Gilbert, M.J., & Coomes, J. (2010). What mathematics do high school
teachers need to know. Mathematics Teacher, 103(6), 418-423.
Through research done with several different teachers and their classrooms, this conclusion was reached, "How teachers hold knowledge may matter more than how much knowledge they hold." Several points were made within this article to support that teachers deep understanding of a small amount of mathematical knowledge is more beneficial to their students than having large, but shallow, amounts of mathematical knowledge. It is vital that teachers have this deep understanding of the material that they are teaching to their students so that the teacher will be able to quickly recognize and even anticipate student misconceptions and errors. The sooner a teacher acknowledges a student misconception and corrects it, the better. If a students misconception is not properly realized and corrected, then they will take that incorrect information with them into their future mathematics learning. It is vital that teachers not only know how to answer the questions they ask their students, but that they will be able to understand several different solutions to any mathematical question they ask. If they do not have this understanding, then they may not be able to notice and fix students' errors. Having this understanding of why a student made a certain mistake will provide the teacher with the opportunity to guide the student to developing more careful thought processes that will prevent them from making that mistake in the future.
I agree with the main point made in "What Mathematics do High School Teachers Need to Know?" because of three reasons. First, I have had several experiences that support that teachers need to have a deeper understanding of what they are teaching. I cannot count the number of times that I, or another student in my class, has asked a question of our teacher wherein the teacher gives an answer, but they do so without addressing the question asked because they did not understand what the student was asking in the first place. They had simply assumed they knew and had continued from there. Second, I have had experiences wherein I was attempting to teach a mathematics principle to someone else and have been unsuccessful. I was unsuccessful because I did not have a deep enough understanding of the material that I was trying to teach, so I could not recognize their misconceptions and correct them. Third, the article gives excellent examples from the classrooms that were studied of numerous representations and misconceptions that students gave/had about one problem. If the teacher had not been able to first interpret the different solutions given, and then realize what precisely it was that the student had made an error on, they would not correct the student on the precise point that the student didn't understand and although the student might be shown how to get the right answer, they could still have that misconception. For these reasons I feel that it is more important for a teacher to have a deep understanding of a small amount of mathematical knowledge, rather than a shallow understanding of a large amount of mathematical knowledge.
Subscribe to:
Post Comments (Atom)
I thought the writing in both of these paragraphs was very strong. Both paragraphs had clear topic sentence, and the main points of these topic sentences were further supported and developed in the paragraphs. The descriptions in the first paragraph helped me understand what the authors were getting at in terms of what type of content knowledge teachers need. The three reasons for why you agreed with the authors were easily identifiable and persuasive.
ReplyDeleteHave you thought much about how teachers can develop this type of knowledge? They don't get it from their college mathematics courses, because these courses cover mathematics different from what the teachers will actually teach in the public schools. They also can't depend on their knowledge of mathematics from junior high and high school, because they usually weren't taught in a way that would help them develop understanding. What do you think teachers should do to develop this type of knowledge?
I think the content was clear. Tone was professional. Topic sentence was present. Overall I think you did a good job on this blog.
ReplyDeleteI wonder if the article discussed the possibility that a teacher might know only a few things so well and in great depth, that that there knowlege well is a mile deep but only an inch across. In other words that they know a few things very well, but only a few things so the topics they can teach are limited. Does the article mention that senario?