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I had asked the title question in an answer here, but it didn't get any recognition, so I'm posing it formally.

The key word in the question is should. In my Mathematics Education degree education, I have had the option to take many content classes, but few methods classes. As current teachers, if you were to design a degree program, what classes would you ideally offer?

For the construct of this hypothetical question:

  • A Masters (not dually earned with undergraduate) degree consists of 12 courses, and most students go on to become secondary school teachers;
  • A PhD or EdD degree consists of 25 courses, and many students go on to become post-secondary teachers or researchers.

A (perhaps) similarly relevant post can be found here: What are the differences between graduate and undergraduate classes, relevant to course design and teaching?

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  • $\begingroup$ It might be helpful to give more context as to why you're asking this question. As in, what is the purpose of the question and why are you asking it? I would give a very different answer to someone looking to enroll in such a program versus someone who was in a position to write such a curriculum versus someone who was a policy maker or accreditator trying to understand such programs. I'm also curious whether you are just asking for a wish list of courses or whether you want pointers to actual programs that exist. $\endgroup$ – James S. Nov 19 '14 at 0:08
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    $\begingroup$ @JamesS., the question was posed merely as a hypothetical. The programs that I'm familiar with all seem to be lacking in methods courses. I thought it was clear that I, myself, am not looking to enroll in a program, as I'm finishing up my degree now. Perhaps one day I will be in the position to create or mold such a program, and can use the suggestions from answers provided to craft the ideal program. $\endgroup$ – Andrew Sanfratello Nov 19 '14 at 5:34
  • $\begingroup$ I don't think a methods course would really be that useful, unless it is directly tied in with a teaching apprenticeship. What I mean is "Student teach" in the morning, and then discuss teaching ideas at night.... $\endgroup$ – Kara Nov 20 '14 at 5:44
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If I were to take my master's degree again, I would take: 1-2 courses in abstract algebra, 1-2 courses in analysis, 1-2 courses in topology, 1 class in statistics, and 1 class in combinatorics for a total of 5-7 classes to get a good solid background in mathematics.

I would then set up a year long apprenticeship with a master teacher. I guess this would would count as 2-3 courses.

I would take: 1-2 classes in classroom management and pedagogy (discussing and reflecting on the apprenticeship) and 1-2 classes that give a deeper look at the math content of high school math.

I think a high school math teacher should have a very solid understanding of math, but that most of the learning of how to teach would happen in the apprenticeship with the master teacher.

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    $\begingroup$ A serious question: Why do you think there should be multiple courses in abstract algebra, analysis, and topology? These would amount to something like Galois Theory (after an intro to Groups, Rings, and Fields), Measure Theory (after, e.g., constructing the real numbers in a first course on analysis, and the material along with it), and Algebraic Topology (after covering some of point-set topology in a first course). If I have understood you correctly: Why do you think these courses (especially the second ones) would be important for high school math teachers? $\endgroup$ – Benjamin Dickman Nov 17 '14 at 22:58
  • $\begingroup$ I went to school after my MA in math ed to take more math courses. My MA offered one course in Abst Algebra and one in Analysis, which were watered down versions. I took these courses as pure mathematics courses because teachers should not take watered down courses. The only difference should be that the math courses for teachers should include the professor making connections between the higher math and the high school math curriculum. I think there should be multiple courses in Abstract Algebra, Analysis, and Topology because as far as I can tell, these three form the foundation of math $\endgroup$ – Kara Nov 18 '14 at 17:56

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