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1500 questions
17
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10 answers
How to teach Mathematical Induction mathematically?
I am exhausted of teaching Mathematical induction to my little brother. I have given him many examples, Domino effect, aligned shops of hot dogs etc and every time he says that he got it but when I come across the problem mathematically, he starts…
Sufyan Naeem
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3 answers
Language as a barrier to learn math
It is well recognized that learning number names is not an easy task for native English speaking children. For example, the number name for "11" should be learned quite independently from the name of previous numbers, rather than as "ten-one" like…
Amir Asghari
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votes
4 answers
Teaching a very enthusiastic and bright 5 year old
I was asked to give extra lessons to a 5 year old boy who loves math (he says he likes 3 sports: football, swimming and math). However, I have never taught at this age and I am unfamiliar with the best theoretical way to proceed.
Hence, I would like…
Lucas Virgili
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3 answers
What teaching strategies can we learn from this logic puzzle going viral?
By now I'm sure everyone has run into the math puzzle where Albert and Bernard try to deduce Cheryl's birthday, which is all over social media, and even traditional media! If you don't know what I'm talking about, see e.g. this Washington Post…
hunter
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17
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6 answers
How can students self-check derivatives?
It is a good thing for students to self-check their work.
The results of some calculations can be checked easily. For example, the solutions to an equation can be substituted back into the original to see if they really work, and integrals can be…
DavidButlerUofA
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17
votes
3 answers
How to help students bridge the gap between highschool and university mathematics?
Mathematics at highschools is quite different from that in universities.
Instead of calculating numbers and finding solutions to specific problems, freshmen end up proving theorems and figuring out what happens in general.
(By in general I mean, for…
Joonas Ilmavirta
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17
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6 answers
Explanation for cutting a Möbius strip at one-third its width
Can anyone offer a concise, convincing explanation for why cutting
a Möbius strip along a line, not midway but rather one-third of the width of
the strip, and eventually joining back to itself, produces two linked, twisted
loops, one long, one…
Joseph O'Rourke
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17
votes
1 answer
How to assign grades to proofs: what do(es) the literature/experts suggest?
I am teaching an introductory course on proofs in mathematics in a mid-size American public university, and trying to develop some kind of consistent grading meta-scheme for grading proofs. I am writing to see if anyone can refer me to math ed…
David Steinberg
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4 answers
Surprising examples of Cavalieri's principle
I showed my calculus students two circular cones with the same base and height, but one of them "right" and the other slanted, and asked which had a greater volume. They all answered correctly that both have the same volume, but a lot of them had…
Mike Shulman
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17
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3 answers
Teaching a class you never took
How can you design an adequate course for a subject you never formally had classes?
This is similar to teaching somebody else's class.
As an example, suppose you are an algebraic geometer and you are asked to prepare an introductory algebraic…
Mark Fantini
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17
votes
4 answers
Is extra credit appropriate?
It is very tempting to assign extra credit problems that are (a) substantially more difficult than others on the problem set, (b) ask for the history of something we discussed in class, or (c) are related to something just barely outside of the…
Gamma Function
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4 answers
What is the right way to order the topics in a first ODEs course?
This question is long but I am asking for educated opinions on a question of math education and for this reason I'd like it not to be closed on the grounds that it invites subjective discussion. Educational practice is not a subject on which there…
Ryan Reich
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5 answers
Discovery-based and inquiry-based learning
In general, I think (and I am told by students) that I am good as a tutor. However, I would like to become more rigorously familiar with the discovery-based and inquiry-based learning applied to mathematics. Can you suggest some reference material…
user10024
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6 answers
Convincing a student it's OK to move on to another problem
I'm tutoring a very bright middle school student in a difficult geometry class. He understands most of the material, but struggles with some of the hardest problems and proofs. I find that when he goes through his homework, he gets stuck on the very…
Jakob Weisblat
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17
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14 answers
How is education in mathematics relevant to law?
Many students who take courses in mathematics go on to pursue "non-mathematical" careers. I'm wondering, in particular, about those who go on to study Law, and how mathematics is (or can be made) relevant to them in the classroom. I have not…
user155