Slashdot Mirror

← Back to Stories (view on slashdot.org)

Study Suggests the Number-Line Concept Is Not Intuitive

Posted by samzenpus on from the learning-to-count dept.

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."

9 of 404 comments (clear)

  1. The Story of 1 with Terry Jones by StarWreck · · Score: 4, Interesting

    I just watched a documentary about this on Netflix, called The Story of 1, starring Terry Jones of Monty Python fame.I think it mentioned the ruler wasn't invented until sometime in ancient egypt.

    --
    ... and in the DRM, bind them.
  2. Anyone who has ever taught math knows this by Anonymous Coward · · 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.

  3. Counting? by deodiaus2 · · Score: 5, Interesting

    I wonder how far this goes! Is the notion of the counting numbers innate? I have heard that monkeys cannot count beyond 4. The way that people figured this out is that if five hunters go into a forest as a group, split up and hide. Then one by one, four hunters leave one at a time. The fifth hunter stays in hiding, the monkeys come out of hunting, and the hunter shoots a monkey. This does not happen when there are less than five hunters initially.

    1. Re:Counting? by blankinthefill · · Score: 5, Interesting

      Numbers are not an intuitive concept. As I've learned more and more math, I've had numerous discussions about this topic. The conclusions that tend to be reached are that sets are intuitive. A set is very intuitive, it's just a bunch of objects that are grouped together. You may not THINK of these things as sets, but that's what they are. You have a pile of apples, or a herd of sheep, or a group of hunters. Those are all sets of objects (or some philosophers would argue that there's a difference between the set and the group of physical objects, but I don't think that this ruins the intuition here). You can also label those things however you want, or not label them at all. Very intuitive. But numbers are when intuition starts to get messed up. A number can be disassociated from a concrete set, and that can make it hard to deal with, if you're not used to it. What is 1? What does it mean? What does it even mean to talk about 1 sheep, if it's completely hypothetical? There's no concrete sheep there, so what does it MEAN to be talking about 1 sheep? It's not even like you're talking about a sheep that's going to be born, or that belongs to your neighbors. This sheep is basically just imaginary. That's really a huge jump in cognition, especially when you start to consider other crazy things about numbers, like what's the biggest number, and what's a negative number, and what if you can't divide your numbers evenly. Anyways, nothing scholarly to back this up, just my experience in mathematics :)

    2. Re:Counting? by blankinthefill · · Score: 3, Interesting

      The problem with this argument is that it assumes that set THEORY is intuitive, which I do not agree with. While a SET is an intuitive concept, the ZF axioms of set theory and what they imply are NOT intuitive. There may be basic operations that are more intuitive, like the union of two sets or the intersection of two sets, but that intuition is almost entirely tied to the physical manifestation of the set. As soon as you introduce the formal idea of a set, especially as an abstract construct, I believe that, just like what I said about numbers, you remove a large amount of the basic intuition behind them. While a lot of the things that happen here seem intuitive to us, I feel like that is almost solely due to the fact that we are introduced to this abstraction at such an early age, and we deal with it so much, that we internalize it. Without that exposure, I'm not so sure the abstractions of sets and numbers is totally intuitive.

  4. Logarithmic vs linear scale by tukang · · Score: 5, Interesting

    The same subject has been covered in "Here's looking to Euclid". It describes tests done on an Amazon tribe to see how they visually interpret numbers. Unlike most modern adults who visualize number spaced linearly, they visualized them spaced logarithmically. Their reasoning was that the intervals between numbers start (relatively) large and become smaller as the numbers get larger. i.e. from 1 to 2 it's a 100% increase but from 2 to 3 it's only a 33% increase and so on.

  5. ask your non-nerd friends by gavare · · 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.

  6. That was the Peano Construction, not ZFC by TheEmperorOfSlashdot · · Score: 4, Interesting

    It also contains an error: Peano defined 2 as { {}, {{}} } = {0,1}. 3 is 2 U {2} = { 2, 1, 0 }. Larger numbers are defined inductively as (n+1) := n U {n}.

    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.

  7. They have the problem ass backwards. by janimal · · Score: 3, 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.