Jasper
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12 answers
16 votes
7k views
Is there a simple example that empirical evidence is misleading?
Accepted answer
29 votes

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 ...

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5 answers
7 votes
830 views
In teaching mathematics, should one always follow some international standards such as ISO 80000-2?
14 votes

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 ...

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9 answers
14 votes
6k views
Why do inequalities flip signs?
12 votes

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, "...

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6 answers
17 votes
5k views
How to deal with a "protest" assignment?
7 votes

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 "...

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7 answers
6 votes
1k views
Are these fraction problems different enough to warrant individual consideration?
6 votes

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 ...

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5 answers
13 votes
356 views
How to read chained equalities out loud?
6 votes

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 ...

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4 answers
17 votes
4k views
Why we don't normally teach chord, versine, coversine, haversine, exsecant, excosecant any more?
6 votes

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 ...

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1 answers
4 votes
97 views
Can we use "specific" and "particular" interchangeably all the time?
6 votes

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: ...

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3 answers
3 votes
784 views
The term "unique" for functions and operations
5 votes

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 ...

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4 answers
6 votes
576 views
How to make a mathematical dynamic graph?
4 votes

Somewhere in the comments somebody asked the same question and this link is the answer: https://talkingphysics.wordpress.com/2018/06/11/learning-how-to-animate-videos-using-manim-series-a-journey/ A ...

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2 answers
4 votes
411 views
How many hours / school years does it take for the average child to memorize the $10\times 10$ addition and multiplication tables?
4 votes

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 ...

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4 answers
7 votes
420 views
Writing up a proof that assumes what is to be proven?
4 votes

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 ...

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3 answers
5 votes
405 views
Limit of questions that a student should ask in class without upsetting professor?
4 votes

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 ...

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2 answers
4 votes
887 views
Software to make illustrations for exercises
4 votes

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 ...

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2 answers
0 votes
113 views
Pro's and cons of number line model vs color counter model
2 votes

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 ...

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2 answers
2 votes
179 views
Urn (containing colored balls) generator?
Accepted answer
2 votes

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

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1 answers
10 votes
370 views
Where can I find a set of these 'logic' blocks?
Accepted answer
2 votes

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 ...

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15 answers
16 votes
27k views
How to explain the difference between the fraction a / b and the ratio a : b?
2 votes

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, ...

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3 answers
10 votes
390 views
Framework for Compound Inequalities
1 votes

"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 $\...

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7 answers
5 votes
374 views
Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)
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\...

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3 answers
3 votes
103 views
How to verbalize the correct statement of mixed units?
1 votes

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 ...

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4 answers
6 votes
412 views
Why do standard geometry textbooks not start with trigonometry?
1 votes

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 ...

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6 answers
2 votes
284 views
Which examples should we mention when teaching the concept of derivatives?
1 votes

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 ...

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2 answers
4 votes
867 views
Should young math students be taught an abstract concept of form?
1 votes

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 ...

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2 answers
3 votes
367 views
How is it correct for a lecturer to prove and "explain" a proof while explicitly knowing students are not familiar with logic itself?
1 votes

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 ...

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6 answers
17 votes
1k views
How to teach students when they can and can't cancel factors in a fraction?
1 votes

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 ...

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20 answers
31 votes
4k views
How to explain that a negative number multiplied by a negative number is a positive number, and that $-(-x)=x$?
1 votes

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)...

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6 answers
8 votes
479 views
Definitions of factors and terms
0 votes

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 ...

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5 answers
6 votes
423 views
How to define "axes with the same scale" in Secondary/High School?
0 votes

Since the axes you're talking about are real things on paper or on a screen, I think it's easy and I'd go with something very similar to your proposal: A coordinate system has axes with the same ...

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6 answers
4 votes
3k views
How to convince students of the implication truth values?
0 votes

You can introduce implication and equivalence side by side to make the difference clear. Implication: If A, then also B. (But if not A, this statement does not tell us anything. See the umbrella ...

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