Tuesday, October 14, 2014

Teach Like a Freak, Part One

Inspired by the latest installment from Steven Dubner and Steve Levitt, Think Like a Freak, in this two-part series I consider what it might mean to Teach Like a Freak. In part 1, I take up the idea of experimentation and how I am currently experimenting with my teaching.

One of the central premises of Think Like a Freak is that one should be willing to experiment, and to make decisions based on the data gathered. For quite a long time, I have been teaching using inquiry-based learning (IBL), a mode of instruction in which students are the focus of classroom activity, deeply engaged in collaboratively making sense of the content. Evidence has been mounting that IBL specifically (http://www.nctm.org/publications/article.aspx?id=42527) and active learning more generally (http://www.pnas.org/content/111/23/8410.abstract) are more effective than lecture across multiple outcomes. At the same time, I have been reading research about Interactive Engagement (http://www.ams.org/notices/201308/rnoti-p1018.pdf), and have been experimenting with trying to blend IE with IBL. The question for me is how to structure my class to take maximum advantage of these approaches. To force myself to take this question seriously, I promised to speak about what I learned at the JMM 2015 in San Antonio. 

Last year, when I taught Transition to Proof, I had made a handful of IE questions, but class time was spent mostly on students presenting their work, and our discussions of those presentations, and a little bit of pair work. What I am doing this semester is using IE questions every week, which means about 15-25 minutes out of 150 minutes are spent on these short questions, with the rest of the time being spent the same way as last year. So, my goal is to compare the two classes in their understanding and skill in writing proof. The next step is to decide how to assess the impact of blending IBL with IE. This involves deciding what to measure. Another issue is that, once I decide on appropriate measures, it can be difficult to get good comparative data. For purposes of assessing impact, I do not have two classes running simultaneously with which to carefully set up a comparison. The best I can do is to use the data I still have from last year’s class. More specifically, in the previous year's course, I had tried a handful of IE questions, and so I have the results from those as well as exam scores for that class. The key component of my assessment, then, is to compare student exam performance last year to the performance this year, when I am using IE questions on a weekly basis. I do not claim that this will give me a definitive answer, but at least it will be a start. Another thing I have been doing is keeping track of participation in whole class discussions, so that I can compare the number of participants in discussions on IE days with discussions on non-IE days. Although counting the number of participants in whole-class discussion is a somewhat superficial measure, it gives me some quantification of how things run differently with the IE questions. If it seems that students are benefiting from more IE questions, I will keep making time for them in class.

Backing away from the specifics of this question, one thing that I have decided to do with courses that I teach regularly is to keep results of exams broken down by question. The reason for this is that I often modify exams from year to year, and so exam scores from year to year are not directly comparable, but there will be questions that are directly comparable. Another thing that I am learning to do is to keep a log of each class day’s activity. This way, in addition to evidence of student learning, I have a record of the kinds of interactions that occurred in class meetings. Together, these provide two kinds of data that help me to know whether what I am doing is working. Although I have always modified my teaching over time, by Teaching Like a Freak, I can hope to have evidence of whether the changes are making a positive impact.

In part 2, I will take up two other ideas from Think Like a Freak, targeting small problems and thinking like a child. 


  1. Can you provide a few examples of what IE looks like in your Transition to Proof course?

    1. A lot is grounded in definitions. For instance, "TRUE or FALSE: For all functions f:X --> Y, if x is in X, then there is a y in Y with y=f(x)." "Let f:A --> B be a function. Which of the following statements is true? (A) The image of f is a subset of A. (B) The image of f is a subset of B." "Which of the following is the contrapositive of the statement..." "TRUE or FALSE: In a proof by contradiction, you begin by assuming what you want to prove."
      The students seem to really like this part of the class. It seems to put the focus on a single narrow point that we might hit in a larger proof, but this way, we are focused directly on exactly one issue that I think gives them trouble.

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  3. Cool, thanks. Feel free to send me your whole list of IE problems;)