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1500 questions
15
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4 answers
How to teach affine geometry to future high-school teachers?
This question is a follow-up to that one, where I expressed doubt about the use of abstract affine geometry in undergraduate education.
However, future high-school teachers need to be able to relate their higher education to what they will teach,…
Benoît Kloeckner
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15
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4 answers
Remedial students struggle with factoring $x^2+bx+c$ and $ax^2+bx+c$
Remedial students have seen quadratics before but, perhaps they don't elicit positive memories. The textbook (designed for people taking the course for the first time, not for remedial students) spends a long time on "multiplication of binomials"…
futurebird
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15
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2 answers
How can you determine the quality of your teaching, or someone else's?
The question in the title is immensely subjective and broad, and so I would like to narrow it to an answerable question:
What measures are in common use by administrators and researchers in determining the quality of an instructor's teaching? What,…
Brian Rushton
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15
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Thought experiment: Utopian college-level math curriculum without external constraints
An old favourite topic of mine to daydream about on pleasant afternoons is this:
If you could completely redesign the university-level mathematics curriculum from the ground up to be as good as it could be, but without external constraints (e.g.…
Daniel Moskovich
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15
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6 answers
Geometry with a view towards differential geometry textbook
I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or Erlangen geometry.
I would have liked to do…
Mike Shulman
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1 answer
What experimental studies have been done on the Kumon method of teaching and learning mathematics?
My dissertation involved, among other things, the East Asian way of teaching and learning mathematics. (See, for example, Leung (2001).) I was particularly interested in the Kumon method. Although I found a nice paper in a refereed journal that…
JRN
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15
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1 answer
Order of Topics in Introductory Proofs Class
Beginning next semester I am teaching a course in proofs and mathematical problem solving at my local university. For some background, the university is primarily a commuter university and the students I will be teaching will be mostly math…
Ryan
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15
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3 answers
How should I deal with overenthusastic students?
This is sort of an opposite question to keeping quicker students engaged?.
Sometimes I encounter students who are overenthusiastic about the course; they're constantly moving faster than the rest of the class and anticipating material (say, asking…
user37
15
votes
2 answers
How to make calculus lecture time more interactive?
I taught my first university course last Summer. It was integral calculus that usually has about 200-300+ students during the school year, but my Summer class had only about 35 students. I taught by lecturing during the whole class time. I am…
Felix Y.
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3 answers
Calculation versus writing in mathematics
Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas along with the results of calculation.
In…
Jon Bannon
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15
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1 answer
Proving theorems on one's own: how long should one persist?
I've recently started learning linear algebra on my own. I always try to prove the theorems I encounter by myself, without looking at the book (only to check if my proof is correct), because I found out that this way I can remember both the…
Adrian
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15
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2 answers
The Fundamental Theorem of Calculus and Vegetables
When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who presented it to me and my internet searching has not…
Chris Cunningham
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15
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3 answers
Recommendations for inquiry based/aided discovery textbooks
I've recently dipped my toes into the world of number theory; and I've bought a book that to me is quite unconventional: R. P. Burn, A Pathway into Number Theory. I've yet to put the book through its paces, but it seems agreeable enough to me. The…
seeker
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15
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5 answers
Cost and benefits of compartmentalization in k-12 curriculum
This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic.
K-12 mathematics textbooks (understandably) divide their content into chapters. My concern is that the…
NiloCK
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Should students get full credit for getting the correct answer (without work)?
Pre-algebra
If the student is taking this branch of mathematics, they are expected to show their work because they're expected to solve specific problems in a certain way. Ex, when they're solving for a variable they're supposed to manually find the…
Cilan
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