Work

Basic mental models of the definite integral: Conceptual understanding of undergraduate students in India and Sri Lanka

Year: 2025

Type: article

Abstract: This study expands the work that has been done in Germany developing the theory of grundvorstellungen , or basic mental models, and applying them to the definite integral. Using an existing survey instrument, we administer questions related to the basic mental models of the definite integral to 342 university students in India and Sri Lanka. By conducting a quantitative analysis of the data, we are able to determine whether students are more inclined to view the integral in terms of an area, an average value, an accumulation, or the construction/reconstruction of a quantity under different scenarios. Compared with earlier studies, we find a smaller gap between the preference for the area model and the other three described, indicating a greater propensity for students in India and Sri Lanka to interpret the definite integral in a variety of ways. We then interpret the results in terms of the teaching that the students receive and the differences in the curriculum.

Source: Asian Journal for Mathematics Education

DOI: 10.1177/27527263251324950

Authors: Ashish Bhatt, Mangalagama Dewasurendra, Barry J. Griffiths

Institutions: Vellore Institute of Technology University, University of Peradeniya, University of Central Florida

Language: English

Topic: Mathematics Education and Teaching Techniques

Subfield: Education

Field: Social Sciences

Domain: Social Sciences

SDG: Quality education

Open Access status: diamond

OpenAlex ID: W4408856679

FWCI:

Cites: 27

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Related to: 10