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.