I led a short workshop yesterday about logic puzzles. I think it went pretty well. People seemed to have a good time and there were some really good discussions about the kinds of thinking participants were using when they worked on the puzzles. Without me explaining it, people figured out my goal: to get students to develop language and reasoning skills which lead to proof.
I based my workshop on the methodology that Jeffrey J. Wanko laid out in his article Deductive Puzzling which was published in the May 2010 issue of Mathematics Teaching in the Middle School. Sadly, I don’t think that you can access the article unless you have a subscription. In a nutshell, I had participants look at a solved puzzle and try to figure out what the goal of the puzzle was. Then they worked on an unsolved puzzle with a partner or small group and I asked them to think about strategies for good starting points while they worked. After most groups had solved the first puzzle, I called the group together and we solved a similar puzzle together on the computer. I had people tell me what they wanted me to do and also why they knew that step had to be true. We did this process for three different puzzles: Shikaku and Hashiwokakero, which are in the MTMS article, and also Slitherlink, which I worked on almost obsessively last school year.
Anyways, I just wanted to jot down some observations so that I remember them the next time I give this workshop. So, I thought it went well enough that I’d like to do it again. That’s something!
I thought the order in which I introduced the puzzles was good. The one I started with was definitely the right one—it was accessible and easy to figure out what the rules were. I want to experiment with flipping the other two, doing Slitherlink second and Hashi third. I was surprised by the seemingly common belief in the room that Slitherlink was much harder than the other two puzzles. I want to play around with that and see if that remains the case with the order switching. I conjecture that part of this difficulty arose from it being very different game-play than the preceding puzzle. And I think it is a little more similar to the first puzzle’s game play.
I want to highlight something that arose naturally, the idea of developing a common language to talk about the puzzle-solving. People made up some really good terminology—“hallways”, “end-stops”, “corridors”, “double-bridge”, etc.—which is something that is extremely helpful when solving a puzzle together. I’ve usually only solved puzzles by myself, in which case there is no need for this. I also loved that it happened organically, that it was participant created language, not terminology I forced them to adopt.
I would like to have a little more time to discuss the overall “how might we use this in our classrooms?” question at the end. I know we started late, so I didn’t have my full 90 minutes, and maybe doing three puzzles in that amount of time was a little ambitious in the first place. We did have plenty of time to do all the puzzles, but more discussion time would have been nice.
I want to stick firm to my “no answers provided” policy. I might even want to make this explicit to people who want the answers. Part of what I am trying to accomplish is the idea of proving your ideas. If you know what the solution is and you check your work against it, I think this undermines that. You have to first prove things to yourself in order to convince anyone else.
And one last little side note. There was a comment that was voiced a few times in this workshop that just irritated me. If you’ve read this far, I’d love your feedback on ways to respond to this. Someone said: “There’s no way my students could handle this” (or words to that effect). I get an internal reaction similar to the sound of fingernails scraping down a chalkboard when I hear someone say this. And it’s not like I’ve never thought this myself. I completely understand where this comes from and I empathize with the feeling. However, I have learned to re-frame this reaction in my own mind and state it more along the lines of “I’m not sure how to make this idea accessible to my students yet”. The “yet” is really important, as is the “I”. Ultimately, I’d love to have a non-preachy response locked and loaded that I can say when someone says this in a workshop.
 If you would like to read the article, give me your email address and I’d be happy to send you a copy.
 I used the sample puzzles on Nikoli.com, which have really awesome game play, including the ability to easily undo multiple steps, and a “try” feature which outlines moves in a different color.