I feel like these children have been enlightened into number theory, but their original answers were nevertheless more correct than the later answers.
Education is a serious of increasingly smaller lies
"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
#42I 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. :')
"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 totally different definition: A round number is a number that is the product of a considerable number of comparatively small factors. That means that 24 is rounder than 25.
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#43Earlier 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.
In this context, a line is what you draw with a ruler to get the correct answer.
My math teachers would have marked it incorrect if I didn't indicate it went on forever, unless the problem stipulated bounds.
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#44I 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…
Kids these days are indeed very willing to admit when they don't know things! I do suspect the openness is downstream of the slow cultural realization that there is just too much to know for any one human being to truly know it all. Smart parents are more willing than ever on the margin to say they don't know things, and the children learn from that example that this is okay to admit.
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#45Earlier 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? Most plots aren't lines, so there's no reason this task would require defining a line. In fact, the shape formed by a graph is called a "curve" for just this reason.
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Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#46Zero is interesting because it is the only natural number that is a cardinal number but not an ordinal number. An array can have zero (no) elements, but it can't have a "zeroth" element. Despite some programming languages suggesting otherwise.
Just imagine how perfect the world would be if we started counting at zero, though
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#47I 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…
"I didn't know kids are that smart." Yes!! I wish more people recognized this. There's a "Free Range Kids"[0] movement growing out of this fact. A lot of people have ended up in a place where unstructured/unsupervised time is seen as a "waste" for kids, but I think this is the wrong direction. I think Khan Academy's new experimental high school[1] is also built around this fact (that kids are smart & just need access to resources & meaningful work)
[0] https://www.freerangekids.com/ [1] https://khanlabschool.org/About-Khan-Lab-School
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#48It seems to me after the lessons, more students are in the "because you said so" camp whereas before the lesson they have more reasoning. I wonder, as parent, how much "indoctrination" and how much "reasoning" shall we impart to our children.
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#49The simplest definition of natural numbers is as the free algebraic structure generated by a nullary and unary operation (conventionally named "zero" and "succ"), which makes it natural to associate zero as the value of the nullary operation, so that one can be it's successor and addition by one works as expected.
Not having zero and associating one as the result of the nullary operation works as well, but then the natural definition of addition will result in x + y - 1 rather than x + y and it seems likely extension to rational numbers would not give an intuitive result.
Re: "Is Zero a Number?": Interviews with a Whole Class of Kindergartners
#50Good 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.
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).