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1500 questions
12
votes
3 answers
Which math subjects should I know well to tutor competitive mathematics?
I may one day be interested in teaching students who are preparing for, say, the IMO or other math competitions. However, I haven't found a particularly clear statement about exactly what material is on it. I know they contain algebra, geometry,…
Addem
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12
votes
3 answers
Example of function with *all* the features of differential calculus at first-year level
I'm teaching a first-year calculus course, that is mid-way between a first intro to university-level calculus, and intro to real analysis (I'm based in Australia, for reference). We assume the intermediate value and extreme value theorems, but do…
David Roberts
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12
votes
4 answers
What should you do if you lose your student's exam?
Several times, I have come close to losing a student's Calculus exam. These exams are usually common exams, with everyone grading 100's of stacks. I've had exams go in wrong piles or get squished in the bottom of backpacks.
If an exam were lost in…
Brian Rushton
- 11,680
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11
votes
2 answers
Words used in quantifier proofs
I'm creating a list of "gotcha words" that are often used in writing proofs (particularly quantifier proofs), but frequently in more than one possible way, and that beginners frequently misuse or misunderstand. But it seems likely that there are…
Mike Shulman
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11
votes
1 answer
Method for teaching factorization
A while back I stumbled on teacher's website that advocated a different way to teach factorization. Rather than jumping straight to factorization practice, the teacher first had their student's practice finding pairs of numbers with a given product…
Nathan
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11
votes
2 answers
Visual questions for 6th graders
I'm tutoring a 6th grader in math at the moment and because she never has a ton of homework I like to give her some interesting extra problems to do. It seems she really enjoyed a problem I showed her the other day where we counted up how many ways…
user5726
- 111
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11
votes
2 answers
How to motivate 'Theory of Computation'?
I am teaching Theory of Computation for the first time soon, and need a short
introduction and justification to motivate students who have only Introductory Programming behind them.
I am torn between:
(1) Emphasizing the limits of computation,…
Joseph O'Rourke
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11
votes
1 answer
Has any research been done on the topic of "fact-based" versus "rule-based" understanding?
Consider the following piece of reasoning:
$$x+3 = 5$$
$$x=5-3$$
Based on my own experience back in school, and helping people with their math homework, as well as in talking to other people about math education, it seems that in the minds of most…
Jack M
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11
votes
1 answer
How to design exercise groups in very advanced course?
In very advanced courses, typically there are only a few students attending and sometimes they are not willing to put so much efford into the course to participate or to pass an exam.
So I made the experience that hardly anyone will do the…
Markus Klein
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11
votes
8 answers
Intergration by differentiating will get you $0$ marks - but how to explain why?
When integrating and differentiating, sometimes one direction is easy and the other is harder. A nice example is $\frac{d}{dx}\tan x=\sec^2x$, where differentiating is easy but integration (without knowledge of the other direction) is difficult. So…
user1729
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11
votes
4 answers
$1000 to spend on a math classroom?
Every so often I run across someone online asking what they should spend a sizable (but not enormous) amount of money on for their middle or high school math classroom. The dollar amount varies, but it's often in the 500 to 1000 dollar range. That's…
Justin Lanier
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11
votes
2 answers
Does "factor" mean simply the multiplication (of any functions, numbers etc)
I am sorry I am not directed with the education of math.
But granted, let me ask the above question.
In my language (actually Japanese), the words corresponding with the factor and divisor, seem to have come from English. (Not confirmed.)
Now when…
user5245
11
votes
1 answer
Solving linear equations by factoring
I usually teach solving linear equations by balancing both sides e.g.
$$\begin{array}{cccc}
2x&+&3&=&5\\
&&\color{red}{-3}&&\color{red}{-3}\\
2x&&&=&2\\
\color{red}{\div2}&&&&\color{red}{\div2}\\x&&&=&1
\end{array}$$
Recently I have been considering…
Karl
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11
votes
5 answers
A Method to Grade a Multiple Statement or True and False Question
I am trying to come up a method to grade a multiple choice question. I prepared a test that consists of some questions and each question has 10 options for which 3 to 5 options are correct. When I grade them, I want to give high points if the…
Co Koder
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11
votes
1 answer
Use of symbolic math apps in teaching
Symbolic math apps, such as Mathcad, are extremely useful in doing exploratory/experimental math. I've frequently used it to run numerical checks on mathematical expressions I've derived; put up quick plots to understand the qualitative behavior of…
Tom Copeland
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