My initial thoughts when I have heard about mathematics teachers implementing games in their classrooms was “Great, I would definitely include games in my regular task selection, but I do not see how they can be operated effectively to encourage student thinking in a mathematical mindset.” Time and time again I have played games without giving much thought to the mathematics behind them. My thought as a teacher was that games are fun and exciting, but rarely can be used to effectively promote student learning in mathematics class. That all shifted on Tuesday April 19th during a teacher named Mrs. Soto’s senior statistics course. As I observed her teaching I began to see the tremendous potential for mathematical growth locked within games rather than focusing solely the game itself.

My long time beliefs on the nature of games in a mathematics classroom were influenced by a lack of experience considering the mathematics behind the games I played as a child. Also my negative beliefs stemmed from a misunderstanding of the love students have for games. I saw games as pointless at times, and also a source of competition which is often based on luck. Before observing Mrs. Soto’s class I likely would not have used many games in my first year of my teaching because I perceived games as too relaxed for effective mathematical learning to occur. In my experience, I have rarely made sense of the problems in games, critiqued the reasoning behind their various methods or persevered in solving problems that occur within games. Now I realize that mathematics by its very nature is meant to be a subject of discovery and exploration. Games are an awesome opportunity for students to expand their critical thinking and to gain a deeper understanding of seemingly simple processes! I often forget that mathematics provides the “why” for much of the phenomena that occurs in games and in gambling as well!

### So how did all this change in my thinking come about?

Mrs. Soto began her class with a game where students placed bets on horses based on their projected odds of winning the race. Then, she ran horse race simulations from a site to see which bets won. Each student received a payout when their horse won a race. There were only 5 races, so students needed to pick the horses they thought were going to win carefully. Students picked based on the odds for each horse winning in a single race which were set at 7:1, 5:1, 7:2, 13:5, and 18:1.

Students played the game and did not win much because their understanding of the odds of winning was skewed because they had not worked with this kind of probability much. Eventually, students were able to ask questions and discover while playing the game that the horse that had the best odds of winning was the horse with 13:5 odds. Students discovered after a while that picking the horse with the best odds each time paid the biggest dividends. I asked Mrs. Soto after class about how she goes about running games in the classroom and if she runs them regularly.

Mrs. Soto explained that the key to teaching with games is to demonstrate the game as a group first with a few students. Then answer any big questions about the game before starting. Mrs. Soto said that games are now a part of her routine in her statistics classes because she found that students thought they were the best part about her class from year to year. She regularly has about 2 games per week. She said that she used to avoid games because she did not think that they were very good for math teaching, but now she has found that students love them and learn a lot from them, so she tries to use them regularly.

After my observation with Mrs. Soto I would say that I have a much greater understanding of just how engaging mathematical games can be, and how students can easily be encouraged to actively think about what is happening mathematically within a game. Student thinking can be probed as a teacher can see how the student is developing while playing the game. Mathematical games seem to me like a tremendous opportunity for students to think critically, make sense of problems, and to learn how to reason abstractly. There is so much more to games than meets the eye. I hope to reveal that to students in my future classroom by playing content related games from the real world on a regular basis. Also I can relate them to what students are currently learning while encouraging students to be themselves and think critically about the outcomes in games.

I am very thankful to Mrs. Soto for the opportunity to observe her class. One observation between teachers can change your thinking, and I am so excited about what I have learned from Mrs. Soto’s classroom. I look forward to implementing my observations in the future!