Goodman, T. (2010) Shooting free throws, probability, and the golden ratio. Mathematics Teacher, 103(7), 482-487.
Goodman's article focuses on the application of shooting basketball free throws to probability and finding the golden ratio. The article starts with a real-life example of a girl on a high school basketball team and her free-throw shooting percentage. The problem starts with a one-and-one free-throw situation and trying to decide how many points-0,1, or 2-is the most likely outcome. Using a table or a probability tree, students can find which outcome is most likely. The problem can then be expanded to a general case for different shooting percentages or shooting more free throws. Teachers should encourage these expansions so that students can discover patterns and mathematical rules. When analyzing the situation for a general case, students can find which point outcome is most probable based on different shooting percentages. One of the results of this analysis is the discovery of the golden ratio, which exists when for a line segment divided into two parts, the ratio of the shorter part to the longer part is the same as the ratio from the longer part to the entire line segment.
The connection between algebra and shooting free-throws is very innovative and useful in learning many aspects of algebra. When I first read the article, I kept being surprised about how much you could do with a simple example of shooting free-throws. There were so many extensions and applications by changing different aspects of the problem slightly, such as shooting percentage or how many shots were being taken. Expanding the idea to a more general case helped students to know more about probability as well as showing them what to do in future problems if they want to know about the general case. I also really enjoy basketball, which made the article fun to read, but it actually applied to what the students were learning. I also loved when whatever concept we were learning connected to real life. It would also stick in my memory more because I was not working with an abstract concept, but rather something real that I could relate to. This article is an excellent example of applying math to real life.
Bibliography Feedback: you need a period after the second parathesis (following the year).
ReplyDeleteAfter reading summaries from many other students of this particular article, I think that maybe there is a bigger idea than the one identified in the first paragraph. In other words, many students seemed to think that the author is presenting this particular example to illustrate a point about how mathematics should be taught. Do you agree or disagree with them? I should also say that of all the other summaries I've read of this article, yours is the only one that contains information about how the golden ratio related to the probability of shooting a free throw.
I think that you may have captured the author's main idea better in the second paragraph than the first. I think that the author would probably agree with you on every point you made in that paragraph.
I liked the detail that you put into describing the free-throw problem because it helped me understand the probability, connections and extensions that can be seen from the problem. I don't understand how the analysis of this problem lead into the discovery of the golden ratio and I'm quite sure if the students would be the ones discovering the golden ratio, or if the teachers discovered that the golden ratio was applicable to this problem. Maybe it's just because I don't have much experience with the golden ratio. I thought you did a good job though and your paragraph was organized around your topic sentence, which made it easy for me to follow.
ReplyDeleteI actually know nothing about baseball except you shoot a ball throw a hoop.
ReplyDeleteTo be honest, given the above sentence, your first paragraph actually did not make any sense to me. I don't know about the point system so saying they were trying to find the outcome whether it would be 0 1 or 2, and finding the golden ratio of lengths made no sence to me.
It is probably just me though, so I woudn't worry about it too much.
You did a good job of explaining the main points of your article, but it was somewhat hard for me to see the authors point for the article in what you wrote. You mantained a very professional voice and it was well structured. This article seemed somewhat interesting, although it was hard to see the aplication to teaching. I would have been more interested in seeing that connection. Overall, good job.
ReplyDeleteLucky Club Casino Site - Lucky Club Casino No Deposit Bonus
ReplyDeleteLucky Club Casino is an online casino for players 카지노사이트luckclub from the United States, South Africa and South Africa. We review the latest bonuses, games,