Active Learning in an Undergraduate Precalculus Course: Insights from a Course Redesign

Abstract

Addressed toward course coordinators and departmental leaders interested in redesigning an undergraduate mathematics course, we highlight the steps our team at the University of Maryland, College Park has taken in bringing active learning to our Precalculus course. We provide examples of ways in which we have coordinated active learning across redesigned sections, as well as preliminary results of the effects of active learning on student success. Finally, given the broad set of experiences and backgrounds of our team members, we argue for the unique insight our redesign offers in restructuring a gatekeeper mathematics course to be focused on active learning.

KEYWORDS:

• Active learning
• Precalculus
• undergraduate mathematics
• course redesign

Additional information

Funding

This work was supported by the National Science Foundation [grant numbers 1624610, 1624628, 1624639, 1624643].

Notes on contributors

Sean Gruber

Mr. Sean Gruber is a Mathematics Education Ph.D. graduate student in the Department of Teaching and Learning, Policy and Leadership at the University of Maryland, College Park (UMCP). Since beginning his doctoral program, Gruber has taught a section of Math 115 Precalculus through the Freshman Connection program offered at UMCP, three sections of Elements of Geometry and Measurement, and one section of Mathematical Reasoning and Proof for Pre-Service Middle School Teachers. Gruber is a former UMCP graduate, earning both a Bachelor’s in Mathematics and a Master’s in Curriculum and Instruction through the MCERT program at UMCP. He taught three years in a high school in Montgomery County, as well as six summers in the Summer Transition Program offered through the Academic Achievement Programs at UMCP. His research interests include exploring how the social norms and teacher practices observed within a college math classroom affect students’ self-efficacy, achievement, and persistent in mathematics and more broadly, STEM fields of study. More specifically, Gruber is interested in researching and implementing student-centered instructional practices (i.e., active learning) to improve college students’ views of and experiences with mathematics.

Raluca I. Rosca

Dr. Raluca I. Rosca is a lecturer in Mathematics and is in her fourth year as chairperson of the Math 115 Precalculus lecture course. She has over 10 years of teaching experience at the college level, and since coming to UMD has taught Math 115 in both the large lecture format, and the single contact Math 115 Freshman Connection format for thirteen semesters. As the daughter of two first-generation college students and the administrator of an outreach program to middle schools, she is also very interested in using Math 115 as a stepping stone to success in college mathematics, not just in terms of content, but also in terms of creating the social network and the personal skills, habits and dispositions that empowers today’s diverse students of Math 115.

Daniel Chazan

Dr. Daniel Chazan is the Jean, Jeffrey, and David Mullan Professor of Teacher Education in the Department of Teaching and Learning, Policy and Leadership, Director of the Center for Mathematics Education, and co-Director of Terrapin Teachers. Chazan’s professional interests include student-centered mathematics teaching, the potential of history and philosophy of mathematics for informing such teaching, the role of technology in supporting student classroom exploration and practice-based teacher education, exploring possibilities for constructive links between educational scholarship and practice, and the preparation of future teachers.

Elizabeth Fleming

Dr. Elizabeth Fleming is currently an applied research mathematician with the U.S. Department of Defense. From 2017 to 2018, she was a postdoctoral fellow in Mathematics Education working with Dr Daniel Chazan. She also collaborated with Dr Kasso Okoudjou on a research project about shifts in his pedagogy in his Advanced Calculus course. Her research interests include how to improve mathematics course experiences for undergraduates, and how shifts in undergraduate course instruction may impact student experiences.

Steve Balady

Dr. Steve Balady is an Assistant Professor of Mathematics at Oberlin College and Conservatory. While at UMD, Balady was a lecturer in Mathematics at UMD and taught 13 sections of Math 115 beginning in the fall of 2008, both as a graduate student sole-contact TA and as the instructor of record for Maryland’s Freshman Connection. Balady’s courses — especially Precalculus — were dominated by student-centered collaborative analysis of multistep problems reflecting student questions and logical misconceptions. For his fall 2017 sections of Math 115, Balady moved his class to a Media Share classroom in Maryland’s new Edward St. John Center for Teaching and Learning to promote deeper conversations between students and their proactive use of technology. His long-term research includes how students develop their identities as working mathematicians, particularly those students enrolled in “transition” courses.

Catherine VanNetta

Dr. Catherine VanNetta has 12 years of high school teaching experience in the Baltimore City and the Howard County public school systems. From 2014 to 2018, she was a Master Teacher of Mathematics in Terrapin Teachers, a program designed to produce highly qualified secondary STEM teachers, and a 2017 Elevate Fellow redesigning Math 115 Precalculus. In the fall of 2017 semester, she co-taught the course to a Freshmen Connection section with two undergraduate Terrapin Teacher students. She is interested in facilitating meaningful mathematical discourse and supporting productive struggle in the high school mathematics classroom.

Kasso A. Okoudjou

Dr. Kasso A. Okoudjou is Professor of Mathematics. He regularly teaches the Calculus sequence, in large lectures. In the fall of 2017, his Math 140 Calculus I lecture course was taught in one of UMD’s Terp rooms designed to encourage peer-to-peer interaction. From July 2016 to June 2018, he was the Associate Chair for Undergraduate Studies and led an effort to administer Learning Outcome Assessments in Mathematics courses. In addition, he has been awarded an Elevate Fellowship by UMD’s TLTC to redesign our Advanced Calculus course (MATH 410). As part of this redesign program, he and Fleming conducted a research project on how group work and active learning strategies can help students be more proficient in their advanced calculus course.