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I am just curious whether math students who bound to be high school math teachers have to learn ring theory. If so, why.

Martin Argerami
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Daniel
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    Every university has a different definition of what it means to be a math student. It's not universally the case that all math students must learn ring theory. It's also entirely reasonable for a given school to decide that ring theory is a necessary part of any math education, regardless of a particular student's career goals. – Erick Wong Sep 26 '16 at 17:15
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    This question may be better suited for the math educators stackexchange – Ben Grossmann Sep 26 '16 at 17:16
  • It would be nice to know it. Just in case you get a student who knows all the math you are teaching. – 1-___- Sep 26 '16 at 17:17
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    Also, it is my understanding that a high school math teacher need not have a Bachelor's in math. I believe it is possible and common to teach math after getting a science/engineering degree. – Ben Grossmann Sep 26 '16 at 17:18

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Because it gives them perspective, and practice with abstract thinking. It might also equip them to answer questions like "what is a number?" or "why is $3^0=1$?" that most cannot answer.

My experience is that most if not all of the math education students hate this, and they are convinced that they don't need it in their program. The result we see is that math is taught mostly as a calculation device, or as pointless notation, when the point of having math in school is to stimulate thinking and convey understanding.

And we are within a vicious circle where new students come to college with less and less math ability and knowledge, and these students in turn become teachers, and things get worse year after year.

Martin Argerami
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    Ain't this the universal truth. A former head of our department called it "second generation ignorance". Except that now we have moved on to the third (if not fourth) generation. – Jyrki Lahtonen Sep 26 '16 at 17:22
  • In fact, knowledge of your subject has become a disadvantage for high school teachers. – Rene Schipperus Sep 26 '16 at 17:25
  • Yes, “the point of having math in school is to stimulate thinking”, but the point is also to convey understanding. – Lubin Sep 26 '16 at 17:43
  • Yes, I totally agree. I just didn't think about the working that much. I have edited to include your point, if you are ok with it. – Martin Argerami Sep 26 '16 at 18:02
  • "wording", sorry. – Martin Argerami Sep 26 '16 at 18:08
  • IMO, a good high school math teacher should know many interesting applications of what he teaches, knowing in detail algebraic geometry number theory and differential geometry is less useful than knowing a programming language and the basics of physics and engineering. – reuns Sep 26 '16 at 18:54