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

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

#21

Post by thaumasiotes »

pmontra wrote: post #15

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 numbe…

> 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.

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

#22

Post by boomboomsubban »

lozenge wrote: post #13

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.

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.

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

#23

Post by LudwigNagasena »

asddubs wrote: post #14
ndsipa_pomu wrote: post #8

Earlier quoted context omitted.

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)

That means "huge" and "small" are numbers.

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

#25

Post by ndsipa_pomu »

asddubs wrote: post #14
ndsipa_pomu wrote: post #8

Earlier quoted context omitted.

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)

Yes, measuring is a more advanced concept than counting as it introduces fractions. I don't think simple measuring would include negative numbers though as that would include a measuring direction concept (i.e. vectors) as rulers don't have negative numbers on them and you can't have a speed of -5kph.

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

#27

Post by gizajob »

yodsanklai wrote: post #24

It's a philosophical question which is always fun to think about. As far as teaching maths is concerned, I don't know if it's needed to think too much about it. Could it even be more confusing for kids?

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.

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

#28

Post by hnlmorg »

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?…

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.

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

#29

Post by ben_w »

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?…

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.

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

#30

Post by gizajob »

thaumasiotes wrote: post #21
pmontra wrote: post #15

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 numbe…

> 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.

They’re also correct in saying it represents pure, unadulterated nothingness though. The teacher is confusing number theory with reality by limiting them in the way she does.
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