7k views

There are some collections of such examples at sister sites: Conjectures that have been disproved with extremely large counterexamples? at Mathematics Stack Exchange. Examples of eventual ...

830 views

No. This standard may be useful for professionals in international settings. Most teaching happens in smaller, localized settings and things will differ from country to country (e.g. how large ...

6k views

Depending on the context and the previous curriculum, the following might work: "less than" means "to the left of" on the number line. Multiplying by a negative number flips numbers around 0. Thus, "...

5k views

Now the problem is, I announced that assignments are graded by completion. I don't see a problem if you were clear about how the assignments will influence the final grade, perhaps something like "...

1k views

This depends on when in the "fractions curriculum" this happens. If the children know that "a fraction of" really means to multiply by this fraction, then all problems are equal ...

356 views

When an inexperienced student sees $a=b=c$, I'd assume that both $a=b$ and $b=c$ are clear but the transitivity that yields $a=c$ might not be obvious. That's why I'd focus on this hidden equality ...

4k views

Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point. To the ...

97 views

As a non-native speaker I'd tend towards particular in this context. Any 2x2 matrix would be a specific matrix, but the one used by the student was a particularly bad example. Citing Merriam Webster: ...

784 views

In Germany, we already do this. A function is introduced as an unambiguous mapping in 7th grade (~13 years). While I don't have any data on this, I doubt that German students do significantly better ...

576 views

411 views

Assuming that the German "Kerncurriculum" (actually, there are 16 of them, one for each federal state. I'm referring to the one from Lower Saxony) for primary school is at least somewhat tailored for ...

420 views

I think there are two problems that have to be addressed individually: Wrong usage of implications. Implications just don't describe a relation between terms of the kind that appear here. They can be ...

405 views

I think this depends a lot on the type of questions (or rather prompts); If you keep asking the professor "again, please", you shouldn't do it perhaps more than once. Most likely, (s)he will repeat ...

887 views

I think this depends on your kind of math and physics problems, but GeoGebra and Inkscape can be used to create graphics that can be exported in vector and pixel formats. If you need a strictly ...

113 views

As someone who never heard of the color counter model, I find it overly complicated. I assume that the question is asked in the context of signs when multiplying integers. While both methods arrive at ...

179 views

I whipped up this: urn creator. Maybe it's useful. Feel free to suggest improvements.

370 views

There are several vendors, but I was unable to find shapes that differ in holiness. Instead, they are different in size, color, shape and thickness. They seem to go by the name attribute blocks or ...

27k views

After thinking a while about this question, here comes my first answer on matheducators.SE: First of all, I would leave out ratios entirely, if possible. They aren't as expressive as fractions are, ...

390 views

"By default", all chained inequalities can be considered as illegal, because from an computer scientist's point of view and assuming that $<$ is left-associative: $a<b<c$ simplifies to $\... View answer 7 answers 5 votes 374 views 1 votes I'll go with the common " '$=$' 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\...

103 views

Assuming this is about some kind of exam: If there's still time in class to clear this up, use it. Explain why one might consider 1 foot 13 inches as bad and why 2 foot 1 inch might be better than 25 ...

412 views

Anecdotal evidence from Germany: congruence is taught way before trigonometry (~7th grade vs ~9th grade for trig functions) Why is the course focused more on memorizing theorems rather than ...

284 views

To emphasize the importance of rate-of-change vs. actual value a graph of the world population can be useful. The world population now is more than 100 years ago, but more importantly the derivative ...

867 views

I think an "abstract concept of form" is not helpful in mathematical education up to university level. To quote YiFans comment, I honestly think all this hype about "point slope form", "vertex ...

367 views

A mathematical proof has (among others) the purpose to convince someone of some fact, given some already established facts. Whether or not a proof is valid does not depend on who presents it. That is ...

1k views

I agree with some other answers that "cancelling" is a misleading word. As a non-native speaker I resort to Wikipedia and find that reducing or simplifying would be the preferrable word here. That ...

4k views

Here is another way to show/prove this by treating multiplication as repeated addition: Consider $3 \cdot 5 = 5+5+5 = 15$ as "adding $5$ three times". Now \$3 \cdot (-5) = (-5) + (-5) + (-5) = (-15)...

479 views

In my experience (German high school teacher): A factor is an operand in a multiplication and I would identify 5, a, b and (x+y) as factors. For "term", I'm aiming for a distinction between ...

423 views