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Commentary: The Staircase Problem
The Staircase Problem, like the similar Handshake Problem, is ubiquitous. Making the staircases with tiles and then rearranging them somehow into rectangles is a nice way to connect algebra and geometry and to find “proofs without words,” for the formula. I’ve used the staircase problem many times; the included assignment and handout were attempts at getting the students to focus on the reasoning in more depth, which worked very well for some students; others struggled to make the connections and to understand why the formulas needed to be justified beyond plugging in a few examples. The “Justifying Reasoning” Handout focuses on a method that some students followed in class; it’s not the easiest method, and it might have been better for me to direct other students to some of the other methods, when they didn’t catch on to the ones their classmates’ explored. 8/05
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