Category Archives: Technology

February 14, 2013, 7:45 am

Update on the peer-instruction based linear algebra class

One of the projects I was taking on with my teaching this semester was a revamped linear algebra course built around peer instruction and the use of Learning Catalytics, a web-based classroom response platform. I probably owe you a quick update now that it’s nearly mid-semester (what?).

Linear algebra is a strange course in some ways. There are a lot of mechanical skills one has to learn, like multiplying matrices and performing the Row Reduction Algorithm. If you come into linear algebra straight out of calculus with a purely instrumental viewpoint on mathematics, you will almost certainly think that these mechanical skills are the point of linear algebra. But you’d be wrong! It’s the conceptual content of the subject that really matters. Like I tell my students, you can answer almost any question in linear algebra by forming a matrix and getting it to reduced row echelon form….

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February 11, 2013, 7:45 am

Does Khan Academy help learners? A proposal

Last week’s flare-up over Khan Academy was interesting on a number of levels, one of which is that we got a new look at some of the arguments used in KA’s favor. Perhaps one of the most prominent defenses against KA criticism is: Khan Academy is free and really helps a lot of people. You can’t argue with the “free” part. On the other hand, the part about “helping” is potentially a very strong argument in KA’s favor —but there are two big problems with the way in which this is being presented by KA people.

First, the evidence is almost entirely anecdotal. Look through the Pacific Research Institute whitepaper, for example, and the evidence presented in KA’s favor is anecdotes upon anecdotes — possibly compelling, but isolated and therefore no more convincing than the critics. The reason that anecdotes are not convincing is because for every anecdote that…

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February 5, 2013, 7:45 am

Khan Academy Redux

The last thing I expected to encounter this week was a resurgence in the Khan Academy Debates of this past summer. Those, if you remember, centered around this spoof video created by my GVSU colleagues John Golden and Dave Coffey. My own contribution to those debates remains the single most viewed post I’ve ever published in nearly ten years of blogging. But honestly, I hadn’t thought much about Khan Academy since then — until Monday afternoon.

Dave (Coffey) sent me a tweet alerting me to this whitepaper published by the Pacific Research Institute, a free-market think tank based in San Francisco. “Look at page 14,” Dave said. I did, and found that I was being used as a prime example of a Khan Skeptic. Actually I am the last in a list of skeptics whose skepticism the authors attempt to dispatch. I’m in good company, as Keith Devlin is the first on that list and Veritasium…

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January 15, 2013, 9:10 pm

Lessons learned from wrestling with a MOOC

I’m currently taking a MOOC called Computing for Data Analysis through Coursera. Ths is my fourth MOOC (the sixth one, if you count the two that I started and then dropped). It’s an introduction to the open-source statistical computing environment known as “R”. I got interested in R after learning about this modeling-based Calculus project that uses the statistical and plotting capabilities of R as well as some special symbolic packages as the centerpiece of introductory calculus. I’m leading a taskforce in my department to draft a plan for technology use in the Calculus sequence, and while I don’t think we’ll be using R, I like very much the spirit behind this calculus project, which puts programming at the heart of learning the subject and uses an open-source platform. Plus, I thought R might come in handy for analyzing my own data, and anyway, it’s free, and the course…

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December 18, 2012, 4:17 pm

Doing linear algebra with peer instruction and Learning Catalytics

I’m excited and happy to be teaching linear algebra again next semester. Linear algebra has it all — there’s computation that you can do by hand if you like that sort of thing, but also a strong incentive to use computers regularly and prominently. (How big is an incidence matrix that represents, say, Facebook?) There’s theory that motivates the computation. There’s computation that uncovers the theory. There’s something for everybody, and in the words of one of my colleagues, if you don’t like linear algebra then you probably shouldn’t study math at all.

Linear algebra is also an excellent place to use Peer Instruction, possibly moreso than any other sophomore-level mathematics course. Linear algebra is loaded with big ideas that all connect around a central question (whether or not a matrix is invertible). The computation is not the hard part of linear algebra — it…

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November 7, 2012, 7:00 am

Adopting new instructional strategies: Going with the gut

I’m really excited to be working next semester as a co-PI on a National Science Foundation grant with my Grand Valley State colleagues Scott Grissom (Computer Science), Shaily Menon (Chemistry), and Shannon Biros (Chemistry). We’re going to be interviewing a large number of GVSU faculty to try to understand why some of us adopt research-based instructional methods like peer instruction and why others don’t.

As we were putting together the grant proposal earlier this year, one statistic really impressed the importance of this study on me. GVSU is a fairly big place – we have nearly 25,000 students on multiple campuses with both undergraduate and graduate degrees offered. I don’t know how many sections of courses we offer in a given semester, but it’s got to be in the thousands. We have over 40 sections currently running for just College Algebra! And yet: How many sections…

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October 17, 2012, 7:21 am

MOOCs in Minnesota

I just completed my second MOOC, the “Securing Digital Democracy” course from Coursera. Emboldened by actually completing it with a passing grade I’ve jumped into another Coursera offering, this time “Introduction to Interactive Python“. My colleague John Golden and I are both taking it, and yesterday John tweeted:

Which got this attention-getting reply from Bret Benesh:

Further down the conversation, Bret pointed to this quote in the Coursera terms of service:

Notice for Minnesota Users

Coursera has been informed by the Minnesota Office of Higher Education that under Minnesota Statutes (136A.61 to 136A.71), a university cannot offer online courses to Minnesota residents unless the university has received authorization from the State of Minnesota to do so. If…

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July 30, 2012, 8:00 am

Finding your next job: Three things to do before starting

We’re continuing a series on Finding Your Next Job. In the first post, we stressed the importance of identifying your motivations and coming to terms with the why behind the search. Now we need to think about getting started. Hitting the EIMS website and beginning to compose cover letters is not the start of the job search in my opinion. That comes next. But first there are a few more things to do. Three things, in fact.

1. Determine who the stakeholders are in this upcoming search. This would be any person, other than your current colleagues, whose daily life will be altered by your move to the next job. This is a different and much smaller list than that of the people who careabout your search — hopefully there are a lot of those kinds of people, but it’s likely you have few true stakeholders. The last time I was on the market, in 2010, I identified five stakeholders other…

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July 23, 2012, 10:36 pm

What does Khan Academy need?

Marshall Thompson writes in this blog post from a couple of weeks ago that he’s concerned over the tone of the recent and ongoing Khan Academy/#mtt2k debate and is worried about the cost it incurs. It’s a good post, and in the process of commenting on it I realized a few things. Marshall writes:

I get the impression that KA has a goal of pedagogical soundness. Is this the best way to help them achieve that goal?

Sal Khan is not a dummy. He is clearly working through some of the same pedagogical misconceptions we all worked through (and continue to work through). How can we best help him through his personal journey without alienating him or causing him to be defensive?

I have tremendous respect for Sal Khan, but I have to admit that I’m not really concerned about his personal journey or his working through pedagogical misconceptions. It would be fantastic if he began…

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July 18, 2012, 9:44 am

For proofs, just click “play”

This week I am adding to the playlist of screencasts for the inverted intro-to-proofs class I first mentioned here. There are seven chapters in the textbook we are using and my goal is to complete the screencasts for the first three of those chapters prior to the start of the semester (August 27). Yesterday I added four more videos and I am hoping to make four more tomorrow, which will get us through Chapter 1.

The four new ones focus on conditional (“if-then”) statements.  I made this video as the second video in the series as a prelude to proofs, which are coming in Section 1.2 and which will remain the focus of the course throughout. Generally speaking, students coming into this course have had absolutely no exposure to proof in their background with the exception of geometry and maybe trigonometry, in which they hated proofs. Watch a part of this and see if you can figure out my …

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