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1500 questions
18
votes
9 answers
Good Examples of Questions to have Students Ponder Over Without Paper
A few times now I've found myself in a situation where I want to give a precalculus-level undergraduate student something to think about that's kinda fun and that's well outside of their coursework. But at the same time, I want to ask them a…
Mike Pierce
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18
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10 answers
Complex numbers in high school
Are complex numbers taught in high school in other countries? I am from Germany and complex numbers are next to never touched in high school with the exception of extra-curricular activities, for example.
I guess complex numbers also won't be…
YukiJ
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18
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2 answers
What examples of groups should students in abstract algebra learn to test ideas on?
Having seen many people go through abstract algebra courses, I've noticed that one factor for success is the ability to pull out examples to test ideas on (e.g. if two subgroups have the same index, are they the same? No, the Klein four-group is a…
Brian Rushton
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18
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4 answers
What reasons are there preventing me from using an old edition text?
Background: I'm a final-year math student applying for faculty jobs at small schools in the US.
I'm currently designing a few courses, and this questions has been bothering me for some time now: Why can't I just assign an older edition of a text to…
AegisCruiser
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18
votes
1 answer
Is metacognition ever bad?
Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page treatise on riding bicycles" I'd like to know some…
Jon Bannon
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18
votes
5 answers
What is a variable?
There are two kinds of answers I'm looking for:
What do students think a variable is?
What do YOU, the teacher, think a variable is?
I'm also interested in why you think a variable is what you think it is.
More Context: Historically, there has…
John
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18
votes
4 answers
Why do students only see the last term of a sum abbreviated with an ellipsis?
It's very common in learning mathematical induction to prove statements like
$$ 0^2+1^2+2^2+\cdots+n^2 = \frac{n(n+1)(2n+1)}{6}.$$
I've found that very frequently, on this sort of problem, when students get to the induction step they will write the…
Mike Shulman
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18
votes
12 answers
Real-World Applications of Logic
When introducing logic in a first semester university course, the examples I use are often quite artificial. One example: One of three kids (Annie, Bob, Chris) has broken a window. Annies says "it was Bob", Bob says "it was Chris", Chris says…
Anschewski
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17
votes
7 answers
Why do we teach that every line is a linear function?
Teaching my precalculus class today, I noticed something very simple that I hadn't taken into account previously. The definition in our textbook read:
"A linear function is a function defined by an equation of the form $$y = Ax + B."$$
This…
Andrew
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17
votes
2 answers
Teaching the use of pictures in proofs
Today I realized that many of my students in an upper-division undergraduate (projective) geometry class don't really understand how to use pictures in proofs. Some draw no pictures at all, making their proofs nearly impossible to read; some…
Mike Shulman
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17
votes
3 answers
How do I help a 6-year-old understand the meaning of her sums
I am tutoring a Grade 2 girl in arithmetic. She has demonstrated an ability to add two-digit numbers with carrying. For example:
$$\;\;14\\
+27\\
=41$$
I asked her to write this out horizontally, and this is what she produced.
$$12+47=41$$ …
MathAdam
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17
votes
6 answers
A text-based program to draw geometric figures
I found this question on another forum. Are there any hints how one could make pictures from geometric problems by coding? I mean, if one has a handicap in his hands and he can't use mouse very well, but he would like to learn to draw pictures like…
graphicsfan
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17
votes
8 answers
What to do when your students are all getting A's
Now, the title of the question definitely needs some background!
In some courses, everyone can get an A and it's no problem (especially later grad courses).
However, many times it is good to have a wide spread of grades. Most often, this is because…
Brian Rushton
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17
votes
3 answers
Good lessons/activities for one-day subs
In my school district, and I'm sure most others, every teacher needs to have a set of "emergency lesson plans", in case they are sick or need to be out for a day, so that the substitute can have something for the students to do. They usually are…
celeriko
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17
votes
2 answers
What happens when the state mandates college math placement policies?
The state of Illinois is currently considering a bill to mandate that all public institutions accept a score of 3 on every Advanced Placement exam. Bill here. The lobbyists in favor of the bill claim that similar things have been enacted in Ohio and…
Chris Cunningham
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