By Jo Boaler, Pablo Zoido | SA Mind November 2016 Issue
In December the Program for International Student Assessment (PISA) will announce the latest results from the tests it administers every three years to hundreds of thousands of 15-year-olds around the world. In the last round, the U.S. posted average scores in reading and science but performed well below other developed nations in math, ranking 36 out of 65 countries.
We do not expect this year's results to be much different. Our nation's scores have been consistently lackluster. Fortunately, though, the 2012 exam collected a unique set of data on how the world's students think about math. The insights from that study, combined with important new findings in brain science, reveal a clear strategy to help the U.S. catch up.
The PISA 2012 assessment questioned not only students' knowledge of mathematics but also their approach to the subject, and their responses reflected three distinct learning styles. Some students relied predominantly on memorization. They indicated that they grasp new topics in math by repeating problems over and over and trying to learn methods “by heart.” Other students tackled new concepts more thoughtfully, saying they tried to relate them to those they already had mastered. A third group followed a so-called self-monitoring approach: they routinely evaluated their own understanding and focused their attention on concepts they had not yet learned.
In every country, the memorizers turned out to be the lowest achievers, and countries with high numbers of them—the U.S. was in the top third—also had the highest proportion of teens doing poorly on the PISA math assessment. Further analysis showed that memorizers were approximately half a year behind students who used relational and self-monitoring strategies. In no country were memorizers in the highest-achieving group, and in some high-achieving economies, the differences between memorizers and other students were substantial. In France and Japan, for example, pupils who combined self-monitoring and relational strategies outscored students using memorization by more than a year's worth of schooling.
The U.S. actually had more memorizers than South Korea, long thought to be the paradigm of rote learning. Why? Because American schools routinely present mathematics procedurally, as sets of steps to memorize and apply. Many teachers, faced with long lists of content to cover to satisfy state and federal requirements, worry that students do not have enough time to explore math topics in depth. Others simply teach as they were taught. And few have the opportunity to stay current with what research shows about how kids learn math best: as an open, conceptual, inquiry-based subject.
To help change that, we launched a new center at Stanford University in 2014, called Youcubed. Our central mission is to communicate evidence-based practices to teachers, other education professionals, parents and students. To that end, we have devised recommendations that take into consideration how our brains grapple with abstract mathematical concepts. We offer engaging lessons and tasks, along with a wide range of advice, including the importance of encouraging what is known as a growth mindset—offering messages such as “mistakes grow your brain” and “I believe you can learn anything.”
The foundation all math students need is number sense—essentially a feel for numbers, with the agility to use them flexibly and creatively (watch a video explaining number sense here: https://www.youcubed.org/what-is-number-sense/). A child with number sense might tackle 19 × 9 by first working with “friendlier numbers”—say, 20 × 9—and then subtracting 9. Students without number sense could arrive at the answer only by using an algorithm. To build number sense, students need the opportunity to approach numbers in different ways, to see and use numbers visually, and to play around with different strategies for combining them. Unfortunately, most elementary classrooms ask students to memorize times tables and other number facts, often under time pressure, which research shows can seed math anxiety. It can actually hinder the development of number sense.
(818) 696-1060
