Experiencing Calculus Through Computational Labs: Our Department’s Cultural Drift Toward Modernizing Mathematics Instruction

Abstract

Our traditional model of calculus instruction at a large public research university emphasized factual knowledge and procedural fluency with few realistic applications, leaving a chasm between classroom mathematics and disciplinary practice. Amid an ongoing effort by our department to improve undergraduate learning outcomes, we replaced recitations in Calculus II with computational team labs to bridge this divide. Interview, classroom observation, survey, and gradebook data suggest that the labs facilitated a rich learning experience while student grade outcomes were unchanged. Student engagement, however, was inhibited by institutional structural factors, whose remedy requires a shift in departmental culture concerning the purpose of mathematics instruction.

KEYWORDS:

• Calculus
• computational labs
• problem of scale
• rich learning experience
• modeling
• qualitative assessment
• active learning
• group work

ACKNOWLEDGEMENTS

The authors would like to acknowledge their colleagues Mark Iwen, for co-developing the lab material; and Rachael Lund, for her valuable insights into the existing calculus course material.

Additional information

Funding

This work is supported in part by a curriculum development grant from MathWorks Academic Support.

Notes on contributors

Andrew J. Krause

Andrew “Andy” Krause is a member of the teaching faculty in the Department of Mathematics. Andy has 10 years of teaching experience with lower-division undergraduate mathematics courses in a variety of contexts (including dozens of large-lectures) and 5 years of experience coordinating the Center for Instructional Mentoring, which provides teaching support for faculty, postdocs, graduate teaching assistants, and undergraduate learning assistants. He brings educational research expertise and experience to the project, and the evaluation of the labs is his dissertation research. Having completed his undergraduate and master’s degrees at Michigan State University, Andy is well equipped to understand the learning experiences of our students.

Ryan J. Maccombs

Ryan “calculus overlord” Maccombs earned his MS at Michigan State University and currently is a Teaching Specialist focusing on the core calculus sequence. Ryan is very interested in using technology to enhance student and instructor experience for large courses. In his free time, Ryan enjoys board games, frisbee, and volunteering at a Cat Café.

Willie W. Y. Wong

Willie “course development is fun” Wong is an Assistant Professor of Mathematics at Michigan State University having earned both his BA and PhD in a sleepy little down smack in the center of New Jersey. Outside his day job researching the geometric analysis of hyperbolic partial differential equations and teaching calculus, he is also a $\text{LaTeX}$ ninja and jazz aficionado. He spends his down-time filling in crosswords, both American and cryptic.