March 11, 2013, 8:00 am
It’s been a while since I last wrote about the recently-completed inverted transition-to-proof course. In the last post, I wrote about some of the instructional design challenges inherent in that course. Here I want to write about the design itself and how I tried to address those challenges.
To review, the challenges in designing this course include:
- An incredibly diverse set of instructional objectives, including mastery of a wide variety new mathematical content, improvement in student writing skills, and metacognitive objectives for success in subsequent proof-based courses.
- The cultural shock encountered by many students when moving from a procedure-oriented approach to mathematics (Calculus) to a conceptual approach (proofs).
- The need for strong mathematical rigor, so as to prepare students well for 300-level proof based courses, balanced with a concern for student…
March 8, 2013, 4:30 pm
I’ve been talking a lot with my colleagues about their teaching practices, as part of the NSF grant I’m working on. The inverted classroom (I used to call it the flipped classroom, but I’m going back to “inverted”) has come up a lot as a teaching technique that people have heard a lot about but haven’t tried yet — or are wary of trying. I’ve been wondering about the language being used, namely: Is the inverted classroom really a “teaching technique” at all?
My answer used to be “yes”. When I first started using the inverted classroom idea, I would describe the inverted classroom as “a teaching technique” that involves reversing where information transmission and internalization take place. Later I moved to saying that the inverted classroom refers to “any teaching method” that implements this reversal. Today as I was thinking about this, I think a…
February 14, 2013, 7:45 am
One of the projects I was taking on with my teaching this semester was a revamped linear algebra course built around peer instruction and the use of Learning Catalytics, a web-based classroom response platform. I probably owe you a quick update now that it’s nearly mid-semester (what?).
Linear algebra is a strange course in some ways. There are a lot of mechanical skills one has to learn, like multiplying matrices and performing the Row Reduction Algorithm. If you come into linear algebra straight out of calculus with a purely instrumental viewpoint on mathematics, you will almost certainly think that these mechanical skills are the point of linear algebra. But you’d be wrong! It’s the conceptual content of the subject that really matters. Like I tell my students, you can answer almost any question in linear algebra by forming a matrix and getting it to reduced row echelon form….
January 28, 2013, 7:45 am
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…
January 22, 2013, 8:00 am
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…
October 11, 2012, 9:52 pm
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: …
October 3, 2012, 8:46 am
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…
August 29, 2012, 9:16 pm
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…
August 14, 2012, 8:00 am
I’ve been sort of quiet on the inverted transition-to-proof course (MTH 210, Communicating in Mathematics) lately, partly due to MathFest and partly because I am having to actually prep said course for startup on August 27. It’s almost ready for launch, and I wanted to share a document that I’m going to hand out to students on opening day and discuss. It’s called “How MTH 210 Works”. I’m fairly proud of this document because I think it says, in clear terms, what I want students to know not only about this class but for inverted classrooms generally.
I’ve written before that the inverted or “flipped” classroom approach always tends to engender a lot of uncertainty and sometimes strongly negative responses. With this document, I am hoping to pre-empt a lot of those feelings by stressing what this is all about: Being realistic about their education in the present day for the things that…
July 23, 2012, 10:36 pm
Marshall Thompson writes in this blog post from a couple of weeks ago that he’s concerned over the tone of the recent and ongoing Khan Academy/#mtt2k debate and is worried about the cost it incurs. It’s a good post, and in the process of commenting on it I realized a few things. Marshall writes:
I get the impression that KA has a goal of pedagogical soundness. Is this the best way to help them achieve that goal?
Sal Khan is not a dummy. He is clearly working through some of the same pedagogical misconceptions we all worked through (and continue to work through). How can we best help him through his personal journey without alienating him or causing him to be defensive?
I have tremendous respect for Sal Khan, but I have to admit that I’m not really concerned about his personal journey or his working through pedagogical misconceptions. It would be fantastic if he began…