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

61–70 of 100 posts

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

#61

Post by wiredfool »

ndsipa_pomu wrote: post #42
kaetemi wrote: post #17

Earlier quoted context omitted.

Terminology questions are very very ambiguous in general without academic context bias. Ask toddlers if 0 is a round number. :')

"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.

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

#62

Post by hhjinks »

ndsipa_pomu wrote: post #42
kaetemi wrote: post #17

Earlier quoted context omitted.

Terminology questions are very very ambiguous in general without academic context bias. Ask toddlers if 0 is a round number. :')

"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…

0 is round because it's a circle.

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

#63

Post by [deleted] »

ndsipa_pomu wrote: post #52
boomboomsubban wrote: post #22

Earlier quoted context omitted.

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.

> How did they explain what plotting was without defining a line? Plotting is simply putting a point for a specific value. Drawing the line is inferring the un-plotted points from the plotted ones which may or may not be correct though for y = x - 3, it's easy enough to prove that a straight line covers all the solutions. If "plotting" is only defined in terms of lines, then a student could attempt to plot y = x ^ 2…

[deleted]

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

#64

Post by thaumasiotes »

gizajob wrote: post #30
thaumasiotes wrote: post #21

Earlier quoted context omitted.

> 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.

> They’re also correct in saying it represents pure, unadulterated nothingness though.

This makes me hesitate. For example, if I ask you how many quiches there currently are in your refrigerator, it does not follow that nothing is currently in your refrigerator. The zero is bound to the unit it measures.

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

#65

Post by lionkor »

ndsipa_pomu wrote: post #11
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.

I believe this is an issue of how exams are done. There are certainly exams I've written, in Math, in English, in Philosophy, that tested my understanding, and there are certainly some that didnt.

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

#66

Post by masklinn »

ndsipa_pomu wrote: post #58
masklinn wrote: post #51

Earlier quoted context omitted.

Interestingly in Elements that is a line: a line was defined only by having no breadth (= being 1-dimensional). What is now generally called a line would have to be qualified as straight.

Does that mean that a point is also a line as a point has no breadth

No because a line does have a length. In Elements a point is dimension-less.

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

#67

Post by ndsipa_pomu »

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.

Precisely. With ambiguous terminology, that seems perfectly logical to me.

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

#68

Post by asddubs »

ndsipa_pomu wrote: post #25
asddubs wrote: post #14

Earlier quoted context omitted.

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.

you can measure -5°c though

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

#69

Post by kaetemi »

hnlmorg wrote: post #28
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.

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 taught with complete lowercase words instead of by letter picking.)

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

#70

Post by ndsipa_pomu »

hhjinks wrote: post #62
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…

0 is round because it's a circle.

Except that it isn't
Post reply on HN