In my series of posts on the flipped intro-to-proofs course, I’ve described the ins and outs of the design challenges of the course and how the course was run to address those challenges and the learning objectives. There’s really only one thing left to describe: How the course actually played out through the semester, and especially how the students responded.
I wasn’t sure how students in the course would respond to the inverted classroom structure. On the one hand, by setting the course up so that students were getting time and support on the hardest tasks in the course and optimizing the cognitive load outside of class, this was going to make a problematic course very doable for students. On the other hand, students might be so wed to the traditional classroom setup that no amount of logic was going to prevail, and it would end up like my inverted MATLAB class did where a small but extremely vocal minority simply refused to try anything that wasn’t lecture.
It turns out that I had nothing to worry about — most students, if not all, were really on board with the inverted classroom from the beginning and could really see the value in doing class this way. I don’t know if that’s just being lucky to have a group of students willing to go out on a limb, or if it’s being effective in my 24–7 marketing campaign for my instructional design. Probably some linear combination of those. I found that if I put it in terms of the benefits that students get out of the inverted classroom, it took very little effort to obtain buy-in. Occasionally when there was some griping about doing the lectures outside of class, I would suggest that we could always switch it back, to where we had lecture and examples in class, and then they have not only some reading to do outside of class but also the Proof Portfolio and Homework sets — and the inverted classroom would look a lot better all of a sudden.
Maybe it’s best to let the student speak for themselves. Here are a few of the remarks from the course evaluations:
He would never just give an answer when a student asked a question. Instead, he would in return ask a series of questions that led the student to the answer on their own. Also, he used the inclass quiz data to modify the class material for that day as needed.
Notice that the first sentence is actually intended as a compliment. I consider that a major win in its own right because usually this is intended as a negative.
He was very effective in helping explain things in a clear and meaningful way. The screencast lectures online were very helpful to my understanding of the subject. He gave very specific and direct feedback on portfolio drafts and graded in a timely mannor [sic].
Note that the inverted classroom gives the best of both worlds according to this comment. Students get as many explanations and examples as they want because the screencasts remove the 50-minute time limit on lecturing; and the freed-up time in class allows me to give directed and personalized feedback.
[I]f this was reddit, everything would get an upvote. The videos were universally effective, the quizzes covered (sp?) over topics. Fast grading, fair exams. This class could not be taught any better.
I only included this because I love the Reddit comparison. Two more positive comments:
The “flipped class” structure is very effective in helping me learn. I would do a lot better if all math courses were taught this way.
I really benefited from the flipped teaching method. It was good for me to learn the material outside of class and then apply what I learned in class.
I would say that most of the comments from the two sections I taught tended in this direction, so I’m really pleased that most students had an excellent experience with the way we did the course and really “got” what we were doing.
But it wasn’t all sunshine and roses, of course:
The “in class” group work portion disadvantages some students. As we walk through proofs together there is on course a rush to finish it all in class. A few students (sp)? that are a bit quicker go through it all and the other students are left not understanding the process. I feel terrible when it happens, but I can’t accept sacrificing my time to always continually aid another. I think after the in class work strategies the strong and does little for the weak. A little more structure in the work perhaps not not writing a full proof, or observing.
This is a really good negative comment. It’s a fair point: One of the hardest things to deal with is the disparity in student abilities in the group work. The way I changed the in-class workflow to allow groups to finish up outside of class over the period of a few days was intended to combat this, but I could have done a better job with it all. One way to handle the disparity is to assign groups based on observed performance rather than let groups self-select — put the underperforming students together, or put a strong student with strong exposition skills with a group of at-risk students — but this comes with its own set of problems. I confess I’m still figuring this out.
Didn’t like the teach yourself do homework in class style. If I want to pay for a class in which I teach myself I might as well take an online class and save money. The professor basically got paid to supervise homework time. Would’ve learned the same amount if another student was there instead of the professor.
I’ve mentioned before that actually it’s the traditional classroom design that makes students learn things on their own, not the inverted classroom, but if students are coming from the background that all mathematics is procedure, then this is a really hard conception to change. This and the “I pay for you to teach” mentality. (Which technically they do, since we are a public institution, but the issue here is what the student thinks “teaching” and “learning” mean. )
Could be more willing to help students, I sometimes felt lost, and felt like no one could help me, especially the teacher. Also, I would prefer learning things in class, not through screencasts. I felt like he just watched the class, no many group discussions.
Both of the above comments are fairly common among students in any active learning environment and especially in one where students use class time primarily to work — “The teacher isn’t teaching, he’s just walking around!” This semester in linear algebra where portions of the course I have structured in an inverted environment, I’ve been careful to tell students exactly what I am doing while they work: I am actively observing, making notes in my head about student work, making sure everyone is getting the first portions of the group work done correctly, intervening when necessary, and being available for questions at all times. Students may not realize it, but after an inverted classroom session, I am exhausted! It’s like coaching ten different basketball teams all playing at the same time. But on the surface it looks like I’m just standing or walking around because I’m trying to project an aura of calm and relaxation to keep things loose in the classroom. Maybe I should act more frenetic or something.
Anyway, that’s almost the end of this series of posts on the flipped proofs class. There’s just one more post to write, but I can’t write it yet, and it’s about the data I collected on learning strategies among the students in the class. A colleague and I are going to comb through that data soon, and we’ll report back. What I’m thinking I will see are some significant gains in student self-rating on a bunch of the MSLQ items that correspond to self-regulated learning — at least among the students who passed the course. But we will see.
Thanks for following this series of posts! There will be more on the inverted classroom, as always. In the meanwhile, I’d love to hear your comments.