7

I like the idea here, but I agree that it misleads students, and might have the opposite of intended effect. Why not hand out a paragraph to the students, and ask them to critique it. Say that the paragraph is a fake student response to an exam question. One sentence in the paragraph could be something like ``Since $A \cap B$, there must be an $x$ so that $...


4

The US has different courses at different schools. Sometimes with same name but differences in content or prereqs. It would be more meaningful to sketch this tree for a given school. Or do a few schools. That should give you some feel for the general lay of the land. And I suggest to sketch it yourself, using a course catalog. You'll learn more doing a ...


2

I'll go with the common " '$=$' is a key on the calculator" misconception. Many students don't see a problem with and write down things like $$3 \cdot 4 = 12 - 5 = 7$$ when asked to calculate $3\cdot 4 - 5$. This error is caused (or at least reinforced) by the fact that "$=$" can in almost all cases be read as "calculate the left hand side and write the ...


2

Another example of this sort of issue: I have often seen students write things like $\frac84$ when they mean $4\mid 8$ (i.e., $4$ divides $8$.) It takes a while (for some) to see that the former has a numerical value, and the latter has a truth value.


1

If $A$ and $B$ are two disjoint sets, writing $A\cap B=0$. If $\ln x=2$ then $x=\dfrac{2}{\ln}$. How many corners a circle have? If $\sin x<\sin\frac{\pi}{4}$ than, after simplifying the sines, we get $x<\frac{\pi}{4}$. If $\frac{\pi}{6}<x<\frac{\pi}{3}$ then $\cos\frac{\pi}{6}<\cos x<\cos\frac{\pi}{3}$. What's wrong? I just added a ...


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