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1500 questions
58
votes
4 answers
Future educators writing nonsense questions
I teach future elementary educators mathematics content courses.
We play a lot in class with tasks like "Write a variety of word problems which would require the student to multiply 2.3 by 1.4".
Often the questions which students produce are…
Steven Gubkin
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58
votes
24 answers
Optimization problems that today's students might actually encounter?
Our students are not fencing in farm fields, cutting wires and folding them, or designing windows, so they are often uninspired by the optimization problems we give them. They seem like something that "someone, somewhere" might use, but the examples…
Chris Cunningham
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57
votes
15 answers
Student: Why not use a calculator?
The kid I am teaching math (subtraction for large numbers right now) just said this is all too easily done by a calculator, why don't we use it?
Well, I did tell him that you can only learn more stuff by learning this, but this seems like an…
Rijul Gupta
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55
votes
14 answers
Should we say that fractions "are" or "represent" numbers?
I never gave this a second thought until a friend who works in education brought it up the other day. Should we say that a fraction like $\frac{1}{2}$ "is" a number, or "represents" a number? In particular, should we say that $\frac{1}{2}$ and…
Mike Shulman
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54
votes
13 answers
How do I motivate my students to go to office hours?
I'm currently TAing a Linear Algebra class where a significant portion of the class is struggling, oftentimes getting marked down on homeworks or tests because they misunderstand some concept (rather than some trivial mistake in calculation). The…
user37
52
votes
15 answers
How can we help students learn how to read their textbook?
In most secondary and early undergraduate courses, students purchase expensive and carefully-written textbooks. These textbooks contain, roughly, three things:
Exercises and Answers
Reference Material
Exposition
Students are mostly adept at using…
Chris Cunningham
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51
votes
3 answers
How do blind people learn mathematics?
I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often taught using a lot of visualization; how does this work with blind people?
My interest in this is a little round-about. I have…
Peter Flom
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50
votes
21 answers
How to explain that winning the lottery is not a 50/50 distribution?
When casually discussing with my 13 yo child about probabilities, he told me
there is a 50% chance to win at the lottery
To what I said
no, there is a 1 chance over 90 million
(I roughly estimated $_{7}^{49}\text{C}$ which I think is more or…
WoJ
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49
votes
14 answers
Should we avoid indefinite integrals?
I am very uncomfortable with indefinite integrals, as I have a hard time giving them a precise sense that matches the way they are written and the usual meaning of other symbols.
For example, when one writes
$$ \int \sin(x) \,\mathrm{d}x = -\cos(x)…
Benoît Kloeckner
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49
votes
10 answers
How to handle the situation where a student insists I am wrong during the class?
I had one very vocal student in my Calculus recitation last year. Sometimes she would point out if I made a mistake in the lecture.
However, sometimes she would insist that I had made a mistake, even if I concluded it was NOT a mistake after…
kathleen
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48
votes
39 answers
Real-world examples of more "obscure" geometric figures
As part of my secondary geometry class I like to hook students by presenting real-world examples (usually images I find online or have taken myself) of different geometric shapes from real life. For instance, a lesson on the area of a circle might…
celeriko
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48
votes
14 answers
Big list of "interesting" abstract vector spaces
When introducing an abstraction it is important (in my opinion) to have a wide variety of examples of this abstraction.
Since finite dimensional real vector spaces are classified up to isomorphism by their dimension, it is a little difficult to find…
Steven Gubkin
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48
votes
21 answers
The concept of infinity for a 5 year old
My son, who just turned 5, has been interested in the concept of infinity since long. He asks me a lot of questions regarding infinity. For example, not accepting my infinity + any number = infinity, he asked me how old I will be when he himself…
QMC
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48
votes
8 answers
What do math majors (actually) do after graduation?
It's the time of year for prospective college freshman in the US to make campus visits, and I'm once again confronted with my lamentable ignorance when the students and their parents ask, "So what do math majors do after graduation?"
A web search…
Mark Meckes
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47
votes
24 answers
How to explain Monty Hall problem when they just don't get it
Talking to some friends, I was asked to explain the answer to the Monty Hall problem (see also here;) .... they were having some trouble because whoever explained it to them didn't do a very good job.
#Humblebrag I was able to explain it in under…
Tutor
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