Study Suggests the Number-Line Concept Is Not Intuitive 404
An anonymous reader writes "The Yupno people of New Guinea have provided clues to the origins of the number-line concept, and suggest that the familiar concept of time may be cultural as well. From the article: 'Tape measures. Rulers. Graphs. The gas gauge in your car, and the icon on your favorite digital device showing battery power. The number line and its cousins – notations that map numbers onto space and often represent magnitude – are everywhere. Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don't stop to wonder: Is it 'natural'? Is it cultural? Now, challenging a mainstream scholarly position that the number-line concept is innate, a study suggests it is learned."
The Story of 1 with Terry Jones (Score:5, Interesting)
Anyone who has ever taught math knows this (Score:5, Interesting)
Try getting a bunch of 10-year-olds to understand the number line concept and you will find out in approximately 3 seconds that it is not innate.
Counting? (Score:5, Interesting)
Logarithmic vs linear scale (Score:5, Interesting)
Re:Counting? (Score:5, Interesting)
Re:Counting? (Score:4, Interesting)
ask your non-nerd friends (Score:4, Interesting)
I once took a course in "Math philosophy" (a simple introduction course, with e.g. Gödel numbers, introduction to infinity, and things like that), and at the end of that course we were asked to write about something. I decided to ask friends about how they viewed numbers. To my surprise, everyone had pretty much their own unique way. I think I asked about 10 people. Some viewed numbers as colors ("the number 2 is of course blue" or something along that line), some viewed the numbers as on a traditional line, one guy thought of the numbers as being in a circle and you took one out as you wanted to use it and then had to put it back. Not everyone included the number zero (or negative numbers) in their explanation. My self, I see the natural numbers on a line, but the line has "angles" at the numbers 10 and 20. Perhaps this is because in my native language, the spoken words for 10..19 are not constructed in the same simple manner as 30..39, 40..49, and so on.
That was the Peano Construction, not ZFC (Score:5, Interesting)
You can tell it was supposed to be the Peano construction (and not something else) because the GP defined zero as the empty set and 2 as {0,1}. The error was to also define 2 as {{{}}}, which is clearly not equivalent to {0,1} (since the former set has cardinality 1 and the latter has cardinality 2).
This is an incredibly common mistake even for math undergrads and good evidence that set theory really isn't very intuitive. There's a reason New Math failed.
They have the problem ass backwards. (Score:4, Interesting)
Well, numbers are abstract. I'm not sure how a number line representation, which can take real shape would be an intuitive extension of an artificial concept. It isn't. Actually, it's the other way around, I would think. The number lines help us understand numbers and it's numbers that aren't intuitive.