When the daughter was younger and had yet to start going to a classroom atmosphere, the father asked her to lift her right leg. Being the loving grand-daughter, she did. Then he asked her to lift her left leg and she obliged, by stamping the right foot down and lifting the other. Not satisfied with the legs, he started in with the little arms and asked for the left arm. Then the right arm, and both arms together. (Luckily, we have only 2 arms and 2 legs, for this gripping tale would have had us spouting steam otherwise.)
Having seen all this, he asked her to lift both legs together, to which she hardly spent a moment thinking and simply lay down on the floor and lifted both legs looking like a very adorable pup waiting to be tickled by the owner.
Fast forward to a time when formal schooling did start and the same exercise has her thinking about the problem and saying, “But the only way to do that is jump and see if we can fly!”
What makes me remember this you ask. A book I was reading recently: It spoke about how some tribes know not the notion of time or numbers. (They don’t need either concept for their survival.) This book actually has remarkable powers, because it has enabled me to forget the title and clean swiped the power of resurrecting the title from the dark crevices of the brain.
Anyway, according to the author, who spent many happy months among the tribes, Piraha Tribe in Amazon, trying to observe and study their behavioral patterns, he noticed something. When given a series of dots and told to plot them on a number scale between 1 and 10, the tribes with no formal introduction to numbers placed the numbers closer together as they approached 10, and farther and farther apart near 1 and 2. Their natural instincts were to think logarithmically.
A study that coincided with how kindergartners plotted their numbers. Basically, the tribes and the children saw the combination of dots as the pattern. Two dots together doubles the area of one dot, but 9 dots clustered together is only marginally smaller than 10 dots together.
But as these kindergartners approached second grade, they plotted the numbers from 1 to 10 evenly spaced on the number line. We move away from a more complex method of thinking logarithmically naturally to thinking linearly, and then relearn the logarithmic concept later in life.
It is a fact that structured thinking has its benefits, but I often wonder how different we would be if we were allowed to retain our ability to think with out being clouded by what is taught to us.
Edit: Relevant links: