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1500 questions
13
votes
6 answers

How do I help my student understand concepts such as "$x$ divided by $x$"?

I am tutoring a high school level student (who is currently at the level of being introduced to anti derivatives) who has quite some trouble with grasping mathematics. We have been making good progress but then with this concept I get to a hault: he…
Therkel
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13
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11 answers

Is $a^0 = 1$ for a nonzero, real number $a$, a theorem or an axiom?

For the students of grade 9: Is $a^0 = 1$ for a non zero real a, considered a theorem or an axiom?
Abdallah Abusharekh
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13
votes
3 answers

How to embed English into Calculus lessons

I am teaching abroad to Chinese non-native English speakers with a large variance of language skills. I teach both pre-calculus and AP calculus (AB & BC). For both of those classes I define the new terms. I use word problems, have them read from…
El Santi
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13
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3 answers

Immersive attention when learning mathematics

In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. To my mind, the study of mathematics also…
J W
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13
votes
7 answers

How can you be perfect at maths (highschool)?

I'm in my last year of highschool. And I'm aiming for a perfect grade in maths. The problem is that this year is the hardest year of maths I have ever faced in my entire life. Especially derivation and limits as its the first time I am studying it.…
Vincent
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13
votes
5 answers

Use of mathematical humor suitable for motivation/explaination?

There are some intelligent jokes also explaining (in a very extreme way) how mathamticas works, for exameple A mathematician and a physicist are sitting in the teachers lounge. Suddenly the furniture catches fire. The physicist is able to handle to…
Markus Klein
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13
votes
2 answers

online homework vs paper homework

Some professors assign online homework in lower level courses, such as through services like WeBWorK or WebAssign. Online homework has some clear advantages for instructors. However, in my experience, such systems receive largely negative feedback…
Gamma Function
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13
votes
3 answers

How to effectively run large exercise groups?

The Question Quite often one is faced with the task of running a large exercise group (think 40+ students in the room). What are some strategies to make the most of the (limited) time for the students? The motivation In my time as a student and now…
Willie Wong
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13
votes
3 answers

Appropriate ways/sayings to discourage undergraduate students' overreliance on calculators

Main question: How do I, in a medium- to large-sized undergraduate class setting, appropriately and effectively discourage students from relying too heavily on calculators? There have been several questions here about calculator usage (both in class…
Brendan W. Sullivan
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13
votes
4 answers

Using joke / song / film / pop culture to exhibit a new mathematical concept

Questions: Do you have any examples from pop culture (say, a joke, or an episode of a show, or a song lyric, etc.) that utilize and/or effectively illustrate a mathematical concept? Have you used any examples in class, and have they proven…
Brendan W. Sullivan
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13
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4 answers

Substituting $x=1$ into $px^{p-1}$, why do so many students get $p^{p-1}$?

Substituting $x=1$ into $px^{p-1}$, why do so many students get $p^{p-1}$? I saw this four or fives times in my office hours this week as students worked on the same problem. Not a single student spontaneously got this step right. Some write…
user507
13
votes
7 answers

When should we get into limits in introductory calculus courses?

All of the calculus textbooks I've used (teaching at community colleges) start with the first chapter covering limits. (Perhaps after a review chapter.) I think this order is wrong. Historically, Newton and Leibniz thought in terms of fluxions or…
Sue VanHattum
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13
votes
0 answers

Exercises to go with Simon's "Representations of finite and compact groups"

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had participated as assistant, but then discovered that it…
LSpice
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13
votes
3 answers

Moving From Rote Learning To Creative Thinking

My mathematics education was essentially rote, you learned the formulas and applied them almost algorithmically to the problems you were presented with; the teacher dictated a method and you followed it. This conveyed a dry and static picture of…
seeker
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13
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14 answers

What is the best way to intuitively explain what eigenvectors and eigenvalues are, AND their importance?

How can we break down the complexity of eigenvalues/vectors to something that is more intuitive for students. I feel like the proofy way isn't a good intuitive representation of the mechanism that eigenvalues/vectors represent. What are the best…