Investigating mathematical beliefs by using a framework from the history of mathematics. (English)

Bernack-Schüler, Carola (ed.) et al., Views and beliefs in mathematics education. Results of the 19th MAVI conference, Freiburg, Germany, September 25‒28, 2013. Wiesbaden: Springer Spektrum (ISBN 978-3-658-09613-7/pbk; 978-3-658-09614-4/ebook). Freiburger Empirische Forschung in der Mathematikdidaktik, 197-211 (2015).

Summary: In the theoretical part of the article a framework of eight activities and motives is sketched (calculate, apply, construct, argue, order, find, play, evaluate), which proved to be successful along the history of mathematics. Furthermore, some arguments are presented and discussed why this framework is useful for studying mathematical beliefs. The empirical part is about two case studies using this network carried out in Joensuu (FIN) and Jena (GER). The goal of the first study was to compare mathematical beliefs of student mathematics teachers in Finland and Germany. The second part is about the influence of using a handheld calculator on the belief of a pupil. The first study reveals that neither in Finland nor in Germany the school mathematics seems to give much support for these activities, in Finland university mathematics even less. The only exception is calculating, for which the both institutions seem to give overdose. On the other hand, the finding of the second study that voluntary playing with progressive technology, even during a short period of time, might shift mathematical beliefs in a positive way.