Insights from College Algebra Students' Reinvention of Limit at Infinity

William Holmes McGuffey

The limit concept in calculus has received a lot of attention from mathematics education researchers, partly due to its position in mathematics curricula as an entry point to calculus and partly due to its complexities that students often struggle to understand. Most of this research focuses on students who had previously studied calculus or were enrolled in a calculus course at the time of the study. In this study, I aimed to gain insights into how students with no prior experience with precalculus or calculus might think about limits via the concept of limit at infinity, with the goal of designing instructional tasks based on these students’ intuitive strategies and ways of reasoning. In particular, I designed a sequence of instructional tasks that starts with an experientially realistic starting point that involves describing the behavior of changing quantities in real-world...