TY - JOUR

T1 - Compartmentalisation of Mathematical Sectors

T2 - The Case of Continuous Probability Distributions and Integrals

AU - Hausberger, Thomas

AU - Derouet, Charlotte

AU - Hochmuth, Reinhard

AU - Planchon, Gaetan

N1 - Funding Information: This research grew out of a project initiated within a thematic working group of the CNRS4 consortium DEMIPS5 that federates university mathematics education research in France.

PY - 2021/10

Y1 - 2021/10

N2 - This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense those two sectors may be described as compartmentalised in current textbooks. We then study, by means of a questionnaire, the educational effects of the compartmentalisation: do students’ difficulties in completing “bridging tasks” (tasks that require to relate the two sectors) reflect the partial disconnections revealed by the praxeological analyses? The key notion of ostensive, combined with the role played by the technology in the sense of ATD, is used to interpret the data. Altogether, this study sheds light on the deficit of cognitive flexibility required to change mathematical sectors, which is understood as a result of deficient praxeologies developed within the institutions.

AB - This paper investigates the phenomenon of compartmentalisation of knowledge in the teaching and learning of continuous probability distributions and integral calculus at the secondary-tertiary transition in France. Using the Anthropological Theory of the Didactic (ATD), and in particular the key notion of praxeology, we investigate in which sense those two sectors may be described as compartmentalised in current textbooks. We then study, by means of a questionnaire, the educational effects of the compartmentalisation: do students’ difficulties in completing “bridging tasks” (tasks that require to relate the two sectors) reflect the partial disconnections revealed by the praxeological analyses? The key notion of ostensive, combined with the role played by the technology in the sense of ATD, is used to interpret the data. Altogether, this study sheds light on the deficit of cognitive flexibility required to change mathematical sectors, which is understood as a result of deficient praxeologies developed within the institutions.

KW - Anthropological theory of the didactic

KW - Compartmentalisation of knowledge

KW - Continuous probability distributions

KW - Integral calculus

KW - Secondary-tertiary transition

UR - http://www.scopus.com/inward/record.url?scp=85116055887&partnerID=8YFLogxK

U2 - 10.1007/s40753-021-00143-y

DO - 10.1007/s40753-021-00143-y

M3 - Article

AN - SCOPUS:85116055887

VL - 7

SP - 490

EP - 518

JO - International Journal of Research in Undergraduate Mathematics Education

JF - International Journal of Research in Undergraduate Mathematics Education

IS - 3

ER -