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.

Johnston, C. (2008). What do bouncing tennis balls have to do with algebra. On-Math, Online Journal of School Mathematics, 6(1).

This Article describes how bouncing tennis balls directly correlate to algebra. Each student bounced a tennis ball for a designated period of time and recorded how many bounces they got. Using this information, they later were able to use all of the varied results in the class to find the mode. After unifying the numbers in the results, they discussed what was the constant in the experiment which they found was time. They discussed whether or not time should be on the x-axis or the y-axis. Once deciding that it should be the x-axis, they were able to plot their points. Through this experiment, Christopher Johnston was able to explain how just by bouncing tennis balls, students could then take a real world experiment and directly connect it to math. He shows how through this one experiment one can find slope, mean, median, mode, range, meaning to graphs, x-axis, y-axis, and so much more.

After thinking about this activity, I have come to the conclusion that this would be a very beneficial thing for students to do. At first I thought it was too much like a science experiment but when Christopher Johnston showed all of the mathematical uses to the experiment, I decided otherwise. This activity shows students how something so simple can be turned into a mathematical thing. One of the big issues today is that kids don't see why they need math and this is a fun little activity to show them that math is all around them, even in really random ways like bouncing balls. It also got the kids engaged and working together. Lastly, it encompasses so many different mathematical concepts and ones that tie into each other really well.