Memorizing multiplication tables may be a seminal school experience, among the few that kids today share with their grandparents. But a Stanford University professor says rapid-fire math drills are also the reason so many children fear and despise the subject.
Moreover, the traditional approach to math instruction — memorization, timed testing and the pressure to speedily arrive at answers — may actually damage advanced-level skills by undermining the development of a deeper understanding about the ways numbers work.
“There is a common and damaging misconception in mathematics — the idea that strong math students are fast math students,” says Jo Boaler, who teaches math education at the California university and has authored a new paper, “Fluency Without Fear.”
In fact, many mathematicians are not speedy calculators, Boaler says. Laurent Schwartz, the French mathematician whose work is considered key to the theory of partial differential equations, wrote that as a student he often felt stupid because he was among the slowest math-thinkers in class.
Research cited by Boaler finds that students able to memorize math facts (such as 7 x 8 = 56) and rapidly spit them out don’t necessarily do well once they get to high school because under stress — for instance, during a test — memory channels block and students come away believing, incorrectly, that they have no ability. Sometimes this develops into a lifetime fear.
In my classes at Stanford University, I experience many math traumatized undergraduates, even though they are among the highest achieving students in the country. When I ask them what has happened to lead to their math aversion many of the students talk about timed tests in second or third grade as a major turning point for them when they decided that math was not for them.
Boaler believes that blind memorization and timed testing prevent the essential development of “number sense,” an understanding of the logic behind numbers. For instance: Rather than rely merely memorize the fact that 7 x 8 = 56, a student with strong number sense knows that she can also get the correct answer by multiplying 7 x 7, then adding 7. That’s one of the tenets behind the approach used at Renton’s Lakeridge Elementary with coaching from UW Professor Elham Kazemi, which was featured in Education Lab last year.
“Number sense is the foundation for all higher-level mathematics,” Boaler says. “When students fail algebra it is often because they don’t have number sense.”
Her paper offers several exercises for teachers (and parents) to use with young students. And while she aims to make math fun, Boaler’s message could not be more serious:
When we emphasize memorization and testing in the name of fluency we are harming children … we have the research knowledge we need to change this and to enable all children to be powerful mathematics learners. Now is the time to use it.