PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Making sense of irrational exponents: University students explore
Page: 382
We investigate how students make sense of irrational exponents. The data is comprised of 32 interviews with university students, which revolved around a task designed to examine students sensemaking processes involved in the understanding of the concept. Both the task design and data analysis relied on the concept of sensemaking trajectories, blending the notions of sensemaking and (hypothetical/actual) learning trajectories. The findings focus on three kinds of reasoning utilized in the participants’ sensemaking trajectories while working with irrational exponents: even/odd numbers and functions; range of exponent values; and exponentiation as repeated multiplication. These findings reveal students’ conceptual development of irrational exponents, and could in turn be used for the refinement of tasks aimed at promoting students’ comprehension of the topic.