"Is Zero a Number?": Interviews with a Whole Class of Kindergartners • Hacker News Board

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

#11

Post by ndsipa_pomu » Sat, Oct 28, 2023, 10:22 AM UTC

lionkor wrote: post #3

What a fascinating article, thank you! I see why we have exams in schools. Some of the kids just seemed to entirely miss what they were taught! 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.

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.

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

#12

Post by otteromkram » Sat, Oct 28, 2023, 10:22 AM UTC

I like how one of the students noted that his dad said some kids can be zero years old.

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

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

#13

Post by lozenge » Sat, Oct 28, 2023, 10:23 AM UTC

Good article.

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.

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

#14

Post by asddubs » Sat, Oct 28, 2023, 10:25 AM UTC

ndsipa_pomu wrote: post #8

bawolff wrote: post #6

I mean philosophically what is a "number" is a hard concept. I don't think any of the children saying 0 is not were really wrong so much as had a different definition of number. If you asked most adults what a number is, probably many would come up with a definition that didn't include i.

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.

maybe measuring is more accurate to say than counting. that way you include things like units of speed, and negative numbers (you can't really count -3)

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

#15

Post by pmontra » Sat, Oct 28, 2023, 10:26 AM UTC

The gist of it seems to be: intuitively zero is nothing and not a number but eventually you discover that it's useful to think about it and use it as a number so you change your mind, maybe without even noticing.

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 :-)

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

#16

Post by dkbrk » Sat, Oct 28, 2023, 10:30 AM UTC

> Yes, because you can add it to other things.

Good answer.

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

#17

Post by kaetemi » Sat, Oct 28, 2023, 10:32 AM UTC

bawolff wrote: post #6

I mean philosophically what is a "number" is a hard concept. I don't think any of the children saying 0 is not were really wrong so much as had a different definition of number. If you asked most adults what a number is, probably many would come up with a definition that didn't include i.

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

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

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

#18

Post by morsch » Sat, Oct 28, 2023, 10:35 AM UTC

kaetemi wrote: post #10

Try asking if B is a letter or a word. (Pronounce it as 'b', not 'bee', or you'll just make it more confusing.) 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?…

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.

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

#19

Post by baobabKoodaa » Sat, Oct 28, 2023, 10:36 AM UTC

I was genuinely impressed how good the "before" answers were. Many adults refuse to accept that they don't know something and will rather invent a fictitious answer, start believing in it and proclaim it as fact - but many of these kindergarteners actually said "I don't know". Stunning emotional maturity! Also, the ones who answered yes or no were mostly able to craft arguments supporting their position. I didn't know kids are that smart.

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

#20

Post by gizajob » Sat, Oct 28, 2023, 10:38 AM UTC

I feel like these children have been enlightened into number theory, but their original answers were nevertheless more correct than the later answers.