Category Archives: Teaching

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 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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January 29, 2014, 5:17 pm

An end to unsolicited review copies of textbooks, please

2014-01-29 16.29.42The picture you see here is my afternoon mail today. It consists of two copies of a new Calculus text (hardcover), two copies of another Calculus text (hardcover), and one copy of an intermediate algebra text (softcover).

I did not request a single one of these. I certainly did not request duplicates of two of them. The last time I taught intermediate algebra was the mid-1990′s. I am not on a committee that selects textbooks. I have no use for these books other than to prop open a door. So why did I get them? I have no idea.

When I think about the waste and expense of these unsolicited review copies of textbooks, it makes me downright angry. I went to and used a back-of-the-envelope estimate of weight and shipping distance, and got that the total package of these books would have cost about $20 to ship to me from its point of origin. That’s not a large sum, but how many…

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January 27, 2014, 7:55 am

The inverted calculus course: Overture

3011652637_05f202dca6_n As many Casting Out Nines readers know, last semester I undertook to rethink the freshman calculus 1 course here at my institution by converting it to an inverted or “flipped” class model. It’s been two months since the end of that semester, and this blog post is the first in a (lengthy)  series that I’ll be rolling out in the coming weeks that lays out how the course was designed, what happened, and how it all turned out.

Let me begin this series with a story about why I even bother with the flipped classroom.

The student in my programming class looked me straight in the eye and said, “I need you to lecture to me.” She said, “I can’t do the work unless someone tells me how to get started and then shows me how, step by step.” I took a moment to listen and think. “Do you mean that you find the work hard and it’s easier if someone tells you how to start and…

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January 6, 2014, 4:26 pm

Getting students to want to do pre-class work

Look into any discussion about the inverted classroom and you will find one particular concern rise to the top of people’s questions: How do you make sure students come to class having done the reading and the viewing? Actually, in my experience giving talks and workshops about the inverted classroom, that’s a charitable way of putting it – many times I hear this, it’s more like, I already know my students won’t put in the work outside of class, so why bother?

I saw this tweet yesterday which brought this up:

My response was:


Students are rational actors when it comes to the work they do. They are a lot like faculty in that regard – if the benefit of a task appears to be worth the cost, they’ll do it. If not, they won’t – or they will…

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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 23, 2013, 7:25 am

Khan Academy using contractors for accuracy checking — some thoughts

In this news item from the Washington post (h/t to @ValerieStrauss) we learn that Khan Academy is using “contractors” to check the accuracy of some of its videos. The report is prompted by an email exchange between the piece’s author and Sal Khan himself regarding the accuracy of one of the physics videos. In Khan’s response, he says:

We have deleted the video [a physics video that had an error in it]. We are trying our best to keep up with any errors on the site (both through feedback from users and peer-review from educators). I checked into why we didn’t notice this one earlier, either your friend or someone else did point this out in the comments but they did not surface to the top (we currently have contractors with math/science backgrounds reviewing much of the math material and the comments to find other issues like this). We do need to get better at making sure that…

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