Baldwin Mei, Maya Schwartz

Comparing and Contrasting Secondary and Undergraduate Precalculus Teaching

Introduction

Comparing and contrasting secondary and undergraduate precalculus teaching. Compare secondary & undergraduate precalculus teaching. Explore active learning techniques, contexts, and key issues from high school & college perspectives for pedagogical takeaways.

Abstract

Precalculus is a course that bridges the divide between early secondary mathematics and early tertiary mathematics. As such, it exists in both high schools and colleges, taking different forms depending on the curricular and pedagogical requirements of each institution and student body. Each precalculus class, secondary and tertiary, can benefit from the other's instructional methods. To begin this exchange of ideas, two perspectives of precalculus teaching are presented and contrasted: one from a high school teacher and one from a college instructor. Teaching contexts, key issues, and active learning pedagogical techniques are described, and potential pedagogical takeaways for each teacher’s specific concerns are suggested.

Review

This paper addresses a highly pertinent topic in mathematics education: the teaching of precalculus at both secondary and undergraduate levels. By framing precalculus as a crucial transitional course, the authors highlight the importance of understanding the diverse pedagogical approaches and curricular demands it faces across different educational contexts. The aim to foster an exchange of instructional methods between high school teachers and college instructors is particularly commendable, suggesting a practical and collaborative approach to improving student preparedness and instructional effectiveness. The premise that each setting can benefit from the other's insights is a strong foundation for a valuable discussion. The methodology outlined, involving the presentation and contrast of two distinct perspectives—one from a high school teacher and one from a college instructor—promises a concrete and relatable comparison. By detailing teaching contexts, identifying key issues specific to each environment, and examining active learning pedagogical techniques employed, the paper offers a granular look at the realities of precalculus instruction. This approach is well-suited to uncovering both common challenges and unique opportunities for innovation, moving beyond theoretical discussions to practical applications. Ultimately, the paper aims to provide tangible pedagogical takeaways, suggesting how insights from one setting can inform and enhance teaching practices in the other. This focus on actionable advice for specific concerns makes the contribution particularly valuable for practitioners. Such a comparative analysis is vital for bridging the often-siloed experiences of secondary and tertiary educators, fostering a more coherent and effective educational pipeline for students transitioning into higher mathematics. The work has the potential to significantly contribute to an ongoing dialogue about curriculum alignment and pedagogical best practices in precalculus education.

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