RUME 28
2026
Alexandria, Virginia
Students’ Challenges in Double Integration Over Non-rectangular Regions
Page: 1012
Double integration is challenging for many students. It involves the interrelationship between three variables x, y, z within an object in 3D space expressed in both algebraic and graphical representations. When the integral domain is not a rectangular region, values of x and y along its boundaries may become dependent. However, how students perceive interdependency of variables and what mental actions are involved in double integration have not been fully explored. To answer these questions, multivariational reasoning framework is used in this study to analyze students’ cognitive activities. Interview data collected from a university-level calculus enrichment course is analyzed to explore student’s reasoning. The findings suggest that students demonstrate several mental actions of multivariational reasoning when performing double integration over different regions. They also suggest some possible directions of extending the theoretical framework of multivariational reasoning to adapt some specific concepts such as range and change of variables in double integration.