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1500 questions
29
votes
17 answers
How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?
Consider a real function $f(x)$ and imagine its graph in the plane. Then the graph of $f(x+2)$ is simply the graph of $f$ shifted to the left 2 units while the graph of $f(x-2)$ is that of $f$ shifted to the right 2 units. Also, the graph of $f(2x)$…
user1916
29
votes
4 answers
Students use WolframAlpha. Can we change calculus instruction to exploit it while discouraging 'cheating'?
(This question developed from a comment in the thread "Revisiting the chain rule".)
Students know that WolframAlpha and other software/computational resources exist and will make use of them as they see fit. Is there anything we can change about the…
Brendan W. Sullivan
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29
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7 answers
Why does high school teaching in the USA require a teaching certificate while college/university teaching does not?
Original post: I have a math PhD. In the United States, I can teach at a 4-year university or a community college without any additional training. However, to teach mathematics in high-school I must receive additional state-based certification.
My…
Brian Rushton
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29
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10 answers
What are argument one can give to students on the definition $0^0$?
From high school to introduction courses in university, the expression $0^0$ is some (psychological) problems. High school students just apply it to their calculator and either the result is $1$ or undefined.
In calculus, you may define $0^0$ as a…
Markus Klein
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29
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3 answers
When is it appropriate to warn about the difficulty of a subject?
I've been a TA across every class in the calculus sequence, under the assignment of professors with different teaching styles and curricula. It's often clear to me ahead of time when a certain subject is going to be a lot easier or harder for…
Feryll
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29
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6 answers
Calculus problems arising from real research problems
I am visiting my in-laws for the holidays. My sister in law is a statistician. She asked me to take a stab at a calculus problem which was coming up in her research. The Lambert $W_0$ function is defined as the inverse of the function $f(x) =…
Steven Gubkin
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29
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6 answers
What holds your students back in Calculus?
I teach Precalculus to high school kids, and I know a lot of you all teach Calculus.
What are some issues that your students have in Calculus classes that
you wish had been addressed in a Precalculus class?
e.g. "Man, my kids never know how to…
Michael Pershan
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29
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9 answers
When handing back exams, what should we tell our students about the distribution of exam scores?
I've seen a variety of approaches to the day we hand back our exams.
Show every score listed in order, so every student knows exactly how they compare to others
Show an aggregated histogram, for example saying how many students got each grade
Give…
Chris Cunningham
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29
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7 answers
Teaching logic with a proof assistant
I am thinking about teaching a university-level "introduction to proofs" class (mainly for math and CS majors) making use of a computer proof assistant like Coq. I feel like there is a lot of potential benefit here, in that the students can get…
Mike Shulman
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29
votes
6 answers
How can we help students who are very anxious about math?
In many parts of the world, the majority of the population is uncomfortable with math. In a few countries this is not the case. We would do well to change our education systems to promote a healthier relationship with math. But in the present…
Sue VanHattum
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29
votes
15 answers
What's the point of learning equivalence relations?
I teach an introductory discrete mathematics course at a community college to math and computing majors, usually in their sophomore year. As is common, it's partly used as the first foray into formal and proof-based math courses in the case that…
Daniel R. Collins
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29
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15 answers
How do I teach algebra?
I find that soon I'll be working with high school students that are struggling with math. In particular, we'll be talking a lot about algebra and some basic trigonometry. The latter I have experience with (via working with students in calculus and…
user37
29
votes
17 answers
Examples of Innumeracy
I read Innumeracy by John Allen Paulos and would like to share more up-to-date and relevant examples of innumeracy to motivate my grade 8, 9 & 10 students. Are there any websites, blogs, books, etc. with lots of examples of innumeracy in the form of…
David Ebert
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29
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3 answers
Difference between high school and college calculus courses
I am curious why students who take calculus in high school often do so poorly in college calculus. I am an instructor at an engineering college and I've noticed a decent number of students who have calculus 1 on their high school transcript and yet…
Matt Brenneman
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29
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1 answer
Do "gateway tests" work?
Here is an overview of the practice of "gateway testing", which explains it much better than I could:
https://sites.lsa.umich.edu/michigan-math-in-action/2015/09/24/25-years-gateway-testing-at-michigan/
But for completeness I'll quote the basic…
Mike Shulman
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