December 18, 2013, 1:25 pm
Over three years ago, I wrote a post to try to address a fallacy that is used to refute the idea of novel ways of teaching mathematics and science. That fallacy basically says that mathematics and the way people learn it have not fundamentally changed in hundreds if not thousands of years, and therefore the methods of teaching that have “worked” up to this point in history don’t need changing. Or more colloquially, “We were able to put a man on the moon with the way we’ve taught math for hundreds of years, so we shouldn’t change it now.” I sometimes refer to this as the “man on the moon” fallacy because of that second interpretation.
To understand why I think this is a fallacy, read the post above – or better yet, read this long quote from a 1988 paper by Edsger Dijkstra, one of the great scientific minds of the last 100 years and one of the authors of modern…
October 7, 2013, 9:19 am
For the last six weeks, my colleague Marcia Frobish and I have been involved in an audacious project – to “flip” our freshman Calculus 1 class at Grand Valley State University. I started blogging about this a while back and it’s been quiet around the blog since then, mainly because I’ve been pretty busy actually, you know, planning and teaching and managing the actual course. When I say “audacious project” to describe all this, I’m not engaging in hyperbole. It’s definitely a project – there are screencasts to make, activities to write, instruction to differentiate and so on. And it’s definitely audacious because at the core of this project is a goal of nothing less than a complete reinvention of freshman calculus at the university level. So, no pressure.
What’s surprised me the most about this project so far is one thing in particular I’ve learned about the …
September 1, 2013, 1:49 pm
Week 1 of the new semester is in the books, and with it the first week of the inverted calculus class. I am teaching two sections of this class, one that meets Monday/Wednesday/Friday and the other Tuesday/Thursday. It makes for tricky scheduling, but as I learned this week it also gives an opportunity for second chances, which is important if you don’t always get the in-class portion of the flipped classroom right.
People always seem to focus on the out-of-class experience when they talk about the inverted classroom. How much time does it take to make the videos? How do I make sure my students do the Guided Practice? But that’s not the hard part, nor is it the part where most of the learning takes place. The in-class experience for students is what makes the inverted classroom more than just a lab or a seminar course, and as the instructor, it’s both hard and crucial to get it …
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 6, 2013, 3:02 pm
This will be my last post for a couple of weeks, since my family is headed out of town on vacation to Tennessee and I am determined to unplug for a few days. On the way back, I’ll be stopping in Columbia, Kentucky to give a day-long workshop on the inverted/flipped classroom for the faculty at Lindsey Wilson College. True to the form of the inverted classroom, I’ve given the faculty a homework assignment to finish before the workshop that includes watching two videos (here and here) and reading two documents (here and here) and then answering some questions. I plan on using their responses to the questions to fill in the details of the framework for the workshop that I am putting into place.
I’m happy to say that the faculty are doing their homework. One of the themes from their responses is something I’ve seen quite often before and it’s something that I want to address, an…
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 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 …
July 11, 2013, 8:00 am
It’s my pleasure to introduce a new series here at Casting Out Nines called 4+1 Interviews. In each of these interviews, I’ve picked out someone who I believe has something interesting to say about mathematics, education, or technology and given them four questions to ask. And at the end, the interviewee gets to pick his or her own question to answer, hence the +1. One of my favorite things about my job and about blogging and Tweeting is that I come into contact with a lot of really smart people very frequently, and I thought it would be nice to share these folks with you. I’m hoping to post about one of these every 2-4 weeks, and the lineup of upcoming interviews is very exciting.
Our first interview in this series is with Derek Bruff. Derek is the Director for Vanderbilt University’s Center for Teaching and the author of Teaching with Classroom Response Systems: Creating…