I recently experimented with flipping the classroom in a practice learning situation in my Math Methods class at McGill. This teaching technique involves assigning the expository material as homework (e.g. requiring students watch a video in advance) and using class time for supplementary work and enrichment activities.
I chose to teach a lesson on the expected value of a random variable. You can download my Expected Value Learning Situation . The first page outlines my plan for the class, and the next pages are student handouts to describe the group challenges.
If you’re following the lesson, you’ll also want to watch the Khan Academy video I reference:
Expected Value: E(X): Expected value of a random variable
Finally, my reflection is below.
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I want to use this journal entry to reflect on my Learning Situation presentation, wherein I flipped the classroom.
From the start, I felt a tension between my dual aims: that of challenging the standard classroom model, and that of fulfilling our collective idea of being a “good” teacher.
I’ll take my starting example as a case in point. There was interesting feedback (from Linda, perhaps?) that students want the formula, and that doing the example on a spreadsheet would be confusing. I agree, in that students who have been socialized to do mathematics in the manner now standard in our classrooms would have been uncomfortable with that manner of doing things. Indeed, even I was uncomfortable – and not just that my Bieber example didn’t gain traction with the class, but with the feeling that what I was doing was somehow not “real teaching”.
I think the presentation after mine exactly demonstrates what I mean by our social notion of “real teaching.” Rebecca had a very organized approach, put notes on the board (that presumably would be copied down by students), explained concepts as “one-who-knows” to “many-who-don’t”, solicited suggestions that she pre-knew the answers to, and at the end handed out a worksheet which recapitulated what students just learned. (For what it’s worth, I thought she did this very well… my implicit critiques below should be read not of her, but our collective cultural ideas of teaching.)
As mentioned above, I wanted to challenge this standard classroom process. I have partially explained the reasoning behind this in previous journal entries, and would love to have a class discussion about it, so will focus here on what I learned from my trial.
I suppose I can break down my aim of challenging the standard classroom model into two parts: first, aiming to break down the traditional socialization of math students as inert receivers of the teacher’s knowledge, and second, aiming to build up a class environment where students fully engage in the learning process to construct their own knowledge.
I feel the initial fact of classroom-flipping did not so much achieve these goals–indeed, I am in some ways replacing the teacher with the video-lecturer in being the source of authoritative math knowledge, but not much else has changed so far. However, using the video did two things: enabled the students to come to class ready to engage in media res rather than at the very start, and enabled me to convert class time I would have felt necessary for the transfer of testable knowledge into time for student engagement.
To use this strategy in the future, I feel I have to achieve a better video-class linking, to enable students to access what they learned in the video in class. I started the class in media res but since I didn’t connect enough to the video, many students were lost until we got well into the group activities. I did miss a few opportunities to connect the two. For example, during the LS, when I asked what the students had learned, one of them (Carole, I think) said “The expected value is the population mean.” I agreed, but in retrospect I missed an opportunity to build off the video’s discussion of the links between those two concepts to help my students make this real for themselves.
Apart from the pragmatic critiques of my group activities (they were way too long for the presentation time, some of the instructions were ambiguous, and they were quite difficult) and the very good point on differentiation, I thought the activities worked fairly well to achieve the second objective of helping students construct their own knowledge. The idea was that if students could connect the abstract idea of expected value to the idea of figuring out which game is better to play, or how to design their own game of chance, then this learning could be made more real for them. The evidence halfway through my presentation was promising: almost all of the class was busy working on the challenges, and the atmosphere in the classroom had shifted dramatically, from a pervasive sense that there was a presentation happening to a sense of real engagement and busyness.
But in some ways I am also critical of my choice of activities. I aimed to challenge the classroom model, but in many ways was still limited by my own conceptions (and the expectations I felt upon me being evaluated in a University course). It was still I as the teacher who chose the activities; it was still I who decided who was working on what, when; it was still I who created worksheets that detailed what questions students must answer. So while I did engage students, I feel like from a broader perspective (such as Friere’s notion of a liberatory pedagogy) I failed to really demonstrate an alternative to traditional classroom practices.
I’m not nearly at the point yet where I have a resolution of the tensions I noted above. I do know, however, that I will continue to challenge myself to go beyond my 16-year ‘invisible apprenticeship’ of teaching in the accepted manner, both at McGill and in my teaching practice. I suspect that each lesson will both raise more questions and make it easier to answer them.