PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
How students interpret line and vector integral expressions: Domains, integrands, differentials, and outputs
Page: 673
This study expands on research happening in multivariate calculus education to an exploration of student understanding of line and vector integrals. We describe how students interpreted these types of integrals, including the various symbols in their expressions and their relationships to each other. We found that while students were able to associate mathematical objects with the individual symbols in the integral expressions, the main issues came in trying to coordinate these objects into a comprehensive whole for the entire integral expression. While the literature has discussed connections between the integrand, differential, and integral symbol, we also found that connecting the domain to the other parts of the integral expression was difficult as well. Thus, to give more attention to the domain in addition to these other parts, we have incorporated it into a general “domain-chop-evaluate-add” framework for reading integrals.