PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Student conceptions of definite integration and accumulation functions
Page: 761
Prior research has shown several common student conceptualizations of integration among undergraduates. This report focuses on data from a written assessment of students’ views on definite integration and accumulation functions to categorize student conceptualizations and report on their prevalence among the undergraduate population. Analysis of these results found four categorizations for student descriptions of definite integrals: antiderivative, area, an infinite sum of one dimensional pieces, and a limit of approximations. When asked about an accumulation function, student responses were grouped into three categorizations: those based on the process of calculating a single definite integral, those based on the result of calculating a definite integral, and those based on the relationship between changes in the input and output variables of the accumulation function. These results were collected as part of a larger study on student learning in multivariable calculus, and the implications of these results on multivariable calculus will be considered.