July 30, 2013, 8:11 am
Jennifer Morton writes in the Chronicle this morning about the social and behavioral competencies that students in online classes develop – or rather, don’t develop – as compared to their peers in traditional face-to-face courses. She (quite rightly) points out that MOOCs and the like present an opportunity for disadvantaged students to get the proverbial leg up into higher education at a drastically reduced price, and (again, quite rightly) notes that to the extent that traditional education sticks to outmoded lecture-based pedagogy, there’s no reason for disadvantaged students not to turn to MOOCs. Well, no reason except this:
A college education bestows not just cognitive skills—mathematical, historical, and scientific knowledge—but practical skills—social, emotional, and behavioral competencies. Tenacious, confident, and socially competent employees have an edge over…
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 18, 2013, 8:00 am
Welcome to installment #2 in an ongoing series of 4+1 Interviews with interesting people in math, technology, and education. Our first interview in this series, with Vanderbilt University Center for Teaching Director Derek Bruff, is here. I have several more in process now, and I’ll be posting these about twice a month.
Today’s interview is with Diette Ward. Diette is an Electronic Resources and Instructional Librarian at Lee University in Cleveland, Tennessee. I met Diette during my week at the Appalachian College Association’s Teaching and Learning Institute, where I was a plenary speaker and led some workshops on the inverted classroom. Diette was one of a group of “embedded librarians” who partnered with the workshop track leaders to provide support and insight on how libraries can support instruction. I was really impressed by the intelligence and enthusiasm that these …
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 13, 2013, 8:00 am
Have you ever tried out a new instructional method or course design – like peer instruction or the inverted classroom – and had not just a few students become discontent but entire groups of students who band together to push back? Or even put together a Facebook group to protest? It’s not pretty. Following last week’s Teaching and Learning Institute, where I talked with several college profs about this and other potential pitfalls of the flipped classroom, I happened to catch this answer on Quora to the question, How does a company handle an anti-marketing campaign like Dump Dropbox? and it seemed to me there are a lot of potential applications of this problem to the problem of mass student pushback.
To begin, the answer’s author says:
1. In public, ignore it.
2. Quietly shore up your messaging on any points where they landed a good punch.
Don’t bring up 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…
May 7, 2013, 7:33 pm
I lost a bet with my friend and colleague Dave Coffey (remember him?) over the NCAA mens’ basketball tournament, and as a result, I owed Dave a guest post on his blog DeltaScape. Risky move on his part, in my opinion, since his blog is a consistently excellent source of wisdom about math education and teacher training. I hope I didn’t mess it up too much — my guest post, entitled “Does this make sense?” is about so-called sense-making activities and what they mean for math instruction. It can be found here. Enjoy!
May 6, 2013, 8:00 am
Let’s go back to the research paper on screencasting that I first blogged about here. In that post, we saw that students on the study generally watched the screencasts, even without explicit rewards like grades, and the tended to do so strategically. But what about student learning? Did it help?
To answer that question, we have to go back to a previous paper by the authors [PDF]. (That one is in the queue this week to read and blog about.) In that paper, the authors did find a positive correlation between screencast use (which they tracked using stats for the class’ course management system) and overall performance. But – this correlation does not imply causation, and indeed when the data are sliced along various demographic lines, sometimes the students’ performance was better explained by GPA than by screencast use.
I haven’t gotten into that second paper yet, but what …
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…