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….
December 18, 2012, 4:17 pm
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…
November 7, 2012, 7:00 am
I’m really excited to be working next semester as a co-PI on a National Science Foundation grant with my Grand Valley State colleagues Scott Grissom (Computer Science), Shaily Menon (Chemistry), and Shannon Biros (Chemistry). We’re going to be interviewing a large number of GVSU faculty to try to understand why some of us adopt research-based instructional methods like peer instruction and why others don’t.
As we were putting together the grant proposal earlier this year, one statistic really impressed the importance of this study on me. GVSU is a fairly big place – we have nearly 25,000 students on multiple campuses with both undergraduate and graduate degrees offered. I don’t know how many sections of courses we offer in a given semester, but it’s got to be in the thousands. We have over 40 sections currently running for just College Algebra! And yet: How many sections…
July 18, 2012, 9:44 am
This week I am adding to the playlist of screencasts for the inverted intro-to-proofs class I first mentioned here. There are seven chapters in the textbook we are using and my goal is to complete the screencasts for the first three of those chapters prior to the start of the semester (August 27). Yesterday I added four more videos and I am hoping to make four more tomorrow, which will get us through Chapter 1.
The four new ones focus on conditional (“if-then”) statements. I made this video as the second video in the series as a prelude to proofs, which are coming in Section 1.2 and which will remain the focus of the course throughout. Generally speaking, students coming into this course have had absolutely no exposure to proof in their background with the exception of geometry and maybe trigonometry, in which they hated proofs. Watch a part of this and see if you can figure out my …
July 5, 2012, 4:13 pm
Amid all the shuffle of the #mtt2k phenomenon and my piece on Khan Academy this week — which is well on its way to being the most-read and -retweeted article I’ve ever done — Konstantin Kakaes put up a response to critiques of his Slate piece on educational technology. In it, he addresses both my critique and that of Paul Karafiol. I wanted to give just a few counter-critiques here. I haven’t had a chance to read Paul’s piece, so I’m just going to focus on the part of the response that referenced my post. (Here’s the full post I wrote about the Slate article.)
Let’s go back to the original Slate piece, which said:
Though no well-implemented study has ever found technology to be effective, many poorly designed studies have—and that questionable body of research is influencing decision-makers.
The Slate piece suggests that researcher bias, brought on by having a financial stake in…
June 29, 2012, 2:23 pm
So, the six-week Calculus 2 class is over with — that didn’t take long — and there’s beginning to be enough distance between me and the course that I can begin to evaluate how it all went. Summer classes for me are a time when I like to experiment with things, and I wanted to comment on the outcomes of one experiment I tried this time, which is using a bring-your-own-device setup for clicker questions.
I’ve been using TurningPoint clickers ever since I started doing peer instruction, and I recommend these devices highly. They have a lot going for them in terms of classroom technology: They are small and unobtrusive, relatively cheap ($35), exceedingly simple to use, rely on no pre-existing infrastructure (for example, whether or not you have decent wifi in the room), and are nearly indestructible. They are about as simple, dependable, and inexpensive as a radio-operated garage door…
June 12, 2012, 7:00 am
The first speaker in the Model-Eliciting Activities (MEA’s) session Monday morning said something that I’m still chewing on:
Misunderstanding is easier to correct than misconception.
She was referring to the results of her project, which took the usual framework for MEA’s and added a confidence level response item to student work. So students would work on their project, build their model, and when they were done, give a self-ranking of the confidence they had in their solution. When you found high confidence levels on wrong answers, the speaker noted, you’ve uncovered a deep-seated misconception.
I didn’t have time, but I wanted to ask what she felt the difference was between a misunderstanding and a misconception. My own answer to that question, which seemed to fit what she was saying in the talk, is that a misunderstanding is something like an incorrect interpretation of an idea …
May 8, 2012, 12:52 pm
I blog a lot about peer instruction, but I think this screenshot from this morning’s Calculus 2 class is worth 1000 of my blog posts about just how effective a teaching technique PI can be. It’s from a question about average value of a function. Just before this question was a short lecture about average value in which I derived the formula and did an example with a graph of data (not as geometrically regular as the one you see below). I used Learning Catalytics to set up the question as Numerical, which means that student see the text and the picture on their devices along with a text box in which to enter what they think is the right answer. (I.e. it’s not multiple choice.) Here are the results of two rounds of voting (click to enlarge):
After the first round of voting, there were 12 different numerical answers for 23 students! (Some of these would be the same answer if students …
May 4, 2012, 4:00 pm
Sorry for the boring title and lack of catchy image, but since my first post about the upcoming six-week Calculus 2 course, I’ve expended all my creativity getting the course put together and getting ready for Monday. In the earlier post I laid down some design ground rules for the course. Here, I’m going to say a little more in detail about what we’ll be doing.
It’s especially important on a highly compressed schedule like ours to use the class meetings themselves to jumpstart the assimilation process and then train students on how to carry that process forward as they go to work on the day’s material in the afternoon and evening. This is always an important goal of class meetings in any course — I’d go as far as to say that this is why we have class meetings at all. But when you cram a 14-week course into 6 weeks, it doesn’t take long for one incorrectly-assimilated concept to…
February 27, 2012, 8:00 am
I had the great pleasure this weekend of leading a session at Math In Action, which is Grand Valley’s annual K-12 educators’ conference. My session was called “Classroom Response Systems in Mathematics: Learning math better through voting” and was all about the kinds of learning that can take place in a class where active student choice is central and clickers are mediating the voting. (Here are the slides.)
It always seems like a bait-and-switch when I do a “clicker” workshop, because although people come to learn about clickers, I don’t really have much to say about the technology itself. As devices go, clickers are about as complex as a garage door opener, and in fact they work on the same principle. There’s not a lot to discuss. So instead, we spend our time focusing on the kinds of pedagogy that clickers enable — which tends to excite teachers more than technology does.