Bureaucracy in Math as well as More Games

I read the article Lets Do Math: Wanna Play? by Lach found on the National Council of Math Teachers website. Lach talked about how she implemented her research in teaching math. I am going to step outside the idea of thinking math for a second and think bureaucratically.

            I learned something new in this article about a good way to implement games in my curriculum. Communicating my intentions clearly with administration and with the parents BEFORE doing the lessons with my students makes sense. This may seem obvious to you, but it was not to me. I like learning without first suffering consequences for my mistakes. Phew, another hurdle overcome. Now back to math.

            One of the games mentioned was Rush Hour and I have a similar game on my iPod called Parking Lot so I thought I’d revisit this game and think math strategy. In the first level, things were very easy. My strategy was to think backwards. I need to move the green van down so I can get the red car out of the lot. So to get the green van down, I must move the black car back. Three moves makes a win.
Level three added the challenge of needing to move a car first up to relocate a van, and then down to move another vehicle, adding some new ideas to my arsenal. Sometimes to win, I need to fill the space that I want emptied in order to move other cars and re-park the car that is blocking the exit.

            In level four, there were many cars. Here my strategy involved a few steps. First, I thought about how to move the cars blocking the exit. Then, I realized that one car would be difficult to move and I just couldn’t see how to move it. So, I did the first few moves to get the other two cars out of the way and then looked at the puzzle again. I found that there were two cars this time that needed to be moved and strategized to move other cars to get those two out of the way. By the time they were moved, it was obvious how to finish up to get my car out of the lot – a mere 17 moves.

            As I read what I just wrote, I notice the difficulty I had in clearly explaining what I was doing. This is a skill that takes practice to verbalize. Part of this is because I am not always thinking about my moves so much as anticipating them. Part of my subconscious is working at these problems. As I continue to practice talking out my strategies, this will improve. I must remember to understand this with my students - talking math is a new skill and students will catch on to it at different rates. 

Just a quick note here about another book called Graphs and Applications by Aldous and Wilson. This book has many activities (for university students) that would be very helpful when planning math lessons in high school. For example, there is a cube problem one of my colleagues taught to me. I was given four cubes with four different colours painted on each face (with six faces, two colours were painted on two faces). My task was to stack the cubes one on top of the other so that each side would have one of each of the four colours. After trying for 10 minutes, I was unsuccessful. She showed me how to solve it using math and a special type of chart using dots. No numbers were used in this process. Neither was adding, subtracting, multiplying or dividing. The graphs didn't even look mathematical but they were. An excellent lesson for students who love math and also for those who don't like it too much.