Goodman, T. (2010). Shooting free throws, probability, and the golden ratio. Mathematics Teacher, 103(7), 482-487.
The article written by Terry Goodman had a few main points that were closely intertwined. His main objective was to demonstrate that students often take the initiative and gain a desire to learn more, when a topic of interest is introduced. He was having students work on probability and decided to use basketball free throwing percentages to have his students calculate what probability certain theoretical shots would have. Goodman started the problem out very simply by asking his students if a given player had a free throw shooting percentage of 60% and had a one-and-one free-throw opportunity, what the probability of the player scoring 0, 1, or 2 points would be. After the students calculated those probabilities he continued to challenge them by asking them to create different probabilities in different situations. It came to the point that his students were suggesting to him what different things they could calculate and discover. Through telling the story that he experienced in his classroom Goodman wanted to demonstrate that students do have a desire to learn more. Goodman wanted his readers to realize that if you take something from the “real” world and draw the mathematic concepts out of it, students can be very interested and hard working.
In my opinion the article was not very controversial and the point he made is something that we are all fairly comfortable with. It is important to give students opportunities to apply mathematics to things that they find important. Unfortunately most people spend their school life wondering why they have to learn the math that they do. Using life experiences gives them an example of one of the many situations that they may want to use math. By implementing this kind of instruction on a regular basis, in which life situations are analyzed, students may begin to find meaning in math. Goodman also allowed them to explore his scenario beyond exactly what he had planned out. This allowed the students to discover on their own what they thought might be important. When students begin to explore, I believe that they enjoy their learning more since it is what they are curious about rather than what the teacher feels they should be learning. When students enjoy their learning I believe they succeed much more frequently. One last thing that can be learned from Goodman’s model is to remember not to underestimate what students of any age are capable of discovering and learning.
I appreciated your critique of the article. I agree that his main point is not controversial, and I also agree with your three points about what makes this particular task a good one for students. I wondered a little about how the golden ration fit into the article. Did it play a major role? Was that what his students discovered as they explored the mathematics further?
ReplyDeleteI thought it was interesting that he chose to start with the number 60%. Do you think it makes much difference which number he starts with? What if he were to choose 83% instead? Did he take advantage of particular characteristics associated with the number 60% that he wouldn't have been able to take advantage of with a number like 83%? Are there some advantages to starting with a number like 83%?
I also wondered briefly about whether this task engaged all of the students in his class. For example, did he say whether or not the girls in his class were engaging with the task? Might there be ways that he could adapt the task to engage students who are not interested in basketball?
I read the same article as you did so it was easy for me to follow along. I feel that I would be able to understand what the article covered even if I hadn't already read it. Great job on discussing his main idea in the first paragraph
ReplyDeleteI like that you mentioned that his main idea wasn't controversial. I agree, and I feel that you brought up some great points that correlate with the student's learning opportunities.
Overall I though this was a great summary and I feel like you covered enough of the article that I understood what is was about without have read it. I was however still curious about a couple things; Whether or not the students were all actively engaged in this activity or it it was just the jocks who play basketball and then also if the teacher continued to use this teaching method in the classroom or its it was simply a one time thing, part of an experiment. Another thing I would have added would be one of the examples the students came up with just to clarify that they did in fact understand and had the right idea about this concept of math. Good job though.
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