RUME 27
2025
Alexandria, Virginia
Developing Understandings of Accumulation: A Preliminary Research Report
Page: 1277
This preliminary research report examines how undergraduates develop quantitative meanings of accumulation from rate, a foundation for understanding the definite integral and the Fundamental Theorem of Calculus. This study is a pilot study for a larger project. It consists of a pre-/post-assessment and a teaching experiment. The task sequence provides opportunities for students to develop productive meanings for speed, distance, and their relationship as rate of change/accumulation. Preliminary analysis of the pre-assessment indicates that students struggle to conceptualize average and instantaneous speed, which suggests that the teaching experiment can be productive. In this report, I outline the theoretical framework, task sequence, preliminary findings, and ongoing work. I conclude with areas for audience discussion: Seeking feedback on analysis and ideas for expanding upon this pilot study.