Saturday, August 21, 2010

“Are we going to do something fun in math today?”

I just completed the online course in Probability and am looking forward to my next course which is Statistics. I gain a depth of understanding that I did not previously have with every course that I take in this program. In each class I learn strategies for teaching and how students learn best which helps me to become a more effective teacher. In the Probability course I learned the importance of addressing both theoretical and experimental probability. A simple but powerful way to do this is by allowing students to play games of probability. How many times have students greeted you with the question “Are we going to do something fun in math today?” I have been asked this question countless times and now, when we are beginning a unit on probability, I can finally answer “Yes!” As students play a game, you can assess their understanding of probability by asking them the simple question “Is this game fair?” When they attempt to answer this question, one can ask them to explain how they know whether or not the game is fair. One can easily extend this activity by asking students to design a fair game. This hands-on experience helps students to learn about and understand experimental and theoretical probability.
In this course we had the opportunity to design a game that we could use in our classrooms to help students understand experimental and theoretical probability. We were asked to play this game with some children over the summer and report on our findings. I played the game I designed with children from the ages of 5 to 16 and saw the benefits and learning that occurred for children of all ages. One of my favorite memories this summer is playing the probability game on the beach with a daughter of one of my friends. The game was very engaging and the young lady did not realize she was part of a mathematical experiment. When I asked this child to tell me about her favorite part of the game, she simply stated “I liked that we could play this game on the beach and it was FUN!” I learned a great deal from this activity and plan to incorporate the “Fair Game” activity into my lesson plans next year as it is a powerful learning tool.

Wednesday, August 11, 2010

“Is it a Square?”

In each on-line class that I have taken at Lesley, I have been given investigations and problems that I can use immediately in my classroom. Every week, I anxiously wait to see what problems I will be given to investigate. I am able to select one or more of these problems and give them to my students to explore and solve. I often give one of the problems as a challenge problem. Some of my students have become hooked on these problems and are disappointed if I do not have one for the week. I have been amazed to find some of my students who are not motivated to finish other assignments tackle the challenge problems with enthusiasm. Their passion is contagious. They often want to discuss their progress with me and other students become interested. Soon more students ask for challenge problems to try.
While taking Geometry 1, I was working on a problem for my class. I typically do not give my students a problem until after I have solved it. A copy of the problem was on my desk and another teacher saw it and asked about it. Students overheard our discussion and asked for a copy of the problem so they could try to solve it. I warned them that I had not yet completed the problem, but their curiosity was peaked. It is not often that eighth grade students plead with me to give them a math problem, so how could I say no? I agreed to make copies of the problem during my preparation time. While making copies, two other teachers saw the problem and asked for a copy as well. The problem was simple. There was a diagram of a shape that looked like a square and the question simply was “Is it a square?” It was made up of smaller squares and some additional information was given. Students were also asked to explain their answer. I could see that this was going to be the problem of the day at our school so I solved it during my preparation time. I watched amazed at how engaged students were in trying to figure out this problem. They worked collaboratively and were very creative in their many different approaches. They celebrated when they came up with a solution and were able to prove their answer. They wanted to share their solutions with me and give the problem to their classmates who had not yet seen it. At the end of the day, one of the teachers who had asked for the problem earlier came to my classroom door and simply said, “Is it a square?” I replied, “What do you think?” Our answers matched. I then told him about a student who had solved it in about three minutes which was the record for the day! He shook his head in amazement as he walked away. I am grateful to have a new source of rich problems for my students. These problems bring math alive and help my students practice true problem solving skills. After one of my students solved a challenge problem I was rewarded with her final comment which was, “I think that is the coolest thing I have ever seen in math!”