Category Archives: Math

January 24, 2014, 8:03 am

Weekend reading

Here are some items from around the web for your weekend enjoyment.


  • Here’s a great post on Medium by Nik Custodio in which he explains Bitcoin like I’m five. I think the audience level here is rather older than five, but it’s still probably the best explanation of the problems that Bitcoin attempts to solve, and how it solves them, that I’ve seen. (I wasn’t sure whether to file this under “Math” or “Technology” because it’s a lot of both.)


  • If you’ve ever been interested in standards-based grading, you won’t want to miss Kate Owens’ post An Adventure in Standards-Based Calculus where she lays out why, and bits about “how”, she intends to use SBG in her Calculus 2 course this semester. Don’t miss the link to George McNulty’s calc 2 syllabus at the end, which is a great example of how to use SBG in actual practice.
  • Good report…

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December 29, 2013, 1:05 pm

4+1 Interview: Gavin LaRose

glrsign2After a bit of a hiatus, here is the newest installment in this Casting Out Nines’ series of 4+1 Interviews. In these interviews, I’ve tapped various people who are doing interesting work in some combination of math, technology, and education to see what they’re up to and what’s on their minds.

In this interview, I had a chance to catch up with Gavin LaRose. Gavin is affiliated with the Mathematics Department at the University of Michigan. He is officially listed as a Program Manager of Instructional Technology in the Mathematics Department, but his areas of interest and accomplishment are a lot more varied than what that title suggests. He’s been involved with Project NExT and other programs in the MAA and is well known for his work with innovative pedagogy and instruction, especially instruction using technology, at U-M. 

1. At the University of Michigan, you do some…

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December 18, 2013, 1:25 pm

Dijkstra, radical novelty, and the man on the moon

dijkstraOver 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…

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October 7, 2013, 9:19 am

The biggest lesson from the flipped classroom may not be about math

63217989_efcd3b7c6c_mFor 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 …

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September 1, 2013, 1:49 pm

Week 1 of the inverted calculus class: Failure is an option

failWeek 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 …

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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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August 1, 2013, 7:21 am

4+1 interview with Dana Ernst

img06Welcome 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…

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July 23, 2013, 8:00 am

Doubt, proof, and what it means to do mathematics

8426562723_d5b0d9b0ec_nYesterday 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…

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July 8, 2013, 3:17 pm

What’s in a (gender-specific) name?

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 …

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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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