How math is taught in the United States and how our students perform on international math tests continue to be areas of intense debate. The most recent Program for International Student Assessment (PISA) results for 15-year-olds show a significant drop in math performance between 2012 and 2015 among U.S. students who now rank 40th out of the 73 countries tested. While an international comparison of this sort can never tell the whole story, PISA administrators have started including questions about how students study. The answers to these survey questions about how students approach learning math could help provide some insight into which strategies work and which do not.
In a Scientific American article, Stanford education professor Jo Boaler and Pablo Zoido, the Education Lead Specialist at the Inter-American Development Bank, explain that students reported three main strategies for learning math: memorizing algorithms, relating new topics to those already learned, and routinely evaluating learning and focusing on areas not yet learned. Boaler and Zoido draw this conclusion:
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.
Boaler and Zoido go on to recommend that math teachers focus on presenting students with visual, engaging tasks that let students grapple with the problem, test out various strategies, and thus gain a deeper understanding of core concepts. They point to research showing that students who solve problems by memorizing algorithms use a completely different part of the brain than those who work out the problem with various strategies. They posit that if the U.S. wants to improve the math abilities of its young people, it must heed the research and switch approaches.
Countries like Canada, Estonia, Germany and Hong Kong emerged as leaders in math education from the 2015 PISA results. Not only do students in these countries score well, but the gaps between rich and poor students are much smaller.