Inverted Pedagogy in Second Semester Calculus

Abstract

This study investigates the effects of applying an inverted classroom model in a second-semester calculus course at a large regional university in the southwest during the Spring of 2013. The sample consisted of four class sections with the same instructor, with a total of 173 students; two class sections were in the experimental group, whereas the other two sections served as a control group. In the experimental sections, students watched video lectures of the course content outside of class, and class time was dedicated to solving problems associated with the content. Learning gains and academic differences between the two groups were investigated by analyzing exam scores and homework grades. In addition a survey (Motivated Strategies for Learning Questionnaire) was used to measure the students’ motivational orientations and their use of various learning strategies. Results showed there was a significant difference between the two groups on conceptual portions of some exams, where the control group outperformed the experimental group. There were also some significant differences on some aspects of the survey. This paper will discuss the details of the instructional methods, the results of the data analysis, present reasons for the results, and make suggestions for further study.

Keywords:

• Flipped classroom
• inverted pedagogy
• inverted classroom
• calculus

Additional information

Notes on contributors

Ellie Kennedy

Ellie Kennedy received a BS in Civil Engineering from the Colorado School of Mines and completed her MA in Mathematics at the University of Colorado at Boulder. As a Senior Lecturer at Northern Arizona University she teaches a wide variety of lower-division mathematics courses with an emphasis on the calculus sequence. She has been recognized for her excellent classroom teaching and dedication to student success. Because of her engineering background, she brings a valuable perspective to teaching undergraduate mathematics. In looking for innovative ways to improve instruction, she has become active in national discussions and studies on the flipped classroom. In her free time she enjoys outdoor activities such as rock climbing, trail running, and mountain biking.

Brian Beaudrie

Brian Beaudrie is an Assistant Professor of mathematics education at Northern Arizona University (NAU). Prior to his time at NAU, he was at Winona State University in Winona, Minnesota, and Plymouth State University in Plymouth, New Hampshire. Dr. Beaudrie’s research interests include quantitative literacy, using technology to teach mathematics, including web-based technologies, and students successfully transitioning in mathematics from high school to college. If he had free time, he would spend it with his family, on a beach, or on a golf course (or any combination thereof).

Dana C. Ernst

Dana C. Ernst received his BS from George Mason University, an MS from Northern Arizona University, and completed his Ph.D. at the University of Colorado at Boulder in 2008. He is currently an Assistant Professor at Northern Arizona University in Flagstaff, AZ. Furthermore, Ernst is a Project NExT national fellow and Special Projects Coordinator for the Academy of Inquiry-Based Learning. His primary research interests are in the interplay between combinatorics and algebraic structures. More specifically, he studies the combinatorics of Coxeter groups and their associated algebraic structures. In addition, Ernst is passionate about mathematics education and his scholarly activities include topics in this area with a specialization in inquiry-based learning. Lastly, Ernst is an avid cyclist, trail runner, and rock climber.

Roy St. Laurent

Roy St. Laurent received a BS in Mathematics from Michigan Technological University and a Ph.D. in Statistics from the University of Minnesota. He is currently an Associate Professor at Northern Arizona University (NAU) and has a part-time administrative appointment at NAU. Prior to joining the university, he was on the faculty in the Department of Biostatistics at the University of Michigan. Dr. St. Laurent’s research interests include regression diagnostics and nonlinear regression, measures of agreement, and nonparametric methods. In his limited spare time, he enjoys completing puzzles such as Heyawake and Yajilin, reading science fiction, listening to music, and playing games.