Category Archives: Calculus

August 25, 2013, 2:38 pm

Flipping calculus

56130749_ce37f49f67_mIn 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…

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June 25, 2013, 12:04 pm

What math topic do engineering faculty rate as the most important?

did-an-even-math-problem-by-accident-answer-not-in-back-of-bookI’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…

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June 10, 2013, 3:28 pm

A divide-and-conquer approach to planning a flipped class session

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…

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August 13, 2012, 8:00 am

A free and open-source calculus textbook

Allow me to make a shameless plug for a very cool project currently underway by my GVSU colleague Matt Boelkins. He is writing a free, open-source calculus textbook that will be available in PDF form online for anyone to use and for any instructor to modify. He has already written the differential calculus portion of the textbook — his Winter semester sabbatical project — and he’s about to begin work on the integral calculus portion. You can download the differential calculus parts here. This is at his blog, where he is promoting the book and soliciting feedback. Matt’s also on Twitter.

Matt and I have talked about this project a lot in the last several months, and I’m deeply impressed by his vision for what this resource could become. He sums it up in this blog post:

While on sabbatical during the winter semester of 2012, I began drafting a free, open-source calculus text….

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July 16, 2012, 3:02 pm

What does it mean for kids to be “ready” for math?

USA Today has this op-ed (h/t to Joanne Jacobs) from Patrick Welsh giving thoughts on why kids hate math:

I worry that we’re pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.

We’re asking young kids to move up in mathematics too far, too soon, in other words. Patrick goes on to focus especially on a push in California to get more younger kids taking Algebra and cross-references it with a Duke University study showing negative effects of the same sort of program in North Carolina.

I’m in complete agreement with this op-ed, although thankfully I haven’t felt that push so much with my own kids, ages 3, 6, and 8. There have…

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July 3, 2012, 9:08 am

The trouble with Khan Academy

At some point around the beginning of February 2012, David Coffey — a co-worker of mine in the math department at Grand Valley State University and my faculty mentor during my first year — mentioned something to me in our weekly mentoring meetings. We were talking about screencasting and the flipped classroom concept, and the conversation got around to Khan Academy. Being a screencaster and flipped classroom person myself, we’d talked about making screencasts more pedagogically sound many times in the past.

That particular day, Dave mentioned this idea about projecting a Khan Academy video onto the screen in a classroom and having three of us sit in front of it, offering snarky critiques — but with a serious mathematical and pedagogical focus — in the style of Mystery Science Theater 3000. I told him to sign me up to help, but I got too busy to stay in the loop with it.

It…

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June 29, 2012, 2:23 pm

The summer of BYOD

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…

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June 12, 2012, 7:00 am

Misunderstandings vs. misconceptions

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 …

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June 5, 2012, 8:00 am

Taking time and giving time on assessments

I haven’t given many updates lately about, well, anything, but especially about my Calculus 2 class. Freakishly, we are 2/3 of the way through the course now. First of all let me say that there’s something seriously wrong with having a midterm in a class after three weeks, and then a final exam three weeks later. Students should have more time to dread those things.

I kid, but actually the biggest adjustment I’ve made in the class — and teaching a class that’s as compressed as this one is all about paying close attention to everything that happens and being nimble about making adjustments — has been the testing scheme. I know that I posted earlier about my idea of having in-class assessments that were smaller than the usual test, more frequent, and which leveraged student collaboration and the real-life social network of the class. But after a couple of tries with this, I dropped it…

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May 14, 2012, 7:30 am

Turn to your neighbor… and take a test

Week 1 of the 6-week Calculus 2 course is over, and of course it felt like 2.5 weeks of class because that’s the exchange rate between this course and a normal 14-week course. It was challenging for the students, but I feel like they are on board with what we’re doing. I was especially pleased with the outcome of one of the distinctives of this class: the in-class assessments which are called, er, Assessments.

I said at the outset that the key thing with this class was to force the issue on assimilation of material, and part of that was to engage in early, small, and frequent assessment. For formative assessment, we do daily online homework and clicker questions. There’s no requirement to get clicker questions right at all, and WeBWorK sets have no limits on number of attempts or the amount of collaboration or technology used. For summative assessment, we have a midterm exam and a…

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