"Is Zero a Number?": Interviews with a Whole Class of Kindergartners

"I didn't know kids are that smart." Yes!! I wish more people recognized this. There's a "Free Range Kids"[0] movement growing out of this fact. A lot of people have ended up in a place where unstructured/unsupervised time is seen as a "waste" for kids, but I think this is the wrong direction. I think Khan Academy's new experimental high school[1] is also built around this fact (that kids are smart & just need access to resources & meaningful work)

[0] https://www.freerangekids.com/ [1] https://khanlabschool.org/About-Khan-Lab-School

At that age, isn't not knowing the default, and experienced many times every day? I wonder when we swap to assuming we know or can deduce everything.

Kids these days are indeed very willing to admit when they don't know things! I do suspect the openness is downstream of the slow cultural realization that there is just too much to know for any one human being to truly know it all. Smart parents are more willing than ever on the margin to say they don't know things, and the children learn from that example that this is okay to admit.

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

That's not a misunderstanding. Place-value notation requires that digits are numbers. The fact that 10 is a number doesn't mean that the 0 within the 10 is not also a number; the kindergartener is correct in saying that that location means the 0 is a number.

Imagine the surprise learning that anything other than combinations of 0's and 1's are not numbers. For the same reason, but more extreme and in the other direction.

The simple answer is "it's the set of all points in a plane that are equidistant from two particular distinct fixed points", but that just gives you a clean definition that won't capture any of the properties that make lines interesting.

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.

That doesn't really make sense. How did they explain what plotting was without defining a line? I guess they could have taught how to plot a line segment then explained they go on forever.

Terminology questions are very very ambiguous in general without academic context bias.

Ask toddlers if 0 is a round number. :')

Probably the simplest concept is that they're for counting things, but that doesn't lead to a clear answer as to whether you can count zero things. When you count things, zero has a physical meaning (if you have one apple and give it away, how many apples do you have?), so maybe they should be considering it a number, but not negative numbers until they get a more abstract understanding.

It's a number in Base 18.

Or is that my imagination?

Education is a serious of increasingly smaller lies

My experience of education in the UK is that reasoning and questioning were actively discouraged by some teachers. They were pressured to go through course material quickly, and having students presenting counter-arguments would slow things down.

I think giving them a clear, limited definition when their original answers were more intuitive is the part that introduces the confusion. Toddlers and kindergarteners are always bang on the money and don’t mess around where it comes to confusion, they have other things going on. That is to say, I’ve found that asking under sevens questions in ethics is always a brilliant process - where a professor could spend thousands of words on an article on something like the trolley problem, preschoolers just pull the lever.

Indeed, but even the standard definitions are flawed.

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.

Once you get into academic linguistics, determining what's a letter and what's a word gets very murky again. And you mostly just don't use those categories and talk about phonemes and utterances instead, ie. sound.

My wife is a primary school teacher and I assure you, UK kids are taught terminologies. I don’t think they were when I was a kid but curriculums change.

Yeah cool dad award. I wonder how many hours of questioning came from the back of the car before he explained it.

They may have missed what the teacher was trying to convey but this serves as an example, to me, of how some people just think differently. The girl who was fixated on shape, for instance. She saw two zeros making an 8. I think we need to be able to recognize early on that some people think differently than the "typical" person, and that they should be understood and perhaps taken down an educational path that fits their mind instead of just trying to pound the correct answers into their head. Sure, teach them the concept of zero as a number, but also recognize that these people are not typical.

I used to assume that all humans had an internal dialog. This is not the case. Although most do, some people do not or cannot talk to themselves silently in their own head. This blew my mind. I viewed this as the core of being human.

I had been interviewing for jobs and found that my internal dialog would kick in and just wreck my shit during interviews. After learning that some people don't have this I considered that I can just shut mine off if I need to. Basically telling myself to shut up. This did wonders for me, and helped me stay on track during interviews and helped to stop negative thoughts that I might have at other times. The internal dialog has value, but I have learned to control it because I no longer consider it essential to being human. This had just never occurred to me before.

The point is, there is neurodivergance in humans. We do not all think the same and trying to mold all children into a thinking the same "correct" way is rather barbaric. Failing to acknowledge that people think differently on a fundamental level is also hurting everyone in some way.

Some people can't see images in their head. Again, I had always assumed that all humans could picture anything they wanted, not true. And often these people are visual artists!

Personally, I think exams are a horrible way to determine what people have actually understood. Most school exams are just looking for specific "magic" words that are learnt by rote. Questions might be set up to ask why water appears on the outside of a cold glass and the answer would be considered correct if the answer used the word "condensation" without needing any concept of humidity.

Just imagine how perfect the world would be if we started counting at zero, though