Learning Methods

May is for graduations, for ceremonies and parties. Some high school graduates will give up on further formal education and instead will enter straight into the work force. Others will pursue a challenging course of study at a university: mathematics, science, history, English, or business.

Whichever course a young person chooses, learning should be and can be a life-long process.

In recent days, I came across a 2016 book, by Anders Ericsson, “Peak: Secrets from the New Science of Expertise.” In it, Ericsson, tells the story of how Benjamin Franklin played chess all his life, and yet he never became very good, even though he played thousands of hours.

Ericsson wrote, “This failing was a source of great frustration to Franklin, but he had no idea why he couldn’t get better.” Ericsson explained, “He never pushed himself, never got out of his comfort zone, never put in the hours of ‘deliberate practice’ it would take to improve.”

A search reveals the following for would-be top chess players. Learn to play a series of moves in response to however your opponent opens. Control the center. Develop your pieces. Castle in the first ten moves. Learn an end game with just a rook and a pawn.

Ericsson said that top players recognize patterns of chess pieces at a glance. “They are old friends. These positions are called ‘chunks,’ that they hold in reserve in long-term memory.”

In addition, Franklin often read a daily magazine called the “Spectator,” that Joseph Addison and Sir Richard Steele wrote. Because Franklin admired those two writers’ literary skills, he set for himself a course of deliberate practice.

On paper he copied down their sentences, broke them apart, mixed up the words, turned them into verse, into poetry, and then re-assembled them. He then compared his sentences with theirs.

Whereas Franklin failed to make much headway with chess, he became a first-rate writer.

A question: Why is it that Asian students win the top awards in mathematics competitions?

A search reveals certain reasons. First, those students spend weeks and even months re-learning the basic fundamentals of fractions, multiplication tables, and long division.

Teachers insist that students solve a problem three ways. For example, to solve a quadratic equation, they will use factorization, the quadratic formula, and completing the square.

Teacher insist that their students keep a mathematics notebook where they solve their assigned problems, rather than on random sheets of paper. They call errors “feedback,” rather than “mistakes,” and they note those mistakes in a special section inside their notebook.

Asian students have frequent timed practices, fifteen questions in ten minutes. Teachers allow Asian students to teach others in the classroom. Because they study mathematics every day, the Asian students’ minds are directed to think often in terms of numbers, processes, solutions.

In a 1989 scholarly article, that Allan Collins, John Seely Brown, and Susan E. Brown wrote, “Cognitive Apprenticeship: Teaching the Crafts of Reading, Writing, and Mathematics,” its three authors presented six methods for an effective apprenticeship.

First is “modeling.” Students watch an expert perform a skill. Second is “coaching.” The expert offers hints and challenges, as the students replicate that skill. Third is “scaffolding.” The expert provides formulas, steps, or equations that guide the students.

Fourth is “articulation.” The students explain their thoughts about the skill. Fifth is “reflection.” The students compare their understanding with those of the expert. Sixth is “exploration.” The students seek out more problems to solve.

The goal is to highlight a practical thinking process.

Best wishes to this year’s crop of graduates. You have choices: deliberate practice and the science of expertise, or cognitive apprenticeship.