Gilbert, M.J., Coomes, J., (2010). What Mathematics Do High School Teachers Need to Know? Mathematics Teacher, 103, 418-423.
People assume that if you can do, you can teach. Gilbert and Coomes claim this is a fallacy, and that teaching mathematics effectively requires much more mathematical knowledge than is necessary to merely solve the problem. They list and explain several types of knowledge that a teacher needs in addition to Common Content Knowledge – the ability to solve a problem.
A Teacher must be able to do more than simply mark “right” or “wrong”, as Students will approach a mathematical problem in varied ways and analyzing the methods used by students and allows teachers to assess student learning. This requires that teachers understand and are able to interpret each of these solutions and determine how the student was thinking so that they can best help the student to improve.
For example, it is important for a teacher to recognize common errors and to realize why a student might make these errors. This allows the teacher to provide the student with guidance on which part of their concept model is incorrect, so that they can adapt it accordingly. To increase understanding, perhaps a teacher can teach with these possible errors in mind, outlining why a student should avoid certain techniques and so on. Teachers must also recognize how each approach relates to the other tactics that students use, to help the students develop connections, and allowing the teacher to determine when the students are ready for new material. Additionally, they must understand how these solutions connect to instructional goals, so that they can help their students to achieve them.
I think this is actually one of the main reasons why so many students struggle. I haven’t worked in a high school, but in working with elementary school teachers in their mathematics, I find it is often assumed that a teacher can teach mathematics because they can do the mathematics. But many teachers are simply on a hunt for correct answers – if correct answers are being produced by the majority of students, the teacher feels they have done a good job and their work is done. However, in my observations, it is never this simple. Some students manage to extract a correct answer from dubious methods and are never able to correct their misconceptions because their lack of understanding is rewarded with a pass. Others think deeply about the material but make some trivial calculation error. Their thought processes are correct but they abandon them after being told they are doing it wrong. Others’ responses show that the students have a serious misconception that needs to be addressed, and as such, telling a student to go back and check their work will not be very constructive.
Students always initially try to understand the material. They take the information provided, build a mental model, and apply it as best they can to the problem. Then they are told, no, that answer is not right, but they are confused as to why. Gradually they come to the conclusion that math just doesn’t make sense. Few children can survive years of this treatment and still be willing to actually think mathematically. If a teacher only understands how they would do it themselves, then they will not be able to teach much to the students who don’t think exactly the same as them…. i.e all students.
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Your blog entry is very clear on what the article is about. I loved how you started off with an introduction idea and then went to the topic sentence, it worked well. You did a good job explaining the main point and then giving examples from the article. Though, I would suggest that when you said "they list and explain several types of knowledge," I would have liked you to list some of the types before you went into them. Otherwise, you have a great blog entry!
ReplyDeleteI felt that your second paragraph was very well written, and I completely agree that students need teachers who will not just search for "correct" answers, but teachers who will actually spend the time and effort to really understand what the students are thinking, and how they are understanding concepts. However, I did feel that there were some rough spots in the summary that were a bit hard to follow; I felt that the flow was interrupted a few times. I also felt that there needed to be more of a tie-in to the topic sentence, and the main topic of Gilbert's article. Overall, though, I thought you did good.
ReplyDeleteI think this is a common misconception within the church as well: That those who know how to do something, know how to teach it as well (or would like to teach it). All of your paragraphs are very clear and thought out. An overall job well done.
ReplyDeleteBibliography feedback: include spaces between initials in names; include "&" before Coomes; no comma after J.; italicize journal title and volume number
ReplyDeleteI could tell from your entry that many of the ideas from this paper resonated with you. I liked the way that you took these ideas and made them your own. I liked the passion and found your arguments persuasive. I loved the last sentence of the entry—it really brought your point home.
As for the overall structure of the writing, I would probably suggest a more careful organization. Each paragraph seems like it has two parts, and perhaps the content would be better communicated through four paragraphs. But I think you could have also tightened the structure of your paragraphs a little so that there was no need for splitting. For example, in the first paragraph, your "for example" part could have been better connected to the first part by replacing "for example" with something like "Other types of knowledge needed for teaching might include..." Then the second half would seem like a natural extension of the point you are making in the first half of the paragraph.
I felt like you did an amazing job summarizing your article, great topic sentence and supporting evidence from the article. I got a little confused with the generalization of all students toward the end, but when I reread the second paragraph it fit together and made sense. I loved the topic of this article, it is so true the other knowledge math teachers need besides basic math skills. It was cool to read just a summary of it, I bet the article contains even more information. I agree with your opinion as well, the lack of secondary teaching skills can harm students who learn from these teachers.
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