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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

#81

Post by gls2ro »

(My math is probably old and maybe I forgot some things)

I think zero is kinda strange in a way: it is intuitive mostly when thinking about quantities but when dealing with other concepts I find it strange to think about it. Here are some situations where I know how to answer but reasoning about it is still in a way hard:

N^0 or 0^N or 0! or or more simpler when thinking about limits and zero try to see what happens when you try to reach 0 while going like this 0.9^0.9, 0.8^0.8, … 0.001^0.001, 0.0001^0.0001

In most cases I think we are defining the answer. Maybe there are some complex proof for these answers but they only prove that zero is kinda hard to grasp.

Or it might be that I forgot a lot of math and I am wrong with these examples.

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

#82

Post by gizajob »

thaumasiotes wrote: post #64
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.

> 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.

Not in an empty universe.

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

#83

Post by thaumasiotes »

masklinn wrote: post #50
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…

> This question reminds me that one of Euclid's postulates The question is one of Euclid's postulates (or the combination of two, 1 which defines a straight line segment, and 2 which extends the straight line segment to a straight line).

Postulate 1 doesn't define a straight line segment. It tells you that it's possible to connect two points with a straight line segment. A definition would tell you whether or not something qualified as a straight line segment.

The definition appears to be given, appropriately enough, in the "definitions" section that precedes the postulates, which says "a straight line is one which lies evenly with the points on itself". (As translated in https://farside.ph.utexas.edu/books/Euclid/Elements.pdf )

But although that is indeed how people recognize lines, it's not so easy to define what it means.

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

#84

Post by c22 »

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.

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?

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

#85

Post by areyousure »

pmontra wrote: post #53
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.

I concede that my opinion is worth very little to nothing and I didn't even check what's the mathematical consensus on this matter, but when one sees that 1100, 110, 30, 22, 20, 15, 14, 13, 12, 11, 10, A are all the same number one starts thinking about the difference between symbols as numbers and symbols as digit. I hopefully didn't make mistakes in the several representations of twelve.

You probably meant "C" as the final one, instead of "A": https://www.wolframalpha.com/input?i=12+in+base+13

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

#86

Post by pmontra »

areyousure wrote: post #85
pmontra wrote: post #53

Earlier quoted context omitted.

I concede that my opinion is worth very little to nothing and I didn't even check what's the mathematical consensus on this matter, but when one sees that 1100, 110, 30, 22, 20, 15, 14, 13, 12, 11, 10, A are all the same number one starts thinking about the difference between symbols as numbers and symbols as digit. I hopefully didn't make mistakes in the several representations of twelve.

You probably meant "C" as the final one, instead of "A": https://www.wolframalpha.com/input?i=12+in+base+13

Yeah, a made a mistake on the easiest base

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

#87

Post by hhjinks »

ndsipa_pomu wrote: post #70
hhjinks wrote: post #62

Earlier quoted context omitted.

0 is round because it's a circle.

Except that it isn't

People use the euclidean definition of circle in common parlance? If I can have dark circles under my eyes, then my zeroes can be circles too.

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

#88

Post by ksaj »

In my younger days, I was a Beaver leader. Beavers are Boy Scouts in the 5-6 age group. They are not empty headed. They are extremely inquisitive and easily understand things that are surprising to adults. I would even say on average, their observational skills are better than those seen in adulthood.

They're still young enough to have not had every question they ever hear from an adult as something they'll be graded on yet. Pass or Fail. So when they don't know, they tell you and hope that you'll tell them or guide them to the right answer.

I personally believe this pressure in older kids and adults alike, to not FAIL (ie: not know the expected answer) is because of the way school tends to turn everything into a binary test. We are literally taught to avoid "I don't know."

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

#89

Post by ksaj »

lozenge wrote: post #57
baobabKoodaa wrote: post #19

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 kno…

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.

When they started adding the possibility of a "FAIL" to their tests.

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

#90

Post by ksaj »

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…

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.
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