Basic Mental Models of Integrals - Theoretical Conception, Development of a Test Instrument, and first Results
Please always quote using this URN: urn:nbn:de:bvb:20-opus-232830
- 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 wasA 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.…
Author: | Gilbert Greefrath, Reinhard Oldenburg, Hans-Stefan Siller, Volker Ulm, Hans-Georg Weigand |
---|---|
URN: | urn:nbn:de:bvb:20-opus-232830 |
Document Type: | Journal article |
Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
Language: | English |
Parent Title (English): | ZDM – Mathematics Education |
ISSN: | 1863-9690 |
Year of Completion: | 2021 |
Volume: | 53 |
Pagenumber: | 649–661 |
Source: | ZDM (2021) 53:649–661. https://doi.org/10.1007/s11858-020-01207-0 |
DOI: | https://doi.org/10.1007/s11858-020-01207-0 |
Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Tag: | Grundvorstellung; approaches in textbooks; basic mental model; empirical evidence; integral |
Release Date: | 2021/06/04 |
Licence (German): | CC BY: Creative-Commons-Lizenz: Namensnennung 4.0 International |