Going up the learning curve,the intuitive way

Im much better at it, he said,in a phone interview from his school,New Roads in Santa Monica,California. In the beginning it was difficult,having to work so quickly; but you sort of get used to it,and in the end its more intuitive. It becomes more effortless.

For years school curricula have emphasised top-down instruction,especially for topics like math and science. Learn the rules firstthe theorems,the order of operations,Newtons lawsthen make a run at the problem list at the end of the chapter. Yet recent research has found that true experts have something at least as valuable as a mastery of the rules: gut instinct,an instantaneous grasp of the type of problem theyre up against. Like the ballplayer who can read pitches early,or the chess master who sees the best move,theyve developed a great eye.

Now,a small group of cognitive scientists is arguing that schools and students could take far more advantage of this same bottom-up ability,called perceptual learning. The brain is a pattern-recognition machine,after all,and when focused properly,it can quickly deepen a persons grasp of a principle,new studies suggest.

Scientists have long known that the brain registers subtle patterns subconsciously,well before a person knows he or she is learning. In a landmark 1997 experiment,researchers at the University of Iowa found that people playing a simple gambling game with decks of cards reported liking some decks better than others long before they realised that those decks had cards that caused greater losses. Some participants picked up the differences among decks after just 10 cards.

Experts develop such sensitive perceptual radar the old-fashioned way,of course,through years of study and practice. Yet there is growing evidence that a certain kind of trainingvisual,fast-paced,often focused on classifying problems rather than solving themcan build intuition quickly. In one recent experiment,for example,researchers found that people were better able to distinguish the painting styles of 12 unfamiliar artists after viewing mixed collections of works from all 12 than after viewing a dozen works from one artist,then moving on to the next painter. The participants brains began to pick up on differences before they could fully articulate them. Once the brain has a goal in mind,it tunes the perceptual system to search the environment for relevant clues,said Steven Sloman,a cognitive scientist at Brown University. In time the eyes,ears and nose learn to isolate those signs and dismiss irrelevant information,in turn sharpening thinking.

Good teachers at all levels already have their own techniques to speed up this processmultiplication flash cards,tips to break down word problems,heuristic rhymesbut scientists are working to tune students eyes more systematically and to build understanding of very abstract concepts. Fractions,for one. Most middle school students,though they understand what fractions represent,dont do so well when tested on their ability to change one fraction,like 4/3,to another,like 7/3,by adding or subtracting. In a 2010 study,researchers at UCLA and the University of Pennsylvania had sixth graders in a Philadelphia public school use a perception-training program to practice just this. On the computer module,a fraction appeared as a block. The students used a slicer to cut that block into fractions and a cloner to copy those slices. They used these pieces to build a new block from the original onefor example,cutting a block that represented the fraction 4/3 into four equal slices,then making three more copies to produce a block that represented 7/3. The program immediately displayed an X next to wrong answers and Correct! next to correct ones,then moved to the next problem. It automatically adjusted to each students ability,advancing slowly for some and quickly for others. The students worked with the modules individually,for 15- to 30-minute intervals during the spring term,until they could perform most of the fraction exercises correctly.

In a test on the skills given afterward,on problems the students hadnt seen before,the group got 73 per cent correct. A comparison group of seventh graders,whod been taught how to solve such problems as part of regular classes,scored just 25 per cent on the test.