Learning is non-linear

“Not long ago, in the 1960s, mathematicians and scientists began to notice a property of natural systems that had been overlooked since the dawn of science: that tiny changes of condition, even in stable systems, can have dramatic and often unpredictable effects. … For example, if one adds a reagent, one drop at a time, to a chemical solution, nothing may happen at all until, with the addition of a single drop, the whole mixture changes color.

“I have witnessed the same progression in dozens of students: a surprising leap forward, followed by a period where the student appears to have reached the limits of their abilities; then another tiny advance that precipitates another leap. … Lisa, who couldn’t count by twos in Grade 6, now teaches herself new material from a difficult Grade 9 text.

“The fact that mathematical ability appears spontaneously in a gifted child is cited as evidence that ability is determined by genetics. But if the mind, like other complex systems, is subject to chaotic and non-linear effects, even siblings with the same genetic features, and who are offered the same opportunities, might develop entirely different abilities. Some small event in early childhood or at school might start an avalanche of learning in one child but not another. The fact that an avalanche occurs on one mountain and not another… does not prove that one mountain is more prone to avalanches or that an avalanche could never be started.”

-John Mighton, The Myth of Ability (p.18-20)

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