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

Abstract

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'Amélioration de l'Enseignement des Mathématiques (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.Mathematics education is a multi-facetted endeavour that has been regarded from many theoretical points of view. Some believe that it has to do with the transmission and the acquisition of mathematical knowledge, while others emphasise the learners' mathematical constructions and the teachers' role in providing appropriate mathematical environments. Mathematics education is concerned with the formation of the learners' identities, but also with the institutional (re-)production of a mathematically-educated workforce. It is about the transposition, or recontextualisation, of academically produced mathematics into a mathematics curriculum, and it is also about how people activate and integrate mathematical skills and knowledge in everyday contexts. Mathematics education has been regarded as a process, a product, a discourse, a practice, an activity system, a material reality, a research domain, a fi eld of academic research and an area of study. Most people involved in mathematics education agree that it is complex, multi-layered, dynamic, multi-and interdisciplinary. Some argue that mathematics education is the key to the Looking Back: Developments in School MathematicsMathematics education is political, as can be seen in disputes over the question: "What is school mathematics?" 300 years ago, this question would have been quite diffi cult to pose, let alone to answer. The mathematics that was taught varied heavily across countries and the different institutions of learning according to their education and formation purposes. But then, a process of international modernisation started, and, according to Gispert and Schubring ( 2011 ), two countries were leading this process: France and Germany.