Steven Pinker -- How the Mind Works - Hampshire High Italian ...

342 | HOW THE MIND WORKSpractice, the routes to automaticity, are called "mechanistic" and seen asdetrimental to understanding. As one pedagogue lucidly explained, "Azone of potential construction of a specific mathematical concept isdetermined by the modifications of the concept children might make in,or as a result of, interactive communication in the mathematical learningenvironment." The result, another declared, is that "it is possible for studentsto construct for themselves the mathematical practices that, historically,took several thousand years to evolve."As Geary points out, constructivism has merit when it comes to theintuitions of small numbers and simple arithmetic that arise naturally inall children. But it ignores the difference between our factory-installedequipment and the accessories that civilization bolts on afterward. Settingour mental modules to work on material they were not designed foris hard. Children do not spontaneously see a string of beads as elementsin a set, or points on a line as numbers. If you give them a bunch ofblocks and tell them to do something together, they will exercise theirintuitive physics and intuitive psychology for all they're worth, but notnecessarily their intuitive sense of number. (The better curricula explicitlypoint out connections across ways of knowing. Children might betold to do every arithmetic problem three different ways: by counting, bydrawing diagrams, and by moving segments along a number line.) Andwithout the practice that compiles a halting sequence of steps into amental reflex, a learner will always be building mathematical structuresout of the tiniest nuts and bolts, like the watchmaker who never madesubassemblies and had to start from scratch every time he put down awatch to answer the phone.Mastery of mathematics is deeply satisfying, but it is a reward forhard work that is not itself always pleasurable. Without the esteem forhard-won mathematical skills that is common in other cultures, the masteryis unlikely to blossom. Sadly, the same story is being played out inAmerican reading instruction. In the dominant technique, called "wholelanguage," the insight that language is a naturally developing humaninstinct has been garbled into the evolutionarily improbable claim thatreading is a naturally developing human instinct. Old-fashioned practiceat connecting letters to sounds is replaced by immersion in a text-richsocial environment, and the children don't learn to read. Without anunderstanding of what the mind was designed to do in the environmentin which we evolved, the unnatural activity called formal education isunlikely to succeed.