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1500 questions
15
votes
3 answers
What is a good physical example of Stokes' Theorem?
I find it useful to give physical examples of theorems, especially in vector calculus - for example $\nabla f$ being the direction of maximum ascent on a surface $f$.
What is a good example for Stokes' Theorem?
mirams
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6 answers
Factoring quadratic polynomials
In Secondary education in Australia, the general outline for introducing techniques to solve the quadratic equation
$$
x^2+bx+c=0
$$
is first to introduce the idea to find two numbers $p$ and $q$ such that $b=p+q$ and $c=pq$. After this, the…
Daryl
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Why is rounding half away from zero the only method taught?
Rounding to the nearest even digit is very practical in a lot of areas (e.g. statistics, accounting), but is never taught anywhere from elementary school to college. Even in R, the go-to statistics language, the round function uses this method.…
jpd527
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15
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8 answers
Visual Pythagorean demonstration
I know that there is a visual demonstration of $a^2+b^2=c^2$ using a smalĺ piece of paper, but there are also a lot of variations.
Which visual or drawing demonstration of the Pythagorean theorem can I show to 14-year-old students?
Fractaliste
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Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?
I transcribed this excerpt starting at the 22-minute mark, of Okinawa Institute of Science and Technology’s May 19 2020 podcast with Professor Tadashi Tokieda:
For example, this is a bit too technical, but there's a definition.... a very very…
user95017
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15 answers
Students can't seem to grasp the intent of tangent lines and getting general trends of derivatives from graphs
Background
I'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to be particularly good teacher or good at math.
In…
Krupip
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6 answers
What is important to keep in mind in grading proof-based courses?
I am an undergraduate grader at my institution where I have been entrusted with grading a section of an undergraduate analysis course; it's usual for this role to be offered exclusively to graduate students (who usually serve it as a secondary…
kodiak
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15
votes
4 answers
What are the pros and cons of having students choose which HW problems are looked at?
I am considering a new HW policy that I haven't seen elsewhere. Each week the student must turn in $n$ problems, of her choosing. There will be no HW score beyond documenting whether the student is turning in honest attempts at these $n$ problems.…
WetlabStudent
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15
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Strategies for encouraging student discussion, explaining, and argumentation about mathematics
How do we get students to see their own explanations as valuable to their learning?
For instance, talking can help a student uncover misconceptions that might otherwise remain unexplored until much later. Students can also benefit from examining…
JPBurke
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What are some research-level opportunities in mathematics that do not focus on proofs?
The research level of mathematics (what is done by professors and upper-level graduate students) tends to be heavily portrayed as focused on writing proofs to the exclusion of most anything else math-related. This was certainly the case for me as an…
Robert Columbia
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2 answers
Introducing the Lebesgue integral before Riemann's
Has anyone attempted to introduce, or has data on such endeavor, Lebesgue integration before Riemann? I've seen many discussions about how the Riemann integral is obsolete and that it is presented because it appeals to intuition*, contrary to…
Mark Fantini
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4 answers
Why do we use functional composition in the order we do?
Function composition means, roughly, taking the output of a function and applying it to the input of another function. If we define an object C to represent this operation, we could say $C(f,g) = f∘g$ or $C(f,g)(x) = f(g(x))$.
Say we had a similar…
David Lalo
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15
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5 answers
Why the fear of polynomial long division?
Why do people think long division of polynomials is complicated ?
I heard this expressed recently and it seems like an odd sentiment. For me, synthetic division is complicated and totally adhoc because it looks nothing like the division of integers…
James S. Cook
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15
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6 answers
I want a "true" proof by contradiction of an implication $P \Rightarrow Q$
When teaching proofs by contradiction of an implication $P \Rightarrow Q$, one starts by assuming both $P$ and (not $Q$), and then reaches a contradiction. The problem is, most elementary proofs of this type are "fake," in the sense that the…
Juan Tolosa
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6 answers
Ideal Undergraduate Sequence
What is the perfectly (maybe unrealistically) ideal undergraduate sequence for a undergraduate majoring in pure mathematics who takes 2-3 mathematics courses per semester assuming a strong AP Calculus BC background and wishes to go on to graduate…
user1516
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