August 25, 2013, 2:38 pm
In the last post, I said I might be taking a couple of weeks off, and I ended up taking three. Well, the week before classes start is basically a blackout period during which nothing gets done except course preps, so that’s why.
Yes, it all starts back up again here this week. This semester is going to be fuller than usual for a lot of reasons, three primary: First, I’m up for contract renewal in January, meaning that I am approaching the “midterm exam” at the halfway point toward tenure, which requires the usual aggregation of evidence demonstrating that I’m making satisfactory progress. Second, I’m teaching my first upper-level course since arriving at GVSU, one section of our Modern Algebra course, which I have not taught in a few years and I am anxious to get into it. I’m also trying out a new platform for classroom response systems in that course and I will tell you…
August 1, 2013, 7:21 am
Welcome to the third installment of the 4+1 Interview series. Today’s interview features Dana Ernst. Dana is a professor in the mathematics department at Northern Arizona University, a champion of Inquiry-Based Learning in mathematics, and an active writer about math and math education. I’ve known Dana for a couple of years, and he never fails to impress me with his clear-headed, positive-minded, student-centered approach to his work. His mountain biking exploits also inspire me to get up and exercise sometimes.
Enjoy the interview and make sure to catch Dana’s writing at his personal blog, the new Math Ed Matters blog (see below for more), on Twitter, and on Google+. If you missed the first two installments, you can click here for Derek Bruff’s interview and here for my interview with Diette Ward.
1. You’re well-known as a vigorous proponent of Inquiry-Based Learning. Tell us…
July 23, 2013, 8:00 am
Yesterday I was doing some literature review for an article I’m writing about my inverted transition-to-proof class, and I got around to reading a paper by Guershon Harel and Larry Sowder¹ about student conceptions of proof. Early in the paper, the authors wrote the following passage about mathematical proof to set up their main research questions. This totally stopped me in my tracks, for reasons I’ll explain below. All emphases are in the original.
An observation can be conceived of by the individual as either a conjecture or as a fact.
A conjecture is an observation made by a person who has doubts about its truth. A person’s observation ceases to be a conjecture and becomes a fact in her or his view once the person becomes certain of its truth.
This is the basis for our definition of the process of proving:
By “proving” we mean the process employed by an…
July 8, 2013, 3:17 pm
Here’s an interesting study (paywall) by a team of psychologists from the University of Wisconsin-Whitewater and the University of British Columbia that speaks to just how strong is the link between our personal identity and the way we perform on academic tests, especially mathematics tests. In the study, a group of 110 female and 72 male undergraduates were given a 30-question multiple choice math test. At the beginning of the test, all participants were told that men usually outperform women on math performance. (Never mind whether this is true for the moment.) Then, one group of participants completed the test using their own names on the test papers, while another group used one of four fake names – two of which were male names and the other two females.
The males who took the test did equally well regardless of whether they used an alias or not – even if they used a female …
June 25, 2013, 12:04 pm
I’m at the American Society for Engineering Education Annual Conference right now through Thursday, not presenting this time but keeping the plates spinning as Mathematics Division program chair. This morning’s technical session featured a very interesting talk from Kathy Harper of the Ohio State University. Kathy’s talk, “First Steps in Strengthening the Connections Between Mathematics and Engineering”, was representative of all the talks in this session, but hers focused on a particular set of interesting data: What engineering faculty perceive as the most important mathematics topics for their areas, and the level of competence at which they perceive students to be functioning in those topics.
In Kathy’s study, 77 engineering faculty at OSU responded to a survey that asked them to rate the importance of various mathematical topics on a 5-point scale, with 5 being the…
June 10, 2013, 3:28 pm
I’m returning to the blog after an hiatus brought on by two things: the six-week calculus class I am finishing up right now, and my participation in the Appalachian College Association’s Teaching and Learning Institute at Ferrum College in Virginia last week. The latter was a week-long engagement during which I gave an opening night after-dinner speech, a two-hour plenary talk, and three iterations of an inverted classroom workshop for participants. Between keeping up with the calculus class and prepping for and then attending the TLI, I’ve had no time for anything else. But coming off the TLI, I’ve got a fresh appreciation for the importance of blogging in my professional life. So, back into the habit.
I learned at the TLI that there are a lot of faculty who are interested in the inverted/flipped classroom. Interested — but not yet engaged in doing it, for a variety of…
May 8, 2013, 8:00 am
I was really fortunate this past weekend to host Dana Ernst and T.J. Hitchman, two colleagues (from Northern Arizona University and University of Northern Iowa, respectively) at the Michigan MAA section meeting. They did a discussion panel on Teaching to Improve Student Learning that I organized, and we ended talking a lot about inquiry-based learning, which both of these guys practice. After Dana blogged about the session, he got this tweet:
Dana, Brandon, and I exchanged some tweets after that, and I think generally we’re on the same page, but here’s my reasoning about this question and, more generally, what does or does not fall under the heading of “flipped classroom”.
The main thing to keep in mind is the distinction between an instructional practice and a course design principle. This was the gist of my post a…
April 25, 2013, 2:39 pm
The semester just ended, and I’m now in full retrospect mode. This semester I was fortunate to have only one prep — two sections of Linear Algebra. Linear algebra, for me, is the cornerstone of a modern mathematics education precisely because its concepts and its mechanics lie at the heart of so much real-world stuff — from web search algorithms to scheduling problems to computer graphics and many other areas. And yet, in a typical one-semester course on linear algebra you only get to touch on a handful of applications, and those tend to be sort of domesticated. A few years ago, I decided I wanted students to explore more than just the stock examples in the textbook, and I wanted them to do so in an authentic way that reflects real-world mathematical practice.
About that time, Derek Bruff published this blog post about his use of Application Projects, and I gleefully…
April 4, 2013, 4:48 pm
Screencasting is an integral part of the inverted classroom movement, and you can find screencasting even among courses that aren’t truly flipped. Using cheap, accessible tools for making and sharing video to clear out time for more student-active work during class make screencasting very appealing. But does it work? Do screencasts actually help students learn?
We have lots of anecdotal evidence that suggests it does, but it turns out there are actually data as well that point in this direction. I’ve been reading an article by Katie Green, Tershia Pinder-Grover, and Joanna Mirecki Millunchick (of Michigan State University and the University of Michigan) from the October 2012 issue of the Journal of Engineering Education in which they studied 262 students enrolled in an engineering survey course that was augmented with screencasts. Here’s the PDF. This paper is full of interesting…
March 27, 2013, 8:00 am
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