It is tempting to compare our brains to computers, but when it comes to speed, a neuron takes its time, sending signals at a maximum of 180 miles (280 km) per hour, the top speed of a Formula One racecar, or a quarter of the speed of sound. In comparison, an electrical circuit approaches the speed of light, which is 671 million miles (1.08 billion km) per hour. Clearly, speed is not our strong suit when we are pitted against a circuit board. Our advantage is understanding – not mindlessly crunching ones and zeros. Yet for some reason, math educators continue to emphasize speed at the expense of humanity's greater gifts of interpretation and problem solving.
With schools choreographed by hourly bells and standardized tests timed to the second, we seem to be convinced that the clock is as instructive as the blackboard. Several chains of after-school learning centers reflect this philosophy, notably Kumon, whose students drill math worksheets repeatedly under the unforgiving supervision of a stopwatch. A quick search of YouTube turns up dozens of stressed, frustrated Kumon students venting their rage, even burning the worksheets in one video. Clearly, this type of approach has emotional ramifications, especially for a generation of students who already bring home record amounts of homework.
Is this stress necessary when a calculator is rarely out of reach? Timed repetition does show some improvement within its narrow focus – an observation going back to classroom studies from the 1970s – but drilling scores of similar problems encourages students to develop algorithmic thinking and mental shortcuts that distance their minds from the underlying logic of the equation. In psychology, these crutches are called heuristics (from the French word for “hour). Heuristics save time when solving familiar problems, yet rule out analysis, making unfamiliar ones seem impossible to solve.
Math has become a race, and more like a 100-yard dash than a marathon. The latest fad in math class is the “Mad Minute,” an exercise for which students scramble to answer as many problems as possible in 60 seconds with no option to poll the audience, phone a friend, or even raise their hands. It seems hardly coincidental that the Mad Minute shares its name with a World War I military drill, which trained British soldiers to shoot their rifles so quickly that their enemies could mistake them for machine guns.
The mindset of timed drills treats each problem type as a separate race to be won with reflexes. This approach is disjointed and ultimately ineffective, because math is a continuum of topics. For a deeper understanding, students need a bird's-eye view of how the pieces fit together. The starting gun and the finish line are immaterial.
Though computing power has doubled every two years since 1971, a single processor circuit can still only handle one bit of data at a time. A human brain, however, comprises as many as 100 trillion connections working in parallel. We are hard-wired to put concepts into context, to fit what we are learning into the web of what we know, and then to apply that knowledge to tackling real-life challenges.
An idea learned in isolation slowly fades away without the reinforcement of related knowledge to hold it in place. The champions of memory competitions know this well. They link the digits they memorize with familiar objects or people, then store them in the imagined rooms of “memory palaces.” A stopwatch cannot teach a student to contextualize and apply new knowledge. That would require the patience and attention of a human teacher. Only through discussion will the numbers come alive.
The idea that long-term learning brings long-term rewards is gradually gaining ground. James and Jodi Ralston, who own Mathnasium learning centers in Chatham and Summit, New Jersey, compare the process of learning math to the growth of a tree, which expands outward ring by ring, held up by the wood fiber in its core. If we want students' understanding to last past their next report card, this is a better metaphor to run with. After all, a race ends as quickly as it began, but a tree never stops growing.
© 2012 DREW CAYMAN – ALL RIGHTS RESERVED. Drew Cayman is a freelance writer focusing on math- and science-related matters. Drew can be reached at firstname.lastname@example.org. For more information about Mathnasium's locations in Summit and Chatham, New Jersey, please contact Jodi or James Ralston at 973-377-MATH (6284) or email@example.com.