Limits are foundational to the central concepts of calculus. However, the authors' experiences with students and educational research abound with examples of students' misconceptions about limits and infinity. The authors wanted calculus students to understand, appreciate, and enjoy their first introduction to advanced mathematical thought. Thus,…

After students have constructed a conceptual understanding of a mathematical idea, applying mathematical symbolism to represent and define the idea concisely becomes an easier task. In fact, Moore (1994) found that students "often needed to develop their concept images through examples, diagrams, graphs, and other means before they could…

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…