Calculus limits involving infinity: the role of students’ informal dynamic reasoning

Abstract

Few studies on calculus limits have centred their focus on student understanding of limits at infinity or infinite limits that involve continuous functions (as opposed to discrete sequences). This study examines student understanding of these types of limits using both pure mathematics and applied-science functions and formulas. Seven calculus students’ approaches to understanding, calculating, and interpreting answers to these types of limits are examined. The dynamic reasoning used by these students led to good justifications and meaningful interpretations of their answers. On the other hand, when students engaged less with dynamic reasoning, they struggled more and made less reasonable interpretations of their answers. Furthermore, dynamic reasoning helped the students in this study overcome previously documented pitfalls and encouraged covariational reasoning. The applied-science contexts at times helped the students engage in dynamic reasoning.

Keywords:

• calculus
• limit
• infinity
• dynamic
• covariation
• student understanding