In Terry Goodman's article, "Shooting Free Throws, Probability, and the Golden Ratio," his main idea is to show the difference it makes in a child's learning when topics of interest are used as object lessons. In this particular situation he chose to teach probability and the golden ratio by explaining through free throws in a basketball game. He started out with a word problem where a certain player had playing statistics that showed she made free throws 60% of the time. If this player was in a situation to shoot a one-and-one free-throw (where if she makes it she gets to shoot again, but if she misses she stops) the instructor asked the students what the most likely outcome would be--scoring 0 points, 1 point, or 2 points. After predicting this through various procedures, the instructor continued to challenge them by switching up the given situation several times. Throughout the article he displayed the different procedures that children were using to solve these problems and expressed that they were soon coming up with their own ways of solving them rather than coming to him for ideas. By displaying the thinking process of the children in his class he showed how children really do have a desire to learn and it can be easily encouraged when topics of interest are intertwined in the concept material.
I feel that Goodman's topic is brought up often when discussing mathematical teaching procedures. Although it is a popular idea, I am not sure that it is practiced as often as it should be. I feel that teaching children mathematics with real world objects and activities that they enjoy and participate in often can really have a deep effect on how they learn the material. A topic of interest is a way for them to break the ice with the new concept and tackle problems in a way where they can use knowledge that they already have acquired. It is also a way for them to visualize the problems, and this is helpful because most children at that age are very visual learners. Although this article didn't bring up any huge issues in the math world, I believe that the author did make a good point in illustrating that "explorations such as this one have the potential to help students further develop their mahtematical understanding, skills, and problem solving."
I thought the first paragraph was very strong. You have a clear topic sentence, and the you do a nice job of explaining and supporting the topic sentence throughout the rest of the paragraph. I was wondering at the end, though, about what the golden ratio had to do with shooting baskets. Did he ever say?
ReplyDeleteI appreciated the passion that you express in the critique paragraph. My guess is that the third sentence is your topic sentence for this paragraph. With this in mind, I could only find two reasons supporting this topic sentence. I did think the reasons were strong, though.
What I really like about the ideas that you describe in this article is the way that the real world context was used. Often when real world contexts are introduced in math classes, such as in word problems (e.g., "a train leaves Chicago at noon traveling due south at 55 mph while another train..."), they are so "mathematized" as to be uninteresting to kids. It seems that the author maintained enough complexity and authenticity in this particular use of a real world context so that the kids would "buy into" their exploration.