Challenges and Opportunities for the Flipped Classroom approach in Mathematics

Engineering Mathematics 2E is a large second-year undergraduate course that is required of all Engineering students. One of the stated learning outcomes is:

“develop understanding of the concepts of engineering mathematics and competency in problem-solving techniques and creative and critical thinking”

Unfortunately, the course as currently designed fosters almost no creative or critical thinking!

Students attend lectures of up to 500 people, with a single lecturer (me) taking them step by step through the theory and example problems. Interaction and feedback is limited, although I do my best to take questions from the students, and I give a weekly “pop quiz” that students work on in small groups while I roam the room answering questions. In addition, students attend a weekly hour-long tutorial with a single tutor and 48 students. Students are asked to work through a set of tutorial problems in advance and the tutor then answers questions. In actuality, students turn up without reading the questions, mark their name off the roll, and then silently copy everything the tutor writes on the board. In other words, for the vast majority of the students, the face-to-face lectures and tutorials are not learning opportunities: they are an exercise in stenography.

In FULT Module 2, we discussed the idea of constructive alignment of assessments so that they reinforce and support the desired learning outcomes. In discussion with my peers I came to understand that the assessment structure for my large-enrollment mathematics course strongly constrains the learning outcomes. Indeed, the course essentially coaches students for the exam. Sample test question and past exam problems are presented and solved in lectures. Very little background theory is discussed, on the assumption that students just want to know how to solve the problems. Students are not given an opportunity to experience the beautiful mathematics underlying it all. But this is exactly the opposite of constructive alignment of assessment, which starts with the desired Learning Outcomes and designs the Learning Activity and Assessment Tasks to support these outcomes.

As part of post-activities for FULT Module 2, we watched an interesting video describing how the “Flipped Classroom” approach has been applied to large-enrollment Psychology courses at North Carolina State University. Some ideas introduced in this video include pre-recorded lectures that students review before class; an open-notes quiz to test their understanding; small group discussion and presentation; and video recordings of students that are available for future reflection and feedback.

Some of these are great ideas, and indeed some concepts are already incorporated into the current model for Engineering Mathematics 2E: all lectures are recorded so that students can review them in their own time; tutorials offer an opportunity to get more individual interaction with their tutor; and in-class pop quizzes allow students to review new methods and cement what they’ve learned, with instant feedback provided by simple polling tools available on their phones or internet-enabled device. (I use, which uses QR codes and tiny URLs to direct students to an individualized poll online; this has the advantage of not having to download any apps.)

However, there are big challenges for a lecturer hoping to apply the flipped classroom approach in large-enrollment courses. The first is scale: flipped classroom ideas might work great in small to medium sized lectures, but they quickly becomes unfeasible when you are dealing with hundreds of students on your own. There is no way to interact with all the students in a reasonable amount of time. The second issue is space: in the video (as in my own lectures) the class is held in a traditional lecture room with a stage in front of rows of raked seats. This makes it very awkward (though not impossible) for students to work in small groups, for groups to interact, and for the lecturer to circulate among groups offering feedback and guidance. The smaller tutorial rooms are better suited for this, but we need to redesign these learning spaces with rearrangable chairs and tables suitable for a flipped classroom model.

The third challenge is time: the effort and preparation required of a lecturer teaching a flipped classroom seems downright superhuman. Recording lectures takes as much time (and usually takes much more time)  as the traditional lecturing format. But the additional in-class activities, feedback, reflection, and assessment tasks all require detailed and time-consuming preparation. During FULT Module 2 we had an opportunity to hear from a panel of lecturers who have implemented a flipped classroom approach in their courses, and a repeating theme was the amount of time needed to get these things up and running — months, in many cases. Clearly, this is not compatible with a traditional “Research-and-Teaching” lecturing position where research outputs are valued far above teaching quality. Universities need to recognize the work and effort that goes into preparing these kinds of flipped learning experiences for students!

Finally, I worry, in a vague way, that some of the these approaches take the responsibility for learning away from the student and places it on the educator. As I have thought and read more about the flipped classroom model for university undergraduate courses, and talked with people who have used this approach in their own teaching, I have detected this tendency for the educator to take on more and more of the responsibility for the students’ learning outcomes.

Of course, lecturers need to be aware of the needs and limitations of their students, and there are no shortage of outstanding university educators who work hard to get their students excited about their subject. And I am also aware that minority students in particular are often ill-prepared for the challenges of transitioning from secondary to tertiary education and sometimes need help managing their responsibilities. Community Colleges in the United States, which have large numbers of non-traditional students and high drop-out rates, have begun to address this with a more invasive and individualized University experience, with dedicated “success coaches”  who track each student’s progress and offer help with choosing their courses, planning their timetable, and helping them meet their programme requirements so that they can graduate on time. (For more on this, listen to this fascinating This American Life podcast).

These are important, to be sure. But the ultimate responsibility for learning is with the student. By giving students an opportunity to engage more deeply with the learning activities, the flipped classroom has the potential to let students take their learning into their own hands, reflect on their learning, and get feedback from their instructor and their peers. But to be successful, a flipped classroom has to be very carefully “scaffolded” towards the learning outcomes. I wonder if this places a disproportionate burden of responsibility on the lecturer.

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