# All Questions

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### “We already passed that course!” How to overcome this?

I've heard the phrase "we passed that course already!" too many times when asking for e.g. the derivative of a simple rational function or a simple integral, getting blank stares, and digging deeper. ...
955 views

### A Series of Unfortunate Examples!

All of us know, when teaching, the "right" choice of examples is important. Though, making the "right" choice is one of those things that are easier said than done. Here is the ...
4k views

My daughter showed me the picture below, which came from 9GAG. It shows a question on an exam asking the student to "use the repeated addition strategy to solve: 5 x 3." The student answered "5+5+5" ...
1k views

### What are the historical reasons for the hostility against standardized testing in the US?

NB. Some answers appear to be for a question I did not ask, namely, "Why is standardized testing bad?" Indeed, these answers tend to underscore the premise of my actual question, which can ...
18k views

### How does one explain that transformations 'inside' a function operate in the opposite direction than intuition suggests?

Consider a real function $f(x)$ and imagine its graph in the plane. Then the graph of $f(x+2)$ is simply the graph of $f$ shifted to the left 2 units while the graph of $f(x-2)$ is that of $f$ shifted ...
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4k views

### What is a free and simple 3D plot software for students?

I need any plot software on Linux or Windows that my students should use it for plotting 3D functions. I want introduce any software that be free and useful for bachelor students.
3k views

### What books are like Knuth's Surreal Numbers?

I'm looking to find more examples of books which bridge the gap between "story" and "mathematics" using narrative and all those other wonderful features we might find in Harry Potter or some other ...
2k views

### How to motivate equivalence classes

Equivalence classs are very useful in mathematics, but many of the applications require further background, like quotient spaces in topology or quotient groups in algebra. One good example is residue ...
How to convince a middle school student that $0.50=0.5=0.500=\cdots$? I used the fact that $0.50=\frac{5}{10}+\frac{0}{100}=\frac{5}{10}=0.5$ but that far from intuitive. Then I tried to explain ...