The flipped transition-to-proof class is now finishing up its sixth week. It’s hard to believe we are nearing the midpoint of the semester. The management of the class is still something of a work in progress, and I hope to have more posts up soon about how the class logistics have evolved since August. But one thing for which I am really grateful, and which I frankly find surprising, is that nobody in the class has yet to express any kind of longing for the good old days when professors lectured and students sat there and listened. In fact most students who express anything at all say that having the lectures on video, in addition to having a well-written textbook for reference, is hugely beneficial for their work in the class.
Recently. when I’ve asked students what we could do differently in the class that would help their learning, two items have shown up multiple times (and these are paraphrased):
- Show us more examples.
- Go over proofs more in class.
This is no surprise -- I get variations on this in every class I can remember for the last few years, even when in some cases I am spending the entire class presenting worked-out problems to the class on the whiteboard. In those cases, these requests are tantamount to saying, “Please make the class last 100 minutes instead of 50.” In fact a couple of students in the proofs class asked for this!
These aren’t bad requests as such. But there’s a danger here in how you go about providing a response. One way I could handle a request for “going over” more things is to do some surgery on the class sessions and carve out time for me to present worked examples or proofs. This is the default response for most of us coming out of the un-flipped model of teaching. It’s also the default expectation for students coming out of that model. If I lecture some more on the topics that students want to see, there is objective evidence that I have given students what they want, and so I can say with confidence that I’ve done what I’ve been asked to do. And in the process, perhaps I could even add some value by providing my own perspective on those examples or focusing on the decision-making processes that expert learners undergo when solving a problem.
But as I said, there’s a danger too: By “going over” things in lecture mode, I am making students more dependent on me for their learning than they used to be. This is basic psychology. If a student learns that he can get an example or solution provided to him simply by asking the professor, which is easier than working out those things by himself, what do you expect a student to do? What’s bad about this is that two abilities that are crucial to being an educated person --- the ability to initiate self-help when it’s clear there’s a need to help oneself, and the ability to find and make sense of existing data that pertain to a problem you have --- are bypassed in favor of a quick fix that, more often than not, leaves the student with merely the illusion of having learned something.
So instead, I’m taking the approach of showing students how to find examples and how to evaluate their own work, and giving them opportunities to study worked examples and compare their writing to existing writing, rather than “going over” things and simply lecturing more. And I want to make sure that I am explaining to students why I’m not simply going up to the board to lecture. They’re definitely smart enough to get that.
I’m believing more and more that helping people become become independent learners, capable of managing and directing their intellectual growth over their entire lifespans, is the fundamental goal on which higher education --- maybe all of education --- needs to focus. Developing that independence is something that really ought to start when people are toddlers, continue through the K-12 years, and then universities could serve as a kind of finishing school for intellectual independence. We’re definitely not there yet. But we in higher ed should certain take every opportunity to build independence, and break dependence, even in everyday situations like these.