PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Integrals, Volumes, and Visualizations
Page: 1477
Many studies have been done on student understanding of integration and this research aims to add to that knowledge base with the study of student understanding of integration when applied to volume problems and how visualizations and sketches are used in the problem-solving process. Participants were recruited from a large, public, research university and interviews consisted of students working through routine and novel volume problems while discussing their thought processes aloud. Preliminary results show that students rely heavily on memorized formulas and have difficulties explaining the concepts behind the formulas. The idea of the integral as a sum of small pieces is present in most students studied, but they have trouble relating this idea to the formulas in their volume integrals. All students drew sketches of the geometric situation for all the problems, but the extent to which they could use their sketch meaningfully varied greatly.