Author Archives: Robert Talbert

March 18, 2014, 4:34 pm

What should mathematics majors know about computing, and when should they know it?

5064804_8d77e0d256_mYesterday I got an email from a reader who had read this post called What should math majors know about computing? from 2007. In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them. The person emailing me was wondering if I had any updates on that list or any new ideas, seven years on from writing the article.

If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. Mostly this is because of two things.

First, I know more computer science and computer programming now than I did in 1997. I’ve learned Python over the last three years along with some of its related systems like NumPy and SciPy, and I’ve successfully used Python as a tool in my research. I’ve taken a MOOC on algorithms and read, in whole or in part, books…

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March 11, 2014, 2:34 pm

Getting off on the right foot in an inverted calculus class

5524669257_ab67585fd0_mIn the previous post about the flipped/inverted calculus class, we looked at getting student buy-in for the flipped concept, so that when they are asked to do Guided Practice and other such assignments, they won’t rebel (much). When you hear people talk about the flipped classroom, much of the time the emphasis is on what happens before class – the videos, how to get students to do the reading, and so on. But the real magic is what happens in class when students come, prepared with some basic knowledge they’ve acquired for themselves, and put it to work with their peers on hard problems.

But before this happens, there’s an oddly complex buffer zone that students and instructors have to cross, and that’s the time when students arrive at the class meeting. Really? you are thinking. How can arrival to class be such a complicated thing? They show up, you get to work, right? Well…

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March 7, 2014, 9:00 am

Weekend reading (March 7)

Tacos and Spanish Rice

Here’s a picture of some tacos, for no real reason other than it might make you happy.

It’s been a busy week of blogging around here with the posts about the flipped calculus class. I’m taking a break from that series until next week, but in the meantime here are more items to read and discuss.

  • If you read one thing from this list, read this article in which Evan Selinger and Andrew Phelps argue that colleges need to start acting like startup or face obsolescence. It’s a perplexing read. On the one hand, their thought that innovation is the correct lens through which to consider higher ed is compelling. On the other hand, I think their three pillars of startup-hood – density, shared resources, and nurturing communities – don’t always apply to successful colleges, and the focus on these has the…

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March 6, 2014, 2:25 pm

Getting student buy-in for the inverted calculus class

370413613_6869b53f24_mSo far, regarding the inverted/flipped calculus course, we’ve discussed why I flipped the calculus class in the first place, the role of self-regulated learning as a framework and organizing principle for the class, how to design pre-class activities that support self-regulated learning, and how to make learning objectives that get pre-class activities started on a good note. This is all “design thinking”. Now it’s time to focus on the hard part: Students, and getting them to buy into this notion of a flipped classroom.

I certainly do not have a perfect track record with getting students on board with an inverted/flipped classroom structure. In fact the first time I did it, it was a miserable flop among my students (even though they learned a lot). It took that failure to make me start thinking that getting student buy-in has to be as organized, systematic, and well-planned as…

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March 5, 2014, 2:37 pm

Creating learning objectives, flipped classroom style

1206099628_f04d5d28f9_mIn my last post about the inverted/flipped calculus class, I stressed the importance of Guided Practice as a way of structuring students’ pre-class activities and as a means of teaching self-regulated learning behaviors. I mentioned there was one important difference between the way I described Guided Practice and the way I’ve described it before, and it focuses on the learning objectives.

A clear set of learning objectives is at the heart of any successful learning experience, and it’s an essential ingredient for self-regulated learning since self-regulating learners have a clear set of criteria against which to judge their learning progress. And yet, many instructors – myself included in the early years of my career – never map out learning objectives either for themselves or for their students. Or, they do, and they’re so mushy that they can’t be measured – like any…

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March 4, 2014, 2:59 pm

The inverted calculus course: Using Guided Practice to build self-regulation

7369580478_92ccf6bfbd_mThis post continues the series of posts about the inverted/flipped calculus class that I taught in the Fall. In the previous post, I described the theoretical framework for the design of this course: self-regulated learning, as formulated by Paul Pintrich. In this post, I want to get into some of the design detail of how we (myself, and my colleague Marcia Frobish who also taught a flipped section of calculus) tried to build self-regulated learning into the course structure itself.

We said last time that self-regulated learning is marked by four distinct kinds of behavior:

  1. Self-regulating learners are an active participants in the learning process.
  2. Self-regulating learners can, and do, monitor and control aspects of their cognition, motivation, and learning behaviors.
  3. Self-regulating learners have criteria against which they can judge whether their current learning status is…

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March 3, 2014, 9:00 am

The inverted calculus course and self-regulated learning

895220635_71c0ea6ee4_mA few weeks ago I began a series to review the Calculus course that Marcia Frobish and I taught using the inverted/flipped class design, back in the Fall. I want to pick up the thread here about the unifying principle behind the course, which is the concept of self-regulated learning.

Self-regulated learning is what it sounds like: Learning that is initiated, managed, and assessed by the learners themselves. An instructor can play a role in this process, so it’s not the same thing as teaching yourself a subject (although all successful autodidacts are self-regulating learners), but it refers to how the individual learner approaches learning tasks.

For example, take someone learning about optimization problems in calculus. Four things describe how a self-regulating learner approaches this topic.

  1. The learner works actively on optimization problems as the primary form of…

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February 28, 2014, 11:15 am

Weekend reading (February 28)

This week’s small shiny objects from around the interwebs:

John Cook has an interesting short article on the log semiring. Suitable for nontrivial examples in your next ring theory class.

Here’s a terrific short video that explains the Diffie-Hellman key exchange in terms of color mixing.

Here’s a longer video of John Baez talking about network theory, which we first mentioned a few weeks ago.

And here’s a video by Stephen Wolfram giving an introduction to the Wolfram Language. I’m curious to try this out.

Just in time for the NFL Draft season (OK, it’s still six weeks away, but whatever) here’s an interesting article on how the Dallas Cowboys used statistics and computers to revolutionize their approach to tracking and choosing players. Consider it an early prototype of Big Data.

Are today’s tablet and phone apps turning us into sociopaths? It might be …

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February 14, 2014, 2:00 pm

Weekend reading (February 14)

Look! A small shiny object.

Look! A small shiny object.

From the week that was, here is your random list of shiny objects from around the web.

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February 11, 2014, 2:46 pm

4+1 Interview: Eric Mazur

speaker-eric-mazurI am very excited to present this next installment in the 4+1 Interview series, this time featuring Prof. Eric Mazur of Harvard University. Prof. Mazur has been an innovator and driving force for positive change in STEM education for over 25 years, most notably as the inventor of peer instruction, which I’ve written about extensively here on the blog. His talk “Confessions of a Converted Lecturer” singlehandedly and radically changed my ideas about teaching when I first saw it six years ago. So it was great to sit down with Eric on Skype last week and talk about some questions I had for him about teaching and technology.

You can stream the audio from the interview below. Don’t miss:

  • A quick side trip to see if peer instruction is used in K-6 classrooms.
  • Thoughts about how Eric’s background as a kid in Montessori schools affected his thoughts about teaching later.
  • What’s going…

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