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1500 questions
102
votes
35 answers
What female mathematician can I introduce to my High School students?
I enjoy talking about Pythagoras when I teach the Pythagorean theorem. I sometimes mention Descartes when introducing Cartesian coordinates. And Leibniz and Newton are mentioned in many calculus classes. But all of these famous mathematicians…
David Ebert
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100
votes
20 answers
Unique candidate that fails
In the comments to David Speyer's answer here, he points out that "the distinction between 'if there is a formula, it is this one' and 'this formula works' is subtle."
Does anyone have any simple, natural examples where there is a "unique candidate…
Steven Gubkin
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88
votes
13 answers
How to assign homework when answers are freely available or attainable online?
I find that making homework meaningful is becoming increasingly challenging. Let us suppose that I am planning for next semester's first-semester or second-semester calculus course at my university.
In all likelihood, we will be using one of the…
davidlowryduda
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87
votes
15 answers
Should I design my exams to have time-pressure or not?
Is it better to design an exam with fewer questions and relaxed timing or with more questions and a resulting time-pressure?
One the one hand, it seems that students who really know the stuff will be able to complete an exam quickly, and a…
JDH
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87
votes
21 answers
Why are induction proofs so challenging for students?
This forum already has many
good, simple examples of induction proofs, a great resource.
As I am soon to teach induction for the $n^\textrm{th}$ time—this time to some perhaps under-prepared college students (in the US)—I would like to
understand…
Joseph O'Rourke
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86
votes
19 answers
What is a good handwriting font for mathematics?
My students frequently mix up my $t$'s with my $+$'s and my $y$'s with my $4$'s.
What is a good handwriting font for distinguishing these and other easily confused symbols?
Brian Rushton
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81
votes
6 answers
Issues with "equals", where does this come from and how do I combat it?
An issue I see with students a lot is abuse of the equals sign. For example, one problem asked "what is the degree of the polynomial: $\text{polynomial}$?", and I got answers like "$\text{polynomial}=3$". I tried to explain that no, that polynomial…
user5108
79
votes
17 answers
What's a replacement for "married couples" in combinatorics problems?
Many counting problems start with the assumption that we have a certain number of men and women or a certain number of couples, with the assumption (often unstated) being that that gender is binary (only men or women) and couples are only…
Mathprof
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76
votes
11 answers
Whence the "everything is linear" phenomenon, and what can we do about it?
$$ \color{red}{(a+b)^2 = a^2+b^2}$$
$$ \color{red}{\sqrt{x^4+y^4} = x^2+y^2} $$
$$ \color{red}{e^{t^2+C} = e^{t^2}+e^C}$$
I've observed this phenomenon -- wherein, implicitly, students say, "Everything is linear! Just pass the operation through!" --…
Brendan W. Sullivan
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76
votes
20 answers
Impressive common misleading interpretations in statistics to make students aware of
Statistics are used everywhere; politicians, companies, etc. argue with the help of statistics. Since calculations are needed for the interpretation of statistics, such things should be taught in mathematics in school.
What are the most impressive…
Markus Klein
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74
votes
17 answers
How shall we teach math online?
Many universities, including mine, are now requiring we teach our courses online because corona. How shall we do this? Let’s brainstorm here.
Some challenges:
My school provides limited online resources. I have access to Blackboard Collaborate. …
Stephen Herschkorn
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65
votes
17 answers
Is there a virtue to learning how to compute by hand?
I have been professionally tutoring a wide range of students (from elementary school through graduate school) for many years. Most of them are from the United States. I generally focus on helping my students develop procedural fluency built on a…
Geoffrey
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65
votes
14 answers
Encouraging class participation
I teach calculus to college students, and find it very difficult to get them to speak up in class when I ask questions, or when I'm trying to get a pulse for how much they understand. I think students are afraid of being wrong, or asking questions…
Jared
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64
votes
13 answers
How to get past the "mystique" of Maths
This question is primarily discussing maths education for adult learners, on courses teaching engineering mathematics at an undergraduate level. These students generally never set out specifically to learn mathematics, but need to in order to obtain…
MadScientist
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61
votes
4 answers
Is it worth grading calculus homework?
I am a young math educator. I've TAed four semesters of calculus for various instructors. Some instructors have required me to grade selected problems in homework sets. Another required me simply to note if it was turned in. Yet another did not…
abnry
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