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Results tagged with mathematics-education
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user 1149
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/
185
votes
Examples of common false beliefs in mathematics
Here are two things that I have mistakenly believed at various points in my "adult mathematical life":
For a field $k$, we have an equality of formal Laurent series fields $k((x,y)) = k((x))((y))$ …
105
votes
Too old for advanced mathematics?
This is indeed not a typical math overflow question, but never mind that.
Of course you can learn mathematics at the age of 30 after having stopped studying it at the age of 18! Examples are abundan …
- 65.4k
46
votes
Examples of common false beliefs in mathematics
"A continuous image of a locally compact space is locally compact."
This is tempting because it is true without the "locally"s and it is often the case that topological properties and statements can …
41
votes
How to present mathematics to non-mathematicians?
For some reason, many mathematicians have trouble with the idea that when some layman asks them about their work, the appropriate response is not to try to figure out how to describe the latest theore …
34
votes
Teaching and students
A little bit more information about your background and situation would be helpful. Are you: a graduate student, a post-doc, a tenure-track professor? Are you teaching at a university? Are you teac …
- 65.4k
33
votes
Teaching undergraduate students to write proofs
This is a great question. In fact, I hope people won't think it over-dramatic if I call it one of the great math education questions of our time.
At the University of Georgia, we have decided as a de …
21
votes
The role of the mean value theorem (MVT) in first-year calculus
The purpose of this answer (which I would make CW even if the question weren't) is to collect references to scholarly articles on MVT and its role in introductory calculus courses. Most of these arti …
20
votes
How should one present curl and divergence in an undergraduate multivariable calculus class?
I have taught multivariable calculus exactly once, to engineering students at Concordia University in Montreal. I found the course to be replete with expository challenges like the one you mention: n …
- 65.4k
15
votes
Possibility of an Elementary Differential Geometry Course
I see that someone has mentioned this in the comments already, but I think it deserves to be left as an answer.
Here at UGA we do have a regular undergraduate course fitting your approximate descript …
13
votes
What's a nice argument that shows the volume of the unit ball in $\mathbb R^n$ approaches 0?
By a strange coincidence I found myself thinking about almost this very question last week on a walk home early one morning (yes, that's correct). I wanted however only the weaker result that the rat …
10
votes
How seriously do professors take teaching evaluations?
To answer the second question: professors at most universities these days take teaching evaluations fairly seriously -- not necessarily one by one (although we are human beings and a piece of seemingl …
8
votes
Graduate School
The advice to apply separately for a master's program is very good. If you can take the GREs (general and math subject) and do well, then many institutions will be willing to take a chance on you as …
7
votes
Best way to teach concept of real numbers using a hands-on activity?
The questioner's user page identifies him as an American, so he is presumably asking about the American middle school (grades 6-8) system. (In other words, most entering middle school students will b …
- 65.4k
7
votes
Place of Analytic geometry in modern undergraduate curriculum
I think you're essentially correct that analytic geometry is not considered a worthy topic of study for a contemporary US math major, or at least not worthy enough to be part of the standard curriculu …
- 65.4k
2
votes
Analysis from a categorical perspective
This community wiki answer is addressed to the OP's comment that he is looking for an "axiomatic" approach to the integral.
I don't (yet) understand what axioms have to do with category theory. In pa …