by Barbara Oakley and Terrence Sejnowski
Something has gone awry in American education. For example, over the past decades, the U.S. has dropped to the bottom of international rankings for developed countries in math. This decline has coincided with education reform, a shift that has emphasized understanding and downplayed practice. Could something that sounds so sensible have possibly been responsible for the drop?
The brain has two major learning systems. One is based on practice, and leads to fast, automatic behavior. This system is not accessible by conscious thought and is the source of intuition. The second system is based on deliberate thought—it is slow but flexible. You are consciously aware and can verbalize what you have learned. These two systems are roughly analogous to Nobel Prize winner Daniel Kahneman’s “thinking, fast and slow.”
Students need both fast and slow systems to learn well. Yet over the past fifty years, education—and math education in particular—has paid only lip service to, or outright dismissed, the importance of fast automaticity in learning, insisting instead that students can look up whatever they need to know, and that drill equates to kill. But focusing primarily on slow, flexible thinking, appealing as it may be, is akin to asking a sprinter to run faster by hopping on only one leg.
Fast thinking often involves the procedural system, which deposits neural links in long-term memory primarily through the basal ganglia, a part of the brain with no conscious access. Slow thinking, on the other hand, uses the declarative system, which deposits links in long-term memory primarily through the hippocampus. This latter system allows you to “declare” what you’re learning—in other words, you’re conscious of it.
These fast and slow neural links in memory are accessed and used differently, depending on whether you are doing something habitually or deliberately. But the two systems often work together—as when you are reading these letters with the aid of your procedural system and simultaneously grasping the key ideas with your declarative system. The two ways of learning work together seamlessly like a hand in a glove, helping each other navigate the vicissitudes of the real world.
But why can’t we just use the declarative system and have done with it? Part of the issue is that declarative learning is flexible—but that very flexibility means it is also slow. After all, deliberation can cost precious time—from an evolutionary perspective, you could be dead before you figured out which hand to use to pick up a spear. By contrast, procedural learning involves activities you do a lot—so often, that you don’t even want to bother to think consciously about them. If you practice a lot with a spear, for example, throwing becomes speedy second nature. Practice a lot with writing, and eventually, you can write without worrying about punctuation. Practice a lot with arithmetic operations, and you can do them without conscious thought, allowing the brain to focus its deliberate, conscious thinking on more complex ideas.
Although the procedural system has been dismissed as the domain of undesirable “rote” learning, in reality, it is an extraordinarily powerful pattern recognition system. This is the system that allows us to solve a Rubik’s cube, learn the intricate patterns of our native language, or feel, intuitively, why 2 × 6 = 13 must be wrong. (Our procedural systems gradually intuit that 2 multiplied by any number must be an even number.) Constructivists are right—children do construct their own knowledge. But they can’t construct that internal, neurally-based knowledge if we insist, as do some modern educators, that students can always just “look things up.”
Another challenge involves the idea that students only understand a concept if they can explain it. Declarative explanations can be memorized and regurgitated with no real understanding of the concept at hand. By contrast, a student who has learned a concept well through their procedural system may find it well-nigh impossible to put their understanding into words even though they have developed a superb intuition and can perform an expected calculation in their head with ease. This can result in the strange outcome that a student with no understanding can receive a perfect grade as they “explain” a concept they are largely regurgitating from memory, while a student with well-developed intuitions and speedy and accurate problem-solving skills receives a failing grade. The cookie-cutter, one-size-fits-all declarative-only approach can be a disaster when it comes to inclusive teaching in today’s diverse classrooms, causing talented students to become more frustrated with school and ultimately to tune out altogether.
Both schools of pedagogy and educational societies need more balanced approaches that take advantage of the flexibility of declarative learning and also acknowledge the habitual ease and enjoyable comfort that procedural learning can bring. These new approaches will give our children—and the world—the best possible educational tools to embrace the realities that science has unveiled.
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