Mathematics

The purpose of Flipping Calculus is to transform the teaching and learning of Calculus by inverting traditional instruction and incorporating pedagogical practices that are steeped in our understanding of how students learn most effectively. Flipping a course describes an instructional approach in which the delivery of a majority of the content is moved outside of class, via online videos, lecture notes, and readings, while "homework," such as problem sets, labs, and applications, often completed in small groups, is shifted into the classroom. In a flipped course, students have the ability to access prerecorded presentations and problem solutions before class on an array of mobile devices and can pause, rewind, and fast-forward these videos, so they have more control over their own learning. More importantly, as there is little time spent lecturing, instructors in flipped courses are free to devote class time to supporting small groups of students who are engaged in collaborative discussion and problem-solving.

The primary objectives of Flipping Calculus are to:

• Create a complete library of brief, engaging videotaped lessons or screencasts of key concepts and worked solutions to problems for our Calculus I course. Expected outcomes are that students will better understand key calculus concepts and skills as they have the ability to view, and review, course videotapes on demand.
• Develop, adapt and refine meaningful guided problem sets and discussion questions to be completed by students working in small groups during class meetings. Expected outcomes are 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.
• Develop, adapt, and refine short assessments to evaluate students' understanding of out-of-class readings and videotaped presentations. These assessments will allow us to gauge the extent to which students are making sense of content they view outside of class.
• Flip half of the sections of Calculus I during fall 2012 which would involve the participation of approximately 120 students.
• Conduct an exploratory 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. The data generated will be useful as we continue to refine our model of flipping Calculus in subsequent semesters.
• Create a website for flipping calculus on which we will post our videos, course materials and reflections on lessons learned. By sharing our work publicly, we can share our model of flipping and begin to form a network of mathematics faculty interested in transforming their instruction.

Intellectual Merit: The proposed project activities are based on research on how students learn and are designed to actively engage students in Calculus, so they are able to understand, remember and apply the skills and concepts they learn. This project builds on the past and current innovations of the PIs and the entire mathematics department at the University of Hartford.

Broader Impact: This project will involve at least six mathematics faculty members and could directly impact more than 200 students during the first year of the project and upwards of 300 students in year two. We will extend the impact of this project by presenting at regional and national conferences, sharing the videotapes and problem sets, labs and discussion questions on a website dedicated to flipping calculus, and publishing articles in mathematics education journals.

Project Description

The purpose of the proposed project, Flipping Calculus, is to implement flipping pedagogy in Calculus I and conduct an exploratory study of its effectiveness. In particular, we will create a set of curriculum materials designed specifically for the flipped Calculus classroom and implement flipping pedagogy in half of our sections of Calculus I. The curriculum materials will include (1) concept videos or screencasts that provide an out-of-class introduction to new material with, when possible, embedded reasons to know the content, (2) guided problem sets and good questions to engage students in learning mathematics with peer and instructor support in class, and (3) assessments including quizzes and homework problem sets to provide more opportunities for practice and feedback on student performance. Student and instructor data will be collected from both flipped and non-flipped sections of Calculus to identify the benefits and challenges of this pedagogy and its impact on student understanding.

We developed a set of eight to twelve-minute videos that capture the essential aspects of the topics in our first-semester calculus course. In addition, we designed corresponding sets of entrance quizzes and in-class problem sets. The students are expected to watch one or two videos before attending class. We have also developed a set of problems for the students to work on during class in small groups of 2 or 3.

There is minimal traditional instruction. In general, direct instruction occurs on an as-needed basis in the form of 5 - 10 minute-long "mini-lectures."  The instructor spends most of his or her time answering questions for individual groups or orchestrating larger class discussions. Students frequently present and explain problems at the board for their peers.  While there are some differences between flipped classes, in all cases, the emphasis is on students doing and discussing mathematics.

What is a typical class like?

Each class generally begins with a 1- or 2- question entrance quiz to check that students have watched the video. What happens next can vary - depending on the instructor and the topic. Some instructors start class by answering questions about the content in the video and on homework questions, others might start class with a classroom voting question to get a discussion started, another might start class with an activity related to the content from the video. For a large portion of the class period, the students work on problems in small groups while the instructor circulates the room, posing and answering questions or providing feedback. If the instructor notices a common difficulty, he or she might stop class and give a short mini-lecture. The class also includes opportunities for students to present and explain solutions at the board.

What is the physical set up of the classroom?

Most of our flipped classes are taught in rooms tables that are circular, or that can be grouped to provide working space for four students. In addition, the chairs have wheels making it easy to for students to quickly changing locations. We are fortunate that these rooms also include multiple boards and multiple projection units which facilitate the sharing of student work.

How many students are typically in your classes?

We have 24 - 26 students enrolled in our flipped classes.

How do you monitor whether or not the students view the video?

Most of us administer a short "quiz" at the beginning of the period to help us assess whether or not students have viewed the video. There are 1 or 2 question on these quizzes (included on the website) that usually mimic the content from the videos. Some instructors encourage the students to take notes on the videos and let students use their them on the quizzes as well.

Do you lecture?

There is usually a little bit of lecture included in every class. We refer to these instances as "mini-lectures." They are short and to the point and are not the emphasis of the class period. Usually, the instructor will step in with a mini-lecture when he/she sees that the whole class could benefit from a discussion about one student's question or when more than one group of students have similar questions. These mini-lectures rarely occur at the start of class.

Do the students have homework?

Students enrolled in our flipped classes have regular homework assignments. At the University of Hartford, we use WeBWorK as our online homework system.

• Schroeder, L. B., McGivney-Burelle, J., & Xue, F. (2015). To Flip or Not to Flip? An Exploratory Study Comparing Student Performance in Calculus I. PRIMUS, 25(9-10), 876-885.http://dx.doi.org/10.1080/10511970.2015.1050617
• McGivney-Burelle, J. & Xue, F. (2013). Flipping Calculus. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 23(5), 447 - 486.http://www.tandfonline.com/doi/abs/10.1080/10511970.2012.757571#preview
• Schroeder, L., Xue, F. & McGivney, R. (2013). Flipping Three Mathematics Courses: Common conclusions and plans for the future. MathAMATYC Educator, 4(2), 63 - 68. http://www.amatyc.org/?page=EducatorFeb2013#schroeder
• Schroeder, L. B. & Dorn, B. (2013). Flipping Calculus with TrACE: A web-based media player for collaboration in Calculus I. In& Martinez, M. & Castro Superfine, A (Eds.). Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago, IL: University of Illinois at Chicago.