TY  - JOUR
A1  - Greefrath, Gilbert
A1  - Oldenburg, Reinhard
A1  - Siller, Hans-Stefan
A1  - Ulm, Volker
A1  - Weigand, Hans-Georg
T1  - Basic Mental Models of Integrals - Theoretical Conception, Development of a Test Instrument, and first Results
T2  - ZDM – Mathematics Education
N2  - A basic mental model (BMM—in German ‘Grundvorstellung’) of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific teaching approaches: the BMMs of area, reconstruction, average, and accumulation. Based on theoretical work, in this paper we ask how these BMMs could be identified empirically. A test instrument was developed, piloted, validated and applied with 428 students in first-year mathematics courses. The test results show that the four normative BMMs of the integral can be detected and separated empirically. Moreover, the results allow a comparison of the existing individual BMMs and the requested normative BMMs. Consequences for future developments are discussed.
KW  - basic mental model
KW  - Grundvorstellung
KW  - integral
KW  - empirical evidence
KW  - approaches in textbooks
Y1  - 2021
UR  - https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/23283
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-232830
SN  - 1863-9690
VL  - 53
ER  -