Understanding and Basic Mental Models of the concept of derivative

Titelangaben

Weigand, Hans-Georg ; Greefrath, Gilbert ; Oldenburg, Reinhard ; Siller, Hans Stefan ; Ulm, Volker:
Understanding and Basic Mental Models of the concept of derivative.
In: Bosch Casabò, Marianna ; Carreira, Susana ; Bolondi, Giorgio ; Gaidoschick, Michael ; Spagnolo, Camilla (Hrsg.): Proceedings of the Fourteenth Congress of the European Society for Research in Mathematics Education (CERME14). - Bozen : ERME , 2025 . - S. 4168-4175
ISBN 9791221086553

Volltext

Link zum Volltext (externe URL):

Abstract

An empirical study with 501 university students of mathematics, mainly at the beginning of their
studies, investigated the relation between the understanding—concentrated in basic mental models
(BMMs)—of the derivative and the capability of solving derivative problems. The results show that
the BMM of tangent slope is of central importance, it is much less for the local rate of change, while
the local linearization plays no role. The study emphasizes the meaning of BMMs for successfully
solving problems related to the concept of derivative.