**May 28, 2012**

Not many people know that the telecommunications giant Nokia Corporation originated in the small town of Nokia, Finland. Another noteworthy datum about Finland is that Finland scored significantly above the OECD average on the PISA test in *all* subjects — reading, mathematics, and science. How did Finland’s students score so well? The Finnish education system immediately became the subject of a multitude of research, including that of Stanford professor Keith Devlin. According to Dr. Devlin, Finland does not focus on performing well on international tests. Instead, they aim to prepare students for the real world. And subsequently, students learn math along the way.

To grapple with the novel situations of our rapidly changing world, we need to use existing techniques and find new ones. This requires innovation, brainstorming, collaboration, and communication. Hence, this is what students must learn to do in the classroom. In the United States, students rank significantly below the OECD average not because we are lacking the brains (in fact, the US has some of the best minds in the world), but because we lack the *quantity* of innovative thinkers. We need more – many more – students to think outside the box.*

Unfortunately, in math classes across the United States, students are still being told to memorize a set of rules and procedures. I witnessed a result of this when I moderated a focus group of six eighth grade boys for Math *inquiries* Project on May 22, 2012. I asked them to rank the importance of various factors in learning math. They ranked “understanding how the math works” first, followed by “memorization.” They considered memorization to be more important than teachers, peers, textbooks, tutors, and technology. Their main example was the quadratic equation. Only one of the six was able to recite the formula, but none could describe what it is used for. They told me that the point is to plug *a*, *b*, and *c* from the equation “ax + bx^{2} + c = 0” into the formula to solve for *x*. (As I’m sure you’ve realized, the quadratic expression that they set equal to zero renders the quadratic formula completely invalid.) “What is *x*?” I asked. Responses included “a variable,” “an unknown,” and “a number.” Not one could tell me that it is the solutions, or x-intercepts, of the quadratic function. This is what we get with all memorization and no understanding.

We need to teach fewer topics in-depth and for a longer length of time, from a variety of angles. We can’t teach kids the quadratic formula without teaching them about roots, factoring, and completing the square. Students should know how to derive the quadratic formula so that memorizing it becomes an option, not a requirement to solve a quadratic equation. This is just one example of a topic that can be looked at from multiple angles. Collaborating and communicating with peers is a great way to expose students to ever more ways of viewing things. The more perspectives students acquire, the more innovative they become.

*This was Keith Devlin’s main argument at his lecture at the Tech Museum in San Jose, California on May 27, 2012.