SAMS Subject Classification Number: 16

In their first year at university, engineering students study single variable integration followed by their progression to multivariable integration in second year. This transition from first to second year integral calculus can present challenges that can be attributed to students’ conceptions of integrals established in first year. The approach taken to address this transition was to conduct an assessment in the form of a written test administered to second year engineering students at the University of Cape Town, followed by in-depth interviews with six students purposively selected from students who had written the test. Descriptive statistics and qualitative content analysis were used to analyse students’ conceptions of integration.

Results show that students had three variations in associating single with double integrals, 1) interpretation of a single integral as an area under a curve associated with a double integral as a volume below a surface, 2) an area under a curve conception of a single integral with the double integral as a summation of vertical area slices, and 3) it was found that students who were able to relate double integrals to the Riemann sum were able to sketch images that represented both single and multivariable integrals.

The results suggest that certain integral conceptions such as an area under the curve may contribute to the difficulties students have in multivariable integrals. These difficulties are likely to affect performance in vector calculus topics like Stokes’ theorem. It is important therefore, in the pedagogical approach, to include different integral conceptions that will enable students to understand single and multivariable integrals. Understanding how students’ conceptions of single integrals impact their understanding of double integration and other vector calculus topics can enable educators to design instructional instruments that will help students understand double integrals and improve performance in multivariable calculus and in other engineering courses.