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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."

11 of 404 comments (clear)

  1. 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.

    1. Re:Anyone who has ever taught math knows this by Anonymous Coward · · Score: 5, Insightful

      Math is a set of ways of mapping some of the real world into a world of artificial symbols and concepts.

      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).

      "The map is not the territory"

      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.

  2. Re:The Story of 1 with Terry Jones by Anonymous Coward · · Score: 5, Funny

    I thought the concept of "ruler" started with King Arthur, after a watery tart lobbed a scimitar at him.

  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 pthisis · · Score: 5, Funny

      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.
      I should hope not: if there are four hunters initially, then one by one four hunters leave, there are no hunters left to shoot the monkey. And if there are 3 or fewer hunters initially than the scenario's impossible.

      --
      rage, rage against the dying of the light
    2. 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 :)

  4. Vertically, it is. by pushing-robot · · Score: 5, Insightful

    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?
  5. Re:The Story of 1 with Terry Jones by Anonymous Coward · · Score: 5, Funny

    Bah. Farcical aquatic ceremonies are no basis for a system of measurement.

    Use of the number line is derived from a mandate of the masses. Everyone knows that.

  6. 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.

  7. Re:Ordered sets by Anonymous Coward · · Score: 5, Informative

    If you read the article, you'll see that the subjects of the study do understand order, but that they lack the intuition of another property of the number line that you are so accustomed to that you're not aware of it. When asked to place numbers from 1 to 10 in order, control subjects (from the US) produce an arrangement like this:

    1...2...3...4...5...6...7...8...9...10

    The people of the Yupno Valley tend to do something more like this:

    1.2.3.4...................5.6.7.8.9.10

    A number line has more than order; it also has equal spacing. That idea seems not to be innate.

  8. Re:Valleys and Language by JoshuaZ · · Score: 5, Informative

    The Piraha are in South America and they have a language that is lacking many words considered normal in other cultures. http://en.wikipedia.org/wiki/Pirah%C3%A3_language. They give directions primarily in terms of the relation to the river (towards or away from the river or up or down the river) which may be what you are thinking of. There's a highly readable book about the tribe and their language- "Don't Sleep, There Are Snakes" by Daniel Everett, a linguist who spent decades with them. However, there's some degree of question by other scholars about how accurate Everett's description of their language was, and research is ongoing.