
06601007
j
2016d.00440
Bosch, Marianna
Winsl{\o}w, Carl
Linking problem solving and learning contents: the challenge of selfsustained study and research processes.
Rech. Didact. Math. 35, No. 3, 357399 (2015).
2015
La Pens\'ee Sauvage, Grenoble; Association pour la Recherche en Didactique des Math\'ematiques (ARDM), Institut Henri Poincar\'e, Paris
EN
D50
D30
problem solving
problem posing
anthropological theory of the didactic
study and research processes
mathematical inquiry
Summary: A main difference between the mathematical activity of students and that of researchers is that researchers pursue their mathematical work in a seemingly selfsustaining dynamics of questions and answers, while students rely on teachers to sustain this dynamics. Unlike researchers, students generally do not construct the questions they work on, and do not search, rearrange and question the established contents they need to answer the questions. The basic problem approached in this paper is: could students also engage in a more selfsustaining and complete work with questions and answers? We first present an analysis of four main paradigms of teaching and learning mathematics, based on different approaches to learners' work with questions and answers. We then discuss and exemplify certain principles for selfsustained mathematical activities using Chevallard's Herbartian schema. The access to new external answers and their test against an appropriate experimental milieu is shown to be a crucial bootstrap for the dynamics of research and study processes.