## Good PISA results are not what matters; it’s how the students get them.

Dr. Keith Devlin, Stanford University (Emeritus)

Nations are proud when their students score well on international mathematics assessments like PISA. But they should be cautious before cracking open the champagne bottle. In an era when all procedural mathematics is done by machines, what really matters is *how* the students achieved those scores. If they simply mastered (by rote practice) procedures they then applied in the test, that high scores hides the fact that they have devoted hours of precious educational time learning how to be a relatively slow, more error-prone, and very limited, pocket computer. What counts in today’s world is mathematical thinking: how to take a quantitative problem and use computational technologies to solve it. With good mathematical thinking skills, students can tackle questions on a PISA test by *creative, analytic thinking*, rather than applying a previously mastered procedure. Mastering mathematical thinking still requires a lot of repetitive practice. But it needs to be deliberative practice, not the rote repetition that was important in previous eras.