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

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.