Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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2 answers

Comparison of different concepts of integral

As the following math stack exchange question (and answers) show: https://math.stackexchange.com/questions/703212/is-dxdy-really-a-multiplication-of-dx-and-dy There are a lot of different ways to think about the integral. Any ideas about how the…
kjetil b halvorsen
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Can homework play a substantial role in the assessment of understanding in university math?

Ideally, I'd like my students' grades to be based on more than just exams, because I think that certain tasks, such as writing proofs, aren't best performed in a test environment. Using homework for assessment seems like an obvious way to…
N. W. Clerk
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How to deal with very motivated students having "off-topic" interests?

There are some very motivated students who are very interested in math (in general), where the interest takes over most of their time. The problem is that they don't put enough time in the lecture they are attending, which leads to bad grades or…
Markus Klein
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Good examples of Lagrange multiplier problems

I've noticed that most Lagrange multiplier problems I've seen can be solved with other methods. Often the method of Lagrange multipliers takes longer than the other available methods. I don't like forcing my students to use Lagrange multipliers on…
Seth
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Is it natural for self-learners to forget most proofs of the theorems they learn?

When I read a theorem and read its proof and fully understand it, am I supposed to know the proof even after a long time or is it natural to forget the it? I ask this question as I'm a self learner who forget many many proofs of the theorems I study…
FNH
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Linear algebra textbooks presenting an eclectic, geometric approach to the subject

I am teaching an undergraduate course in linear algebra this fall. I am dissatisfied with most existing textbooks, and indeed with the way in which this subject is usually taught. I hope to find a textbook that has many or all of the following…
Frank Thorne
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Teaching the History of Mathematics in High School

Is any time being spent on the history of mathematics in high school classes today? Few observations as a student - I had to discover Cantor many years after I was introduced to set theory. I had to discover Fermat's last theorem and Andrew Wiles…
Karthik Thiagarajan
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How to nurture a good student?

When you encounter a very bright student in a first-year (college/university) class (and who is therefore bored), what do you do? Leaving them to their own devices can be problematic. It can lead to a loss of motivation, or, at the other end of the…
user1729
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What is Discovery-Learning, and why is it so controversial?

In my home province Discovery Learning is getting a substantial amount of pushback. I've been trying to follow the discussions, but have been struggling because I can't seem to get a clear answer as to what exactly is meant by Discovery Learning.…
Matthew G.
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What is an efficient way of drawing surfaces in multivariable calculus?

I've noticed that some surfaces are difficult to draw in multivariable calculus. For instance, I always have trouble with hyperbolic paraboloids. What is an efficient way to draw the following surfaces: 1)hyperbolic paraboloid 2)hyperboloid (of one…
Brian Rushton
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Should we teach abstract affine spaces?

In France at least, there is quite an ancient tradition of teaching abstract affine spaces (e.g. as a triple $(\mathcal{E}, E, -)$ where $\mathcal{E}$ is a set, $E$ is a vector space and $-:\mathcal{E}\times\mathcal{E}\to E$ is a binary operation…
Benoît Kloeckner
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What are the major obstacles to crowdsourcing a competitive, free calculus text?

It is well known that Allen Hatcher has created a free textbook for algebraic topology that is high enough quality to be used in a large number of graduate courses in the united states, saving students a large amount of money. Calculus is one of the…
Brian Rushton
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Mathematical problems for preschoolers

What are some mathematical problems that are feasible for preschool children to stimulate their intellectual development? There are multiple natural laws that are not apparent to them, for example: the conservation of number/quantity, sets are not…
dtldarek
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When is it appropriate to lecture?

I take it that lecture is rarely the most effective way for a student to learn. Lecture is a case where, I believe, research on learning firmly backs up the common experience that lecture rarely helps students who aren't able to help themselves. And…
Michael Pershan
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How to explain the difference between the fraction a / b and the ratio a : b?

I found it difficult to explain the difference between the fraction a / b and the ratio a : b. This subject is for pupils of grade 5. So is there a real difference between them and how to explain the difference in simple way ?!
Abdallah Abusharekh
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