I remember being in math class as a student and pretty much everyday was the same. Notes, practice, and then finish up the assignment at home. The only time the patterned changed was if there was a test.
What I have found is that the math culture has changed and students are much more willing to ask the teacher, "why are we learning this" or "when am I ever going to learn this." I remember thinking the same thing, but never saying it out loud.
We all have a natural desire for variety, so I have found that activities and especially games break the monotony of notes and provides a great way of providing learning through peers. I enjoy the conversations that students have with one another while they are laughing and having a blast with the mathematics.
My favorite is Stats Soccer, which I used for my AP Statistics students. They were so competitive that some of them knew the statistics vocabulary better than I did. I have the activity on teacher pays teachers, but the one I want to go over is Greedy Pig. I heard about this game at a AVID conference and I enjoyed it so much, I turned it into an expected value learning activity.
The activity may seem complicated, but I have had upper elementary students all the way to seniors in high school play the activity. All ages enjoy it, because they can all make the simple choice to either stay in or get out of the round. I like them to play the game a few times because they can start seeing a pattern of how long they should stay in. I like to prime them with a few ideas we have gone over in class, to see if they can make the connection. After they answer the final question, we go over the exact answer using algebra or if we have talked about the geometric mean, I show them how to solve it that way. What makes this activity rich, is the problem solving that is needed with a game they have never played before. Everyone is on a level playing field and I have seen the mathematically gifted lose to struggling math student because of strategy. Mathematics goes beyond solving equations and computing difficult arithmetic. It is all about assessing what the problem is and finding the mathematical model that describes it.
