A major proponent of intuition-training research is psychologist Philip J. Kellman, who works at the University of California, Los Angeles. Much like math savant Daniel Tammet, Kellman says even the most rigorous problem-solving ultimately depends on our personal perceptions and instincts:
When facing problems in real-life situations, the first question is always, “What am I looking at? What kind of problem is this?” Any theory of how we learn presupposes perceptual knowledge — that we know which facts are relevant, that we know what to look for. [The question is], What do we need to do to make this happen efficiently?
Kellman is a champion of perceptual learning – the idea that, by honing our semiconscious or nonconscious responses to subtle environmental stimuli, we can teach our minds to correctly use aesthetic and intuitive judgments as guides toward logical answers. This is what mathematicians and physicists mean when they talk about a beautiful proof or an elegant formula.
This line of thinking is based on experiments like the influential 1997 study “Deciding advantageously before knowing the advantageous strategy,” which argued that our minds often “lean” in a certain direction before reasoning even begins:
Overt reasoning [may be] preceded by a nonconscious biasing step that uses neural systems other than those that support declarative [i.e., factual] knowledge. … The results suggest that, in normal individuals, nonconscious biases guide behavior before conscious knowledge does.
To put this in neuropsychological terms, procedural memory helps guide us toward declarative knowledge – an intuitive grasp of how to perform a task gives us a more accurate sense of whether the task’s results were desirable or correct. This might seem obvious, but the implications are huge:
The brain is a pattern-recognition machine, after all, and when focused properly, it can quickly deepen a person’s grasp of a principle. … Better yet, perceptual knowledge builds automatically: There’s no reason someone with a good eye for fashion or wordplay cannot develop an intuition for classifying rocks or mammals or algebraic equations, given a little interest or motivation.
For instance, a 2010 study conducted by Kellman and University of Pennsylvania psychologist Christine Massey used a game that took advantage of positive feedback loops to train problem-solving intuition. Junior-high students were taught to make “best guesses” about the answers to fraction problems based on visual stimuli (pie charts) corresponding to numbers – then immediately given a “right” or “wrong” signal, and the next problem. This associative learning task produced striking results: not only did all the students show significant improvement on tests – their scores remained high five months later, after summer break.
At least one school - New Roads in Santa Monica, Calif. – has taken the hint, and is testing a math curriculum based on this game concept. Playing a rapid-fire multiple-choice flashcard game, students sharpen their instincts for solving equations intuitively. The process can be (understandably) frustrating at first, but the class is showing dramatic improvement already.
These intuition-training games are all based on the same principle: that nonconscious planning – even when highly abstract – is just another adaptation of our trainable pattern recognition abilities. The more a student’s mind associates certain steps and leaps with positive feedback, the more likely that mind will be to instinctively take similar steps in the future. And in the end, even our most precise reasoning seems to be guided by instinct.
In Part 2 tomorrow, I’ll talk about the other side of this coin: how our intuition can be vulnerable to inaccurate leaps, and can often be misled.