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Results tagged with mathematics-education
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user 29316
For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
81
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22
answers
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Are there proofs that you feel you did not "understand" for a long time?
Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ins …
55
votes
18
answers
9k
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How can an extremely mathematically talented young person be helped to fulfill his/her poten...
Obviously, this question is not a research level mathematics question at all. But, I've just met an extremely mathematically talented $11$ years old student and I don't know how I can help him. For ye …
37
votes
Is Euclid dead?
I try to keep my answer short.
Fact: Euclidean geometry is still taught in Iranian middle and high schools.
Observation (based on research): Most teachers do not like to teach geometry. They say, when …
33
votes
15
answers
3k
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Historical (personal) examples of teaching-based research
The phrase "teaching-based research" brings to mind research about teaching, though important, it is not what I mean. Unfortunately, I couldn't come up with a better phrase, thus please bear with me w …
27
votes
3
answers
3k
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Is “problem solving” a subject to be taught?
I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all grades. The peoples involved has sent me the textbook for seven graders (13 …
16
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Parodies of abstruse mathematical writing
The following is somehow a parody of "proof by contradiction" with an obvious educational purpose taken from the book "The Foundation of Mathematics" written by Ian Stewart and David Tall:
COMEDI …
11
votes
Insightful books about elementary mathematics
Mathematics: A Very Short Introduction by Timothy Gowers. It is very short and indeed very insightful. It is not a textbook, but includes some school-mathematics topics. From the cover:
The aim o …
11
votes
4
answers
2k
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Why do mathematicians prefer one definition over the other when they both define the same co...
Here is a basic, though very important, example:
Hilbert takes as primary the notion of “congruence” (or “equal”) between segments. His first axiom of congruence “requires the possibility of construct …
- 2,437
11
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Review papers in mathematics
For a "newcomer", perhaps "The Princeton Companion to Mathematics" would be a good start.
10
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Recreational mathematics: where to search?
This is somehow a copy of my answer to a closely related question:
G4G (Gathering for Gardner) is a Foundation that is worth to connect with. From 2010, people around the world celebrate the birthda …
8
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Recreational mathematics: where to search?
"Tournaments of cities" mentioned in one of the answers just reminded me of a very lively magazine, again with Russian origin, that is unfortunately not published anymore: Kvant (Quantum; Wayback Mach …
7
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5
answers
3k
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What does a mathematician expect from mathematics education? [closed]
Consider that my question is not a personal and/or subjective question. Perhaps, you have hired a mathematics educator in your department and you are interested in finding a way to communicate with hi …
7
votes
2
answers
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How should you respond to a student who asks whether a very nice physical example constitute... [closed]
"Is this really a proof?" is the exact question e-mailed to me today from an undergraduate mathematics student whom I know as a highly competent student. The one sentence question was accompanied with …
- 2,437
6
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An example of a beautiful proof that would be accessible at the high school level?
Here is one that I like and used it for different purposes, e.g. introduction to proofs, algebraic thinking, beauty, and so one. Shuffle a deck of cards. Divide it into two halves. Magic: The number o …
4
votes
4
answers
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When did you "meet Polya"? [closed]
I guess most of us didn't meet Polya in person (this is the answer to the title)! Perhaps, it is much easier to guess that most of us have met one of his writings (or alike) on problem solving, and i …