Entry #7

Gilbert, M. J, & Coomes, J. (2010). What Mathematics do high school teachers need to know? Mathematics Teacher, 103(6), 418-423.

As the title implies, the article discusses what teachers really need to be able to do and know when teaching mathematics. According to Gilbert and Coomes, having a greater understanding of how and why students are doing specific tasks in a certain way is superior in importance to knowing how to do advanced level of mathematics. Responses from different students are provided in the article after being posed with the following proportion problem, “Lincoln Elementary School pairs second- and sixth-grade students as ‘study buddies.’ What is the ratio of second- to sixth-grade students if 2/3 of the second graders are paired with 3/4 of the sixth graders?” Each of the responses published were different, and not all of them were correct. The authors used this to display that it is far more important for an instructor to be able to see things through multiple different view points and be able to determine what is correct or incorrect and why that is so. According to the authors, being able to teach mathematics extends beyond being able to solve the specific problems. Teaching mathematics requires knowledge of how to solve problems but, it also, and most importantly, requires the knowledge and ability to recognize new ways of things or find errors and correct them.

I also believe that it is of greater importance to understand in depth the material to be taught rather than being able to do difficult upper level math. In the article, a teacher that they worked with was quoted essentially saying that she would have preferred to spend her time covering in depth what it is she would be teaching rather than taking upper level math classes. I too have had this issue tug at me. My high school did not offer anything above calculus 1 and statistics. I feel that since I will not being teaching linear algebra in high school and definitely not in middle school, that it is verging on waste time. It may be interesting but since I won’t be teaching in it, I am not sure that it is worth studying. I have found that throughout my entire life I have just done things in math without a sound understanding of what is being done. I agree that it is important so that I will be able to know why things are the way they are in mathematics. I would not consider myself a valuable educator if I could not answer questions of why we use a specific rule or procedure. Lastly, it is important to have the ability to understand approaches by different students so that they can be appropriately addressed. An approach that is successful could be useful in teaching in the future, and an approach that was unsuccessful needs to be corrected so that lasting misunderstandings are not created. It is more important to me to be able to teach and understand adequately what I will be teaching than it is to be able to do highly sophisticated mathematics.

Entry #6

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.