. I also observed unexpected effects on teachers and mentors.

TEACHING MATHEMATICS TO SHOP-ASSISTANT APPRENTICES EXPLORING CONTENT AND DIDACTICAL SITUATIONS

This article presents the results of a research study conducted with apprentices in order to examine the double hypothesis that vocational training incorporating work placement gives the opportunity to construct authentic situations out of the everyday practices of students and that these situations allow students to improve their understanding of mathematical problems. After analysis of workplace situations had shown that the only mathematical concept used by apprentices was that of proportionality applied to percentage calculations, we first analyzed the way in which students at several levels handled this idea of percentage. We then devised an experimental framework in order to help the apprentices to transfer their knowledge.

Communication Inside and Outside the Classroom: A Commentary

There is no doubt that technology facilitates access to information and induces new modes of communication. No doubt also that we should go beyond the technical aspects of the tool and explore how it can change classroom practice, pedagogical activities and the role of actors. This is what the five chapters in this Section explore.

Linking Professional Experiences with Academic Knowledge: The Construction of Statistical Concepts by Sale Manager Apprentices

As it builds a partnership between the school and the firm, the French alternance system helps us to link mathematics to students’ professional experience. In this paper, we will describe a pedagogical device we experimented with manager apprentices in order to make them confront the different conceptualisations they built through their multiple experiences, at school and at work.