Goodman, T., (2010). Shooting free throws, probability, and the golden ratio. Mathematical Teacher, 103 (7), 482-487.
The main point of this article is to show how a contextual problem can be used to provide students with many opportunities to apply the mathematics that they've learned. The author goes through and shows how shooting free throws and probability can go hand in hand. The students reasoned about the likelihood of a student making a certain amount of points if they usually could make a certain number out of so many. This exercise allowed the students an opportunity to create graphs and models that showed the data that they collected. It also helped increase the students ability to solve problems.
I agree with the author in many regards but somethings were just confusing to me. I agree that giving the students a contextual problem such as this can be really beneficial and allow students to see how math can fit into life situations. I also think that it was a good exercise for students to collect data and represent it in forms of graphs. It also has potential to help students increase their understanding of the importance of math and help them to develop skills in problem solving. I was confused by the presentation of the experiment that the author made. I found myself struggling to understand the article when the principles seemed much more simple then the way they were presented.
Feedback on the bibliography: No comma after T.; the title of the journal is "Mathematics" not "Mathematical" Teacher; there is no space between 103 and (7).
ReplyDeleteI thought that the first paragraph helped me understand the main point of the paper. I liked how you described what the students were doing. I was wondering how the golden ratio fit with the activity. Did the author ever explain that?
The second paragraph was somewhat confusing for me. I understood that you thought there were benefits from the activity, and you described those very clearly. What was missing for me was a description of what exactly you thought was confusing. It would have helped if you had described what principles you were talking about in the last sentence, how the author thought about them, and how you thought about them in a simpler way. While you shared enough in your second paragraph to show that you were bothered by parts of the article, you didn't share enough so that I could also make a judgment on what bothered you.
I enjoyed your post. Even though you may not have entirely understood the article, you were able to describe it in a way that I could. I would have liked to know what bothered you a little bit more. Altogether, I think you did a good job :)
ReplyDeleteI thought you did a good job of summarizing the article in a way that was clear. I would like to know more about specific reasons as to how the exercise helped students' ability to solve problems (was it because they had a context to talk about the math in, did it help them visualize things better etc.) Maybe the author didn't expand on this, but I think it would be interesting. Good job!
ReplyDeleteI think you stated your stance in the second paragraph very well. I agree that when students practice applying math outside of the usual classroom context, it will help them increase their understanding of the importance of math. The only things that could be explained a little more are the principles that you thought were presented unclearly by the author.
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