Slashdot Mirror
Study Suggests the Number-Line Concept Is Not Intuitive
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."
Any measuring cup will tell you a number line can be very intuitive. Stacking objects, filling a container; many everyday tasks are perfect physical examples of a number line.
Rulers are another example, though perhaps a bit less physical or intuitive.
How can I believe you when you tell me what I don't want to hear?
I don't have the reference to hand but I recall there is a South American tribe which don't have words for left and right as most languages do. There words are equivalent to "Up Valley" and "Down Valley" Similarly, if I recall correctly, there's a Native American language that uses before and behind as an analog for time but the other way around to most languages. Their analogy is that you know the past and you can see what it in front of you so forward = the past. You can't see behind you and you don't know the future so behind = the future
I don't know why this result is surprising. I thought it was generally understand that counting (there are 10 sheep) and measurement (this fence is 10 feet long) were distinct concepts. The point of the number line is to establish a relationship between the two concepts.
Come to think of it, it should be obvious that a number line relates two distinct concepts, just from the form they usually take. A number line, with its regularly spaced markings perpendicular to the main line, has a form similar to that of a line graph, which shows a relationship between two distinct variables.
If your 10 year old doesn't ALREADY understand the number line, you have failed. Hell, if your 6 year old doesn't understand it, you've failed.
I don't get your comment. I teach math to six year olds once a week. They "get" the number line, in that they use it as a useful tool for calculation, and can understand how numbers equate to divisions on the paper. Is it innate? Probably not. Is it something that many six year olds in the US culture have? From my experience, yes.
Where the article veers into the absurd is the suggestion that we should consider "bringing the human saga" into teaching math, and that math isn't objective fact, or black and white. Math is freaking math. There is right and wrong, black and white.
No. The science which maps real-world phenomena onto artificial symbols and concepts is known as physics. Mathematics is only concerned with the artificial symbols and concepts, independent of whether they can be mapped to real-world entities (many things cannot).
Yes. And mathematics is about the map and its rules, without caring about the territory, or even if it corresponds to a territory at all. If you want to learn about the territory, use physics. And yes, you'll use maps (i.e. mathematics) there, too. But those maps are not arbitrary, but carefully adapted to the territory as far as we know it, and actively developed to improve how well it maps the territory.
So in the map/territory picture you have:
Mathematics: The science of maps. Doesn't care about what the maps mean, or if they mean anything at all. As long as a map is consistent, it is accepted as valid map.
Physics: The science of territory. Uses maps to describe the territory. A map is considered valid only if it describes the relevant aspects of the mapped territory sufficiently well.
"Logically consistent" and "able to be used to prove its own consistency" are not the same thing.
You Forth about talking are, I think is what you're aiming for. Your sentence came across as more German than RPN.
No, not joking. There already have been studies that show different cultures have different counting systems. For example, many cultures will have only the most basic of numbers (1, 2, 3, 4, 5) and then jump into the "many" category. Another example of the non-intuitive nature of numbers? 0. That one took a while to catch on. Third example? Describe to me a forest with -10 trees or a person with -1 apple. Negative numbers were not intuitive either. Notice I am avoiding those wonderful numbers like fractions, irrational numbers (pi, e, the square root of two, etc), and complex numbers (i, the square root of -1... graph that on your number line!) - all of which are not intuitive in and of themselves. Final example? If numbers are intuitive, why does it take so long to teach our young to count? Why do so few people understand the concept of billions and trillions of dollars of debt, or the vast distances of the universe, or the very tiny number which represents the time in which million/billion/trillions of molecules collide and interact when undergoing an exothermic reaction?
No, while you have been educated and indoctrinated into a system of numbers, that does not mean it is intuitive. Or another way to think of it - take the pro basketball player who has taught his muscles how to shoot a 3-pointer... he might argue that it is intuitive, meanwhile someone like me (who couldn't make a freaking free-throw shot) would say that it is definitely not intuitive.