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1500 questions
35
votes
7 answers
Uninsulting way to say "this will eventually be easy"
When presenting a proof, there are usually a lot of parts which look like "obvious", "routine" manipulation to me, and between zero and two genuinely insightful steps. I want to point out the difference between these two steps and the others.
I…
David E Speyer
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35
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3 answers
What happened to the Moore method?
I always read about the Moore method with great enthusiasm. Somehow I always felt that it should be how we do it in an ideal world, but it is impossible to use because of time and other constrains.
The most important point is that users of the…
András Bátkai
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35
votes
17 answers
Why are triangles so prevalent in high school geometry?
A colleague and I recently discussed what we call the "Triangle Trap." High school geometry covers a very large unit reflecting the common core:
Classifying Triangles
Triangle Angle Properties
Constructing Triangles
Properties of Triangles (e.g.…
Will Schwartz
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35
votes
11 answers
Epsilons and deltas in a first calculus course
In a freshman calculus course for non-majors;
Is it to the benefit of the students to include discussion of epsilons and deltas?
To what extent, if any, should they be used? For example, just to prove simple limits, or to prove limit laws, or…
Gamma Function
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35
votes
5 answers
Questions with "round" answers only?
Textbook writers are blessed with only solving problems with neat answers. Numerical coefficients are small integers, many terms cancel, polynomials split into simple factors, angles have trigonometric functions with known values. Pure bliss.
The…
vonbrand
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35
votes
1 answer
Metonymy in mathematics
Metonymy is a figure of speech where a word or another expression is used to mean something other than its literal meaning.
This phenomenon is not restricted to the "usual human languages" (such as English or Finnish) but also appears in the…
Joonas Ilmavirta
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35
votes
13 answers
Lecturers "(intentional) mistakes" as a teaching tool
I have heard the story (may be an urban legend?) of a top professor who occasionally wanted to teach freshman analysis. He believed in the method of letting students see how a mathematician's mind works, so he came to the lectures largely…
Jyrki Lahtonen
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35
votes
14 answers
How to handle the situation when you made a stupid mistake in front of the class?
I don't know whether you guys have made a similar experience but it just happened to me: I made a very stupid mistake in front of the class. I can't really tell you how it happened and I feel too ashamed to even tell you what it was (and it doesn't…
vonjd
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35
votes
8 answers
Helping students who make no effort to figure things out for themselves
When I was a student, it was very much frowned upon to ask for help without making an effort, like how math.stackexchange.com operates (for the most part).
In the high school where I work, it is common for teachers to go through full solutions with…
A. Goodier
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34
votes
13 answers
Should I be teaching point-slope formula to high school algebra students?
I'm student teaching this semester, and so far I'm loving it! Our next section in the book teaches point-slope formula, and my cooperating teacher (a 24-year veteran teacher) is convinced that point-slope formula serves no purpose. He said he has…
Wmol
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34
votes
5 answers
Why are there two inverses to exponentiation?
I'm not sure if this is more educational or more "pure math", but:
For multiplication and addition, there is exactly one inverse operation, namely division and subtraction.
For exponentiation, we have both logarithms and roots.
Why is that the case?…
Jasper
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34
votes
7 answers
What to do when you get "the empty stare"?
First, I am not a professor, but I was a teaching assistent for a couple of courses. One time I took over a few sections for a friend who was also a TA. The course was 'math for chemists' (I think it was the second quarter or third quarter of the…
Ruben
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34
votes
11 answers
Is there any proof of the fundamental theorem of algebra that can be introduced to undergraduates who have just completed Calc III?
I am aware of three proofs of the fundamental theorem of algebra, using:
Liouville's theorem
The fundamental group of the punctured plane, or
Multiplicativity of field extensions together with the intermediate value theorem
If I had a small group…
Brian Rushton
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34
votes
12 answers
Should college mathematics always be taught in such a way that real world applications are always included?
I am teaching Linear Algebra this semester with the textbook Introduction to Linear Algebra by Serge Lang and most (perhaps all?) my students are not majoring in mathematics. As I was carefully introducing the vector-space axioms and proving the…
Zuriel
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33
votes
5 answers
What is a good method for drawing a Möbius band on the blackboard?
This week I'm going to give a talk on fiber bundles, and I found myself with an unexpected problem. Since I'm not using slides, I'll need to draw a Möbius band on the blackboard. Usually what I do is simply draw a rectangle with some arrows to…
Newman
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