Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

jennalaib.wordpress.com

Post reply on HN
Print view View original

91–100 of 100 posts

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

#91

Post by ksaj »

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.

That's the argument in a nutshell. Is 10 a single number, or two numbers? In context, it is one number. But I digress because typing it out suggests it is two.

Would you rather have $100.00 or $0100?

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

#92

Post by ksaj »

c22 wrote: post #84
gizajob wrote: post #30

Earlier quoted context omitted.

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.

I agree, I thought a lot of the "before" answers were excellent and insightful. The teacher did these children no favors by foisting such a meaninglessly pedantic distinction on them at this young age. > “When we ask ‘how many,’ the answer is a number. How about a few is a few a number?

Fun way to look at it. In Common Lisp, NULL is not a number. But in Assembly language, it absolutely is.

Is "no" a number? As in "I have no apples." It is strange that we can't say "I have yes apples" otherwise.

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

#93

Post by ksaj »

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.

It's a number in Base 18.

Or is that my imagination?

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

#94

Post by ksaj »

wiredfool wrote: post #61
ndsipa_pomu wrote: post #42

Earlier quoted context omitted.

"Round number" is specifically an ambiguous terminology though. You could use "integer" instead, but it's really more to do with the concept of significant figures. e.g. 129 is an integer, but 130 is a "rounder number" than 129 and 100 is rounder still. To make it more confusing, decimal numbers ending in 5 (before the zeros) are often considered round, 150 is rounder than 130. However, mathematically there's a total…

8 is twice as round as 0. Source: parent of 3.

Technically 3 is equally round as 0, but half as round as 8. It's just split and flipped.

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

#95

Post by ksaj »

asddubs wrote: post #77
ndsipa_pomu wrote: post #71

Earlier quoted context omitted.

Yeah, but that's just an artefact of that particular scale. You'd have trouble measuring -5K

you can measure negative pressure, negative acceleration

I've read articles about negative Kelvin where they surmise it would get hotter. Keeping in mind what heat actually is, the atoms would just be out of phase.

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

#96

Post by thaumasiotes »

ksaj wrote: post #92
c22 wrote: post #84

Earlier quoted context omitted.

I agree, I thought a lot of the "before" answers were excellent and insightful. The teacher did these children no favors by foisting such a meaninglessly pedantic distinction on them at this young age. > “When we ask ‘how many,’ the answer is a number. How about a few is a few a number?

Fun way to look at it. In Common Lisp, NULL is not a number. But in Assembly language, it absolutely is. Is "no" a number? As in "I have no apples." It is strange that we can't say "I have yes apples" otherwise.

> It is strange that we can't say "I have yes apples" otherwise.

You do see ungrammatical "yes" applied sometimes when people are stumped as to how to indicate the opposite of a negative sentence.

It is not strange in general that certain things are, for no apparent reason, impossible to say. That occurs in every language. English modal auxiliaries, for example, do not have non-finite forms, so in many sentences it is mandatory to replace modal can with lexical to be able [to...]

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

#97

Post by LudwigNagasena »

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.

Digit is a symbol, number is a concept. It’s a map-territory distinction. While a single digit can be used to represent a numerical value, it isn’t a number per se.

You can’t really use the number 0 to make 100.

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

#98

Post by ndsipa_pomu »

ksaj wrote: post #95
asddubs wrote: post #77

Earlier quoted context omitted.

you can measure negative pressure, negative acceleration

I've read articles about negative Kelvin where they surmise it would get hotter. Keeping in mind what heat actually is, the atoms would just be out of phase.

Yes, temperatures below absolute zero are possible and have been achieved (something to do with flipping the high and low energy states), but I stand by my comment that it isn't easy to measure and definitely a far more advanced concept for kids than negative numbers.

https://en.wikipedia.org/wiki/Negative_temperature

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

#99

Post by nh23423fefe »

ndsipa_pomu wrote: post #54
thaumasiotes wrote: post #33

Earlier quoted context omitted.

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…

> it's the set of all points in a plane that are equidistant from two particular distinct fixed points I don't like that definition as how do you determine the distance from a fixed point without using a line? > it's the shortest path between two points, if you extend it to be infinitely long That's probably a better definition

You use the metric to the measure the distance. the Euclidian metric is the standard sum of squares.

for any pair of points P you can construct a pair of spheres centered on P1 and P2 and take the intersection to find points on the line.

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

#100

Post by kaetemi »

hnlmorg wrote: post #80
kaetemi wrote: post #69

Earlier quoted context omitted.

It is taught in primary school, yeah. I remember learning pseudo terminology like "do-words" for "verbs" in first and second grade. Pre-school they try to teach "reading" letters nowadays, but then they get drilled in that "A is for apple" and now the shape A could mean the sound apple, and they have even less of a clue on what letters are. (Even though in the 90s research already pointed out that reading should be t…

No, they get taught terms like verb, digraph, as well as the difference in sounds between an and A. They don’t even teach uppercase letters until long after kids have mastered lower case. The whole “Annie Apple” thing went out of favour years ago. UK primary schools are very jargon heavy these days and phonics is all about teaching lower case letters. My wife is a primary school teacher, a few of my friends are teach…

UK curriculum sounds good, then.

Where I live a lot of the pre-school kids are excessively exposed to YouTube, which is primarily still drilling on the uppercase alphabet songs.

Post reply on HN