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1500 questions
18
votes
12 answers
Why do we conventionally treat trig functions as going anti-clockwise from the right?
I realise that teachers tend to focus on right-angled triangles when introducing trig functions, and for those I can see that the most intuitive approach seems to be starting with the opposite and adjacent sides of a triangle matching the right and…
Oolong
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18
votes
5 answers
Evidence showing that returning tests helps students
My kids (12, 14) attend a school in the US in which the mathematics department has a policy of not returning tests to the kids.
I have very strong feelings about this (I think it is an obviously bad policy),
but would like to gather any…
copper.hat
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18
votes
3 answers
How to use a CAS in teaching calculus
I want to introduce calculus students to computer algebra systems (CAS) like Sage, Geogebra, and Wolfram Alpha in college Calculus 1 and 2. While I believe in the value of learning to do calculus by hand to a certain extent, I also don't want to…
Mike Shulman
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18
votes
3 answers
Differential forms in mechanics?
I teach mechanics (including large deformation and flow of continua) to mechanical engineering students and have a continuing mission to drag the teaching of mechanics into the 20th century (I'll worry about the 21st later) by introducing 'modern'…
rdt2
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18
votes
1 answer
Impact of philosophy of mathematics upon effectiveness of instructor
Is there any research out there on how an instructor's philosophical beliefs about mathematics might affect some aspect of his or her impact as a teacher? My intended meaning of 'impact' is broad, covering not just how well students perform in test…
Alexander Woo
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18
votes
2 answers
A study comparing effects of calculator usage on later math skills?
Each year my university tries to decide whether or not it will have calculator and CAS based introductory math courses (the calculus sequence, linear algebra, and ODE) or not. Other than some hearsay or personal preference (which looks like "You…
davidlowryduda
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18
votes
4 answers
Inquiry about my note-taking skill
I am a rising college junior in US with a major in mathematics. I recently noticed a problem in my note-taking skill in the mathematics, both from the textbooks and lectures. When I was a microbiology major, I wrote extensive amount of notes from…
MathWanderer
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18
votes
5 answers
When should an advisor assess a student's knowledge independently of their course grades?
In the role of an advisor, I am often faced with the question
Should I retake this [undergraduate] math class?
My first-order approximation to the answer is:
If this is your last math class, a C or better is fine, be done with it.
If you are…
Chris Cunningham
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18
votes
4 answers
Are fractions hard because they are like algebra?
It occurs to me that to really understand the ways that people work with fractions on paper requires a good grasp of the ideas that numbers have multiple representations and that expressions can be manipulated in various ways without changing the…
DavidButlerUofA
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18
votes
4 answers
How can a research mathematician transition into a mathematics education researcher?
Mathematics education research is generally very different than mathematics research. I am interested in collaborating with mathematics education professors at my next institution, and possibly transitioning into mathematics education as my…
Brian Rushton
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18
votes
5 answers
How to convince students of the integral identity $\int_0^af(x)dx=\int_0^af(a-x)dx$?
A common identity in integration is $\int_0^af(x)dx=\int_0^af(a-x)dx$.
The steps to prove it (algebraically, ignoring the geometric method) are as follows.
Let $u=a-x$ so $dx=-du$.
$\int_0^af(a-x)dx=-\int_a^0f(u)du=\int_0^af(u)du=\int_0^af(x)dx$
My…
Trogdor
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18
votes
3 answers
How can I teach Mathematics to genius students?
I'm a Math Teacher for highly talented students in High School.
It's hard for me to determine how fast can I move through topics and how deeply can I dive into different math subjects for enhancing their abilities, while also keeping their interest…
souran
- 181
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18
votes
3 answers
How to create a misuse of calculator!
Let me start by sharing what happened in my class today. The subject was complex number and I started with the historical problem of "finding two numbers whose sum is equal to 10 and whose product is equal to 40". Okay, as you know from experience…
Amir Asghari
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18
votes
4 answers
What are your favorite instructional counterexamples on sequences?
In this article, I give counterexamples regarding real sequences. And in that one some others.
In particular counterexamples answering questions like: "If for all $p \in \mathbb{N}$ $\lim\limits_{n \to +\infty} (u_{n+p} – u_n)=0$ then $(u_n)$…
mathcounterexamples.net
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18
votes
8 answers
Rationale for not dividing both sides of an equation by $x$ (ex: $6x^2 = 12x$)
this came up in class yesterday and I feel like my explanation could have been more clear/rigorous. The students were given the task of finding the zeros of the following equation $$6x^2 = 12x$$ and one of the students did…
celeriko
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