Goodman, T. (2010) Shooting free throws, probability, and the golden ratio. Mathematics Teacher, 103(7), 482-487.
In this entry, Goodman is emphasizing the effectiveness of using real world application type of problems to help students in their math classes. His entry focuses more on a possible use of math outside the classroom, free throw shooting probability, than it does on using the situation to teach a concept. Goodman writes his article describing the process he and his students used to calculate the probability of a basketball player, Paige, making free throws in various situations: first in a "one and one" where Paige only shoots the second shot if she makes the first, second if she shoots both shots regardless of the outcome of the first, and third if there are three free-throws taken. They used the same process with t charts and graphs and writing equations using season percentage, p, as a basis. Once they determined Paige's probability, they applied the same methods and came up with a table for multiple athletes with different initial shooting percentages. Goodman concludes that this type of applicational situation allows students the opportunity to expand their understanding of mathematics and obtain a greater knowledge of the concept.
I agree with Goodman's thinking that contextual situations are beneficial for student learning and ultimate understanding. In all of my experience both attending math class and tutoring peers in them, the biggest road block for students' understanding is their doubt in themselves. They loose the motivation to try to understand a difficult concept because they don't see how it will benefit their life in the future. Goodman's example of free throw shooting proves the importance of having a basic knowledge of math and also the options available when more math knowledge is obtained. This topic is something all types of people can relate to and it is useful, especially in sports. I think more activities using this type of application can only benefit students.
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I thought you did a great job describing one main topic of the paper you chose to read. I didn't exactly understand the procedures they used with the free throw probability, but I'm not that smart so...
ReplyDeleteIn your second paragraph you stayed with the main theme of your first paragraph which was good. But I feel like sports activities have been used a lot for outside classroom math application. I don't particularly like sports, what are other applications you might suggest you apply mathematics?
I think you had a strong topic sentence and this seems like a really good article. I think you pulled in a lot of what the author was saying in the article and I am convinced that the teacher was able to show their main idea with the evidence you provided. There are a few grammatical errors that tripped me up a bit but overall great entry!
ReplyDeleteHaley
I felt that you remained true to the main topic that you focused on from the article. I also agree that Goodman has a good point in making connections with math to real-world situations; without that, students just don't see any point to the mathematics they are learning. I do feel that there were a couple instances that there was more of a personal tone, and that there could be some improvement in the professionality of some sentences. However, I felt it was overall very well done.
ReplyDeleteBibliography comment: no errors!
ReplyDeleteI thought that the summary paragraph was strong. I could easily identify the main point of the paper in the topic sentence. You then developed and supported this idea throughout the remainder of the paragraph. I kind of wondered, however, what the golden ratio had to do with the activity. Was that clear from the article?
I thought that the second paragraph was also strong. Your stance toward the main point was clear and supported throughout the rest of the paragraph. I didn't mind the personal nature of part of your argument, because I thought your experiences were common enough that many people would share your viewpoint.
As for the article itself, I wondered a little about the students pursuing a mathematical activity so as to use the mathematics they knew rather than develop new mathematical knowledge. It seems to me that the teacher probably had mathematics learning as a major goal in this lesson, not just improving students attitudes about mathematics. What do you think?