Category Archives: Math

January 28, 2013, 7:45 am

Inside the inverted proofs class: Design challenges

This is the second post in a series on the nuts and bolts behind the inverted transition-to-proofs course. The first post addressed the reasons why I decided to turn the course from quasi-inverted to fully inverted. Over the next two posts, I’m going to get into the design of the course and some of the principles I kept in mind both before and during the semester to help make the course work. Here I want to talk about some of the design challenges we face when thinking about MTH 210.

As with most courses, I wanted to begin with the end in mind. Before the semester begins, when I think about how the semester will end, the basic questions for me are: What do I want students to be able to do, and how should they be doing it?

This course has a fairly well defined, standard set of objectives, all centered around using logic and writing mathematical proofs. I made up this list that has…

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January 22, 2013, 8:00 am

Inside the inverted proofs class: Why I did it

It’s been a month or so now that the inverted transition-to-proofs class drew to a close. A lot of people, both here at my institution and online, have been asking questions about the design and day-to-day operations of the course, especially if they have ideas of their own and want to compare notes. So starting with this post, I’m going to publish a series of posts that describe exactly how this course was designed and managed throughout the semester. I’m not sure how many of these posts there will be. But the idea is to pull everything together so that people who want to try this sort of thing themselves will have a detailed accounting of what I did, what worked, what didn’t, and how it all went.

Some background on the course (MTH 210: Communicating in Mathematics) is in this post. The short version is that MTH 210 is a course on reading and writing proofs. It’s a…

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December 21, 2012, 8:00 am

We need to produce learners, not just students

Paul Pintrich was the creator of the Motivated Strategies for Learning Questionnaire, which I used as the main instrument for collecting data for the study on students in the flipped transition-to-proof course this past semester. Now that the data are in, I’ve been going back and reading some of Pintrich’s original papers on the MSLQ and its theoretical framework. What Pintrich has to say about student learning goes right to the heart of why I chose to experiment with the flipped classroom, and indeed I think he really speaks to the purpose of higher education in general.

For me, the main purpose of higher education is to train students on how to be learners — people who take initiative for learning things, who are skilled in learning new things, and who above all want to learn new things. My goal as an instructor is to make sure that every student in my class makes some form of…

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December 18, 2012, 4:17 pm

Doing linear algebra with peer instruction and Learning Catalytics

I’m excited and happy to be teaching linear algebra again next semester. Linear algebra has it all — there’s computation that you can do by hand if you like that sort of thing, but also a strong incentive to use computers regularly and prominently. (How big is an incidence matrix that represents, say, Facebook?) There’s theory that motivates the computation. There’s computation that uncovers the theory. There’s something for everybody, and in the words of one of my colleagues, if you don’t like linear algebra then you probably shouldn’t study math at all.

Linear algebra is also an excellent place to use Peer Instruction, possibly moreso than any other sophomore-level mathematics course. Linear algebra is loaded with big ideas that all connect around a central question (whether or not a matrix is invertible). The computation is not the hard part of linear algebra — it…

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December 4, 2012, 4:23 pm

Three things I learned through teaching a flipped class

Right after my last post — nearly a month ago — I began to ask myself, Why is it taking so much effort to blog? The answer was readily apparent by looking at my OmniFocus inbox, which was filled with orange-colored “Due Tomorrow” tasks having to do with making screencasts for the flipped transition-to-proofs course. I realized that I could have any two of my sanity, screencasts completed in time to deploy to the class, or regularly-appearing blog posts. I resigned myself to the fact that this semester I was screencasting instead of blogging. But now — it hardly seems possible — the screencasting is done and we’re moving toward exams next week. So it’s time to release the pent-up blog posts.

I have a lot to say about my experience going full-on flipped classroom with the proofs course. I regret that I couldn’t give more of a day-by-day accounting of how the class has …

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November 9, 2012, 7:00 am

The social element of learning about effective teaching strategies

Speaking of faculty adopting research-based instructional strategies, Theron Hitchman (who blogs at Circles and Tangents) wonders aloud in the direction of math education researchers: Why didn’t you tell me? That is, referring to research-based instructional strategies that seem to work really well with students,

Why do I stumble on these things only to find that they have been understood for decades? Why didn’t someone knock on my door and tell me I was doing it wrong?

My basic point is this: If you do research on teaching and learning, you owe it to society to share what you know. Scholarly publication doesn’t count. The mathematics education community talking to itself is a necessary condition for sorting out the truth of things, but it is insufficient for educating the public and for changing practice on a large scale.

If you know that the standard lecture-homework-exam …

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October 11, 2012, 9:52 pm

What kind of student preparation should we care about?

Whenever I talk or write about the flipped classroom, one of the top two questions I get is: How do you make sure students are doing the reading (and screencast viewing) before class? (The other is, How much work is it to do all those videos?) Everybody seems to have this question, even if they don’t ask it. It seems like an important question. And yet increasingly I think it’s the wrong one.

In my flipped transition-to-proof class, we meet three times a week for 50 minutes each. In between classes, students have roughly 6–10 pages of reading to do in their textbook and around 30 minutes of videos to watch. This is not a huge amount of work to do, but it’s substantial, and the way the class meetings are set up — 10 minutes of quizzing and Q&A, and then launch into a proof-writing problem done in groups — if they don’t prepare, they’re toast.

But here’s the thing:

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October 3, 2012, 8:46 am

Declaring independence

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…

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September 10, 2012, 3:13 pm

How do student attitudes toward learning change in a flipped classroom?

Sorry for the absence, but things have been busy around here as we step fully into the new semester. The big experiment this term is with my flipped introduction to proofs class. As I wrote last time, I was pretty nervous going into the semester about the course. But things seem to be working really well so far. I don’t want to jinx the experience by saying so, but so far, nobody in either of my two sections of the course has given any indication that the flipped model isn’t working for them. In fact, I gave a survey in the first week of class that included an item soliticing their concerns or questions about the flipped model, and here’s a sample of the responses:

  • I think the “flipped” structure will be better for a lot of the students and end with success from more students than normal.
  • I think this sounds really great. The idea of actually working on problems in class …

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August 29, 2012, 9:16 pm

And so the flipping begins

The semester for us has gotten underway, and with it the flipped-classroom introduction to proofs class. This class has gotten a lot of interest from folks both at my institution and abroad. In the opening remarks at our annual teaching and learning conference, our university president gave some love to the flipped classroom model — and correctly pointed out that he’d been using it in his chemistry classrooms for 35 years. Indeed, there’s nothing inherently new about the flipped classroom — the name and the technology we sometimes use are new, I suppose — and yet this idea seems to be getting increasing amounts of interest, more than you’d expect from a mere educational fad.

I have to admit that prior to the semester starting, and after I had made the above blog post publicly commiting myself to running the proofs class this way, I had several bouts of cold feet. The first…

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