By the way, some kids misunderstood the digit zero for the number zero.

> “Yes, you already asked me! It’s a number for nothing. You can use it to make 100.”

> “Yes, you already asked this! It’s in the number 10, so it must be a number. We don’t mix shapes like this.”

Imagine the surprise if told that A, B, C etc are also numbers :-)

So in this light this result is absolutely not surprising. In fact, it’s funny to see that the reason the answers changed is basically “because the school told me so”

Teacher, are you even paying attention? We've been over this.

At age 11, I went downstairs to announce I was ready for tomorrow's maths exam, where we would need to plot equations like y = x - 3.

My dad said, "well, here's my question - what is a line?"

This angered me greatly as I couldn't answer.

If you asked most adults what a number is, probably many would come up with a definition that didn't include i.

I don't disagree with how zero is used but the english language is the debate here not math. Zero is a legitimate concept in math, if a term describes certain things then is the concept of the lack of those things by default considered a member of those things? Sounds like a linguistic convention in part.

Why not have a separate term to describe zero and infinity as part of the same set, "anumerics"?

The teacher is acting as if its existence as a number is obvious.

They're still young enough to have not had every question they ever hear from an adult as something they'll be graded on yet. Pass or Fail. So when they don't know, they tell you and hope that you'll tell them or guide them to the right answer.

I personally believe this pressure in older kids and adults alike, to not FAIL (ie: not know the expected answer) is because of the way school tends to turn everything into a binary test. We are literally taught to avoid "I don't know."

I think zero is kinda strange in a way: it is intuitive mostly when thinking about quantities but when dealing with other concepts I find it strange to think about it. Here are some situations where I know how to answer but reasoning about it is still in a way hard:

N^0 or 0^N or 0! or or more simpler when thinking about limits and zero try to see what happens when you try to reach 0 while going like this 0.9^0.9, 0.8^0.8, … 0.001^0.001, 0.0001^0.0001

In most cases I think we are defining the answer. Maybe there are some complex proof for these answers but they only prove that zero is kinda hard to grasp.

Or it might be that I forgot a lot of math and I am wrong with these examples.

Not having zero and associating one as the result of the nullary operation works as well, but then the natural definition of addition will result in x + y - 1 rather than x + y and it seems likely extension to rational numbers would not give an intuitive result.

Seems a lot of these basic classifications are an early stumbling block. Even if they can count or rattle the whole alphabet, they haven't learned the meaning of the words "word", "letter", or "number" as terminology.

Initially sentences/words/letters/numbers are all just 'sound'. "What's the sound of this?" is equivalent to "Read this."

The phrase highlights the concept of whole vs. fractional numbers.

The way kids approach these questions are very telling on how to teach them, and that teaching math in particular is about understanding, not memorization.

Good answer.

You want something like "it's the shortest path between two points, if you extend it to be infinitely long", which glosses over how you know how to do that correctly, or "it's a 180 degree angle" [same problem].

What did your dad say?

This question reminds me that one of Euclid's postulates was "all right angles are equal". We don't consider that an axiom today, and we don't understand why, in Greek mathematics, this was considered to require noting, or what exactly it meant to them. They obviously had something in mind when they said this, but we don't know what that was.

Thinking of a line as being defined by the 180 degree angle it forms at every point of itself feels like a similar sort of thing to whatever it was that the Greeks were thinking about right angles.

When I fist was interested in NLP, I thought "word" was easily defined as "sequence of letters bounded by non-letters". But we don't normally pronounce spaces, do we? AndyoucanwritewithoutspacestoindicatespeakinglikeYahtzeeCroshawonZeroPunctuation. And when we've got a contraction, is that "we've" two words or one? Compound words in general, for which German is famous ("Antibabypille") but that's also present in English ("antidisestablishmentarianism", or less severely "internet" and "smartphone")? What about single nouns with spaces in the middle like "remote control" or "mobile phone")? And as my original definition was letters, what about the apostrophe in "we've" or "O'Neil", or the hyphen in older posters saying "to-day"? If all names are words, what about numbers in product names such as "iPhone 15"?

And all those pedants complaining about "to boldly go" in Star Trek because of the split infinitive; I'm told that's because infinitives in Latin were single words and therefore un-splittable, but should admit that I don't know Latin and I don't care to learn it.