Digest No. 05 - October 2018

Effectiveness of Flipped Classroom Instruction in Mathematics for Liberal Arts Students

Carter, C. L., R. L. Carter, and A. H. Foss. 2018. “The Flipped Classroom in a Terminal Mathematics Course for Liberal Arts Students.” AERA Open 4 (1) 1–14.


This study evaluated the efficacy of a flipped classroom on the final exam scores of 632 students enrolled in different sections of a terminal general education college mathematics course. The authors adopted a quasi-experimental design, comparing the final exam scores in traditional versus flipped sections of the same math course. In addition to examining these differences in scores, the authors were able to test whether these pedagogical approaches had a different impact on students based on race.
The authors adopted the Flipped Learning Network’s 2014 definition of flipped learning as “a pedagogical approach in which direct instruction moves from the group learning space to the individual learning space and the resulting group space is transformed into a dynamic interaction learning environment where the educator guides students as they apply concepts and engage creatively in the subject matter” (p. 1). Extending this definition and applying it within the context of the study environment, the authors noted that the flipped classrooms examined in their study used online videos of content-related lectures, rearranged seating to increase collaboration, and instructors who served as mentors to guide students through problem-solving activities.
Turning to research design, seven adjunct instructors, who collectively taught 13 sections, participated in the study. In the fall, these seven instructors taught the curriculum using traditional classroom methods. In the spring, these same instructors—after being trained in how to effectively design a flipped classroom environment—delivered the curriculum in flipped classrooms. A common final math exam was administered to students in both iterations of the course.
Of the 632 students enrolled in the fall and spring semesters, 91.1 percent and 92.7 percent were respectively exposed to the traditional and flipped classrooms. Most identified as White (41 percent), followed by African American/Black (11 percent), Hispanic/Latinx (11 percent), and other (4 percent). More than three in five (62 percent) identified as female. Most were first-year students (65 percent) and 22 percent were sophomores. Nearly eight in ten (79 percent) were receiving need-based financial aid. The average math SAT score—based on 519 students—was 440 out of 800.

The authors performed statistical modeling to assess the differences in final math exam scores between students who experienced the traditional versus the flipped classroom. Models included the course condition (flipped versus traditional), race, class standing, financial aid, gender, transfer status, math SAT score, and grade point average.


The authors report that students in the flipped sections scored 5.1 percent higher on average than those in the traditional sections, after controlling for model covariates. In other words, students in the flipped class were, on average, more likely to receive a C+ on the final exam, while those in the traditional class were, on average, more likely to receive a C. These differences were statistically significant.

In addition, there was an interaction effect reported for pedagogy by race. This effect was driven by the differences in exam scores among White and Black students. On average, the final math exam scores for Black students in the flipped classroom environment were 7.8 points higher than scores for their peers in traditional classes, after accounting for model covariates. Course condition (flipped versus traditional) did not influence White student scores to the same degree, with final exam scores for White students in flipped classes only 1.0 points higher than scores for their White peers in traditional classes.


Although the study is flawed by a number of limitations that the authors articulate, it remains an important contribution for CIC leaders as they consider innovative pedagogies and their influence on student performance in mathematics. Recently, CIC spent four years exploring the efficacy of flipped classrooms (among other online modalities) for helping students succeed in humanities courses and found little differences between these pedagogical deliveries with more traditional ones. Perhaps, flipped classrooms are more effective in helping students learn math than subjects related to the humanities.
These questions are critical as leaders assess instructional resource allocation issues. Recent evidence suggests that the more resources institutions directly allocate toward student instruction, the more likely students are to make learning gains (Mayhew et al. 2016). That said, once resources are allocated to help an instructor—like the adjunct faculty members who participated in this study—flip a classroom, that instructor may depart the institution, leaving the institution with little to show for its investment in educator training.

Of course, trade-offs like these are nothing new to CIC leaders. Perhaps the part of the study that might tip the balance involves the math score performance of the Black students in the flipped classroom compared to their counterparts in the more traditional classes. The more individualized attention students receive in the flipped environment may be one key component to helping them succeed, especially in a math context.

About the Authors

Christina L. Carter has most recently taught mathematics at Buffalo State College.
Randolph L. Carter is professor emeritus of biostatistics at the University at Buffalo.

Alexander H. Foss is a senior statistician at Sandia National Laboratories.

Literature Readers May Wish to Consult

Flipped Learning Network. 2014. Definition of Flipped Learning.

Brewer, R, and S. Movahedezarhouligh. 2018. “Successful Stories and Conflicts: A Literature Review on the Effectiveness of Flipped Learning in Higher Education.” Journal of Computer Assisted Learning 34 (4): 409–416.

Mayhew, M. J., A. N. Rockenbach, N. A. Bowman, T. A. Seifert, and G. C. Wolniak, with E. T. Pascarella and P. T. Terenzini. 2016. How College Affects Students (Volume 3): 21st Century Evidence That Higher Education Works. San Francisco: Jossey-Bass.