Rhombic tiling, permutation plot, subset gamegraph, permutahedron, hyperplane arrangement, structure diagram, three-dimensional heap, Cayley diagram, braid graph, and L-tromino tiling.

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When I was preparing my talk for the Legacy of R.L. Moore Conference a couple weeks ago, I reread the student evaluations for my introduction to proof course from Spring 2013. I was really pleased with all the comments, but two of them stood out because they capture the essence of what I want an inquiry-based learning (IBL) experience to be.

Here’s the first comment.

[…] he has found the perfect way to teach this course. […] The way Professor Ernst had us struggle through homework and then come together as a group and discuss the topics was very beneficial. I personally struggled through most of the material and when I finally got to the right concept I felt like I fully understood it because I personally came to that conclusion. Also, when I didn’t fully understand a topic, coming together and discussing it connected all the gaps I was missing. […] As a future educator, I would love to mimic his style of teaching so I can share with my students the same satisfaction that I got out of this style of teaching.

I stripped out a couple complimentary sentences that addressed me rather than the course. Of course, I’m thrilled about this student’s desire to incorporate IBL in their future teaching, but what I really appreciate about this comment is how the student reflects on both his/her independence and collaboration.

Here is the second, very short comment.

Try, fail, understand, win.

Four words of awesomeness. I couldn’t hope for more. This second comment inspired a recent post that Angie Hodge and I recently wrote for Math Ed Matters.