Shay Fuchs is a Professor of Mathematics, Teaching Stream, at the University of Toronto Mississauga. He shares an example from a first year Calculus for Life Science sequence which includes Differential Calculus and Integral Calculus. The sequence is aimed at life science students (majoring in biology, chemistry, psychology, etc.), covering standard Calculus in a single variable, with more emphasis on concepts, techniques and applications, and less emphasis on theory and proofs.
This particular flipped-classroom design (implemented successfully since 2018) involves the following elements and expectations:
- Students are required to read material prior to class and complete a pre-class assignment.
- In class, instructors use a combination of polls, short lectures, and activities to address central notions and ideas, common misconceptions, and practice the material.
- Think-pair-share and discussions are facilitated during class. A teaching assistant is normally present to help out with the activities.
- Students also complete a post-class assignment after attending class.
The use of technology, and, in particular, the use of iClickers, is essential to both engaging the students in content-related activities, and providing immediate feedback to the instructor on the level of understanding of the content. In 2019, Dr. Fuchs and colleagues conducted two experiments to measure the effectiveness of the new flipped-classroom design. The results showed positive effect on student performance, supporting the growing body of literature about digitally-enabled, evidence-based teaching practices. For details on the data collected and the research conducted, see the article by Fuchs and Sahmbi, Investigating the Impact of Active Learning in Large Coordinated Calculus Courses.
Digital Resources
iClickers or any in-class polling tool; MacMillan Learning’s Achieve and Crowdmark platforms
The technological tools used are: (1) Macmillan Learning’s Achieve and Crowdmark platforms to administer pre and post-class assignments (and provide access to an interactive textbook), and (2) iClickers to run polls and activities during class.
The use of iClickers (or, in fact, any tool for in-class polling) engages students in mathematical tasks during class and provides immediate feedback to the instructor and students. Quite often, in-class poll results are surprising and unexpected, requiring the instructor to make adjustments to their lesson plan and address revealed gaps in understanding, misconceptions, and common mistakes.
The Achieve platform gives students access to an interactive textbook (with dynamic diagrams and videos), and a robust homework system, in which students receive detailed feedback on both correct and incorrect answers. An AI tool (embedded in Achieve) can be used to guide students as they practice without revealing the correct answers.
Both tools help facilitate interaction, active participation, and immediate feedback, which are harder to achieve in large classes without technology.
Digital Enablement
On their own, digital tools are usually not enough to support student learning effectively. However, digital tools can be powerful in executing effective teaching practices. The use of in-class polls (iClickers or other), digital textbook and homework platform facilitates the following:
- Engaging students during class in activities that promote mathematical thinking, problem solving skills, and ‘making-sense’ tasks.
- Poll results provide immediate feedback to the instructor, who can then respond to common errors, misconceptions, and gaps in students’ understanding.
- In-class polls and activities require students to ‘retrieve’ information read at home, and hence facilitates retrieval practice and activation of prior knowledge.
- The use of a digital textbook and homework assignments allows students to remain active during the reading by working with interactive diagrams, watching short videos, highlighting parts of the text, taking notes, and using an AI-tutor. Students also receive guidance and immediate feedback on their answers to homework problems, whether correct or incorrect.
Dr. Fuchs gives the following recommendations to instructors considering a flipped-classroom model with polling:
- Finding low-cost tools makes them more accessible to students who experience financial difficulties.
- Using a digital textbook and an online homework system increases accessibility (for instance, font size can be increased, and a read-aloud option is available).
- The mere use of active learning is known to be more equitable, with strong positive effect on women in particular, and members of other underrepresented groups in mathematics. Research results by Fuchs and Sahmbi also support this claim.
- Careful and detailed planning is crucial. Choosing appropriate and well-formulated tasks is critical to the success of the flipped-classroom design. An example in-class slide-deck for one textbook section about Arc Length and Surface Area can be found here.
- Initial and ongoing training of instructors and teaching assistants is important for making sure this design is executed properly and consistently. Videos of polling activities and other resources are used to support instructors learning how to ‘respond’ to poll results and address gaps in understanding revealed by poll results in real time.
- Instructors and administrators should prepare for handling anticipated resistance to “new” pedagogies from students and colleagues alike. Some pushback is expected and well-documented in the literature.