Flipping Calculus: Challenges, Successes, and New Directions

Project No.
PI Name
John Williams
University of Hartford


Abstract 1

Flipping Calculus: Challenges, Successes, and New Directions

Presentation Type
John Williams, University of Hartford Mako Haruta, University of Hartford Larissa Schroeder, University of Hartford Ben Pollina, University of Hartford Fei Xue, University of Hartford


The need to improve the participation and performance of U.S. students in STEM is well understood. At the college level Calculus is a course that has significant potential to serve as a pump for increasing the number of students majoring in STEM fields. Calculus is a foundational course for all STEM majors and if taught well, should provide students with a positive and successful first-semester experience and gateway into more advanced courses.

While there have been significant efforts over the past three decades to reform the teaching and learning of college-level Calculus, this course remains a filter, rather than a pump, for science, technology, engineering, or mathematics majors. The College Board (2010) reported that of the students who entered college in 1995ヨ96 with the intention of pursuing a STEM major only 27% had succeeded by 2001 and calculus courses remains one of the significant contributors to this loss. For example in fall 2010, 325,000 students were enrolled in a college or university Calculus I course and 75% of these students intended to major in science, engineering or mathematics. Yet, while these students demonstrated above average mathematical aptitude (i.e., average SAT Math score of 652 with three-quarters of these students earning at least a 610) 27% received a D or F or withdrew from the course and a further 23% received a C (Boardman, Bressoud, Camp & Kilkelly, 2012).

Despite the growing body of evidence which suggests other instructional approaches are more effective in improving student engagement, satisfaction and performance (e.g., Hake, 1998; Couch & Mazur, 2001) it is still the case that most college mathematics instructors believe that students learn best via lecture (Bressoud, 2011). Anecdotal evidence suggests that concerns about the need to モcover the contentヤ drive mathematics faculty towards a lecture model of teaching since it is seen as the most efficient model for transmitting essential course information. The collective sense is that while it is understood that engaged learning pedagogies may be ideal, they take too much time and resources to implement.

Our project, Flipping Calculus, is important because it has sought to develop, implement and evaluate instructional approaches to improve student engagement, retention and success in first year Calculus. It also seeks to convince mathematics faculty that student performance and success in Calculus can be improved through more engaging pedagogy. Until this project commenced there had been no rigorous attempt to understand the outcomes of implementing flipping pedagogy. Since then we have published one of the most cited papers on flipping pedagogy in college mathematics (see Flipping Calculus by J. McGivney-Burelle and F. Xue) and have a second one on press (see To Flip or Not to Flip, L. Schroeder, F. Xue and J. McGivney-Burelle) which is a controlled study that points to the advantages of a flipped classroom.

This project has benefited more than 500 of our students who now have access to a comprehensive set of materials to support their understanding of Calculus. It has also affected the pedagogy of departmental colleagues and, in fact, colleagues across campus who were initially skeptical of this type of instruction. Finally, it has benefited the hundreds of colleagues across the country who have visited our website, attended our conference presentations, or read published results of our work.


The goals and activities of this project include:
(1) Creating a complete library of brief engaging videotaped lessons or screencasts of key concepts and worked solutions to problems for our Calculus I course.
(2) Developing, adapting and refining meaningful guided problem sets and discussion questions to be completed by students working in small groups during class meetings.
(3) Developing, adapting and refining short assessments to evaluate studentsメ understanding of out-of-class readings and videotaped presentations.
(4) Flipping half of the sections of Calculus I for one semester to conduct a controlled study, involving approximately 120 students.
(5) Conducting a mixed methods study of instructor and student perceptions of the flipped Calculus course, as well as student outcomes in the flipped vs. traditional sections of Calculus I.
(6) Creating a website for flipping calculus on which we will post our videos, course materials and reflections on lessons learned.


The central intervention of this project is applying inverted instruction or flipping pedagogy in Calculus I.

The key project activities or strategies involve developing, testing, revising, and disseminating a comprehensive set of course materials to support instructors' use of flipping pedagogy in Calculus and to conduct a systematic study of the effectiveness of this type of pedagogy.

All members of the project team are involved in a variety of project activities. J. Williams is overseeing the project, developing videos and managing the website. B. Pollina is developing, editing, and revising videos. M. Haruta is developing curriculum materials and overseeing the evaluation component of the project. J. McGivney-Burelle is developing curriculum and managing the research component of the project. L. Schroeder is developing, editing, and revising videos and is involved in data collection. F. Xue is developing, editing and revising videos and is managing the data analysis.


There are a number of expected outcomes of this project.

First, we expect that students will better understand key calculus concepts and skills as they have the ability to view, and review, course videotapes on demand. We also expect that students will be more adept at applying their knowledge of calculus as a result of more time spent working collaboratively in class under the guidance of a faculty member.

We expect that daily short assessments will allow us to gauge the extent to which students are making sense of content they view outside of class and will provide student with regular feedback so they may better monitor and regulate their performance in class.

By sharing our work publicly we expect that our model of flipping pedagogy will inform the work of other mathematics faculty and begin to create a network of mathematics faculty interested in transforming their instruction.

A key finding of our controlled study of flipping Calculus I revealed that students in flipped sections of Calculus I not only performed better than students in the non-flipped sections on the common final exam in Calculus I , but the students in flipped sections of Calculus I did better in Calculus II where no sections were flipped. (See To Flip or Not to Flip, L. Schroeder, F. Xue, and J. McGivney-Burelle. To appear in an upcoming special issue of PRIMUS)

The deliverables of this project include a comprehensive set of videos, problem sets, assessments, and discussion questions to support flipping pedagogy in Calculus I. Moreover, we have developed a project website that has had thousands of 'hits' and have published foundational studies of this type of pedagogy.

We hope to build on the success of Flipping Calculus by securing funding for a Flipping STEM project, which would seek to take our lessons learned and apply them to a range for first-year science, technology and engineering courses.

Broader Impacts

This project has involved the majority of mathematics faculty members at the University of Hartford and has directly impacted more than 500 students enrolled in Calculus I for the past three years. We have extended the impact of this project by organizing and hosting well-received contributed paper sessions at both the MAA/AMS Joint Meetings and the MAA MathFest. In addition, we have made dozens of presentations at regional, national and international conferences; shared the videotapes and problem sets, labs and discussion questions on a website dedicated to flipping calculus; and published articles in peer-reviewed journals.

Unexpected Challenges

We didn't expect the challenges around creating, close-captioning and sharing videos from this project. We enlisted the help of talented juniors and seniors in the computer science program to assist us with this part of the project.


Schroeder, L., Xue, F. & McGivney-Burelle, J. (In press). To flip or not to flip? To appear in a special issue of PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies.

McGivney-Burelle, J. & Xue, F. (2013). Flipping Calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Vol. 23, Issue 5, 447 ヨ 486.

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