TY - JOUR

T1 - An institutional approach to university mathematics education

T2 - from dual vector spaces to questioning the world

AU - Winsløw, Carl

AU - Barquero, Berta

AU - De Vleeschouwer, Martine

AU - Hardy, Nadia

PY - 2014

Y1 - 2014

N2 - University mathematics education (UME) is considered, in this paper, as a kind of didactic practice - characterised by institutional settings and by the purpose of inducting students into mathematical practices. We present a research programme - the anthropological theory of the didactic (ATD) - in which this rough definition can be made much more precise; we also outline some cases of ATD-based research on UME. Three cases are presented in more detail. The first is a theoretical and empirical study of the topic of dual vector spaces, as it appears in undergraduate courses on linear algebra. The second case concerns a similar study of the practices and theories on limits of functions which students may develop in calculus courses. Finally, a third study illustrates the use of ATD to design and experiment innovative approaches to mathematical modelling in the setting of a first mathematics course for engineering students.

AB - University mathematics education (UME) is considered, in this paper, as a kind of didactic practice - characterised by institutional settings and by the purpose of inducting students into mathematical practices. We present a research programme - the anthropological theory of the didactic (ATD) - in which this rough definition can be made much more precise; we also outline some cases of ATD-based research on UME. Three cases are presented in more detail. The first is a theoretical and empirical study of the topic of dual vector spaces, as it appears in undergraduate courses on linear algebra. The second case concerns a similar study of the practices and theories on limits of functions which students may develop in calculus courses. Finally, a third study illustrates the use of ATD to design and experiment innovative approaches to mathematical modelling in the setting of a first mathematics course for engineering students.

KW - anthropological theory of the didactic

KW - duality in linear algebra

KW - limits and calculus

KW - mathematical modelling

KW - university mathematics education

U2 - 10.1080/14794802.2014.918345

DO - 10.1080/14794802.2014.918345

M3 - Article

AN - SCOPUS:84902675984

VL - 16

SP - 95

EP - 111

JO - Research in Mathematics Education

JF - Research in Mathematics Education

SN - 1479-4802

IS - 2

ER -