RUME 27
2025
Alexandria, Virginia
Understanding-Oriented Lectures in Calculus: Practical Strategies for Enhancing Students’ Mathematical Learning
Page: 64
Many instructors observe that students often rely on memorization in introductory college mathematics. However, existing literature on effective teaching strategies does not fully address the need to cultivate both conceptual understanding and deeper orientations towards understanding in students’ learning. This study presents a case analysis of calculus lectures delivered by an experienced instructor at an R1 institution, revealing significant opportunities for enhancing conceptual learning and promoting stronger orientations towards understanding among students. The analysis identified four key strategies employed by the instructor: 1) framing instructional activities as a pursuit of understanding; 2) examining underlying meanings while connecting students’ intuition; 3) providing motivations, justifications, and multiple perspectives; and 4) creating cognitively challenging tasks and encouraging students to embrace discomfort in learning. These simple, practical strategies do not impose significant demands on instructors yet hold great potential for helping more students approach mathematics through deep understanding.