Basic Mental Models of Integrals: Theoretical Conception, Development of a Test Instrument, and First Results

Keywords: Grundvorstellung; integral; empirical evidence; approaches in textbooks

Abstract: Four Grundvorstellungen (basic mental models) can be developed about the concept of a definite integral, some of which are used for specific teaching approaches. This article defines the concept of Grundvorstellungen against the background of personal conceptions and concretizes this concept using the integral as an example. The Grundvorstellungen of area, reconstruction, average, and accumulation are presented. A test instrument for measuring the Grundvorstellungen of students is introduced and analyzed in terms of quality criteria. Results relating to Grundvorstellungen of the integral held by first-year students are presented and discussed. (Click here for article)

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Gilbert Greefrath, Reinhard Oldenburg, Hans-Stefan Siller, Volker Ulm, & Hans-Georg Weigand

11.06.2021

Basic Mental Models of Integrals: Theoretical Conception, Development of a Test Instrument, and First Results

Keywords: Grundvorstellung; integral; empirical evidence; approaches in textbooks

Abstract: Four Grundvorstellungen (basic mental models) can be developed about the concept of a definite integral, some of which are used for specific teaching approaches. This article defines the concept of Grundvorstellungen against the background of personal conceptions and concretizes this concept using the integral as an example. The Grundvorstellungen of area, reconstruction, average, and accumulation are presented. A test instrument for measuring the Grundvorstellungen of students is introduced and analyzed in terms of quality criteria. Results relating to Grundvorstellungen of the integral held by first-year students are presented and discussed. (Click here for article)