The U.S. has a math problem.
Despite all the time, energy and money the country has thrown into finding better ways to teach the subject, American children keep scoring poorly and arriving at college woefully unprepared. Just as bad, if not worse, too many students think they hate math.
I propose a solution: Stop requiring everyone to take math in school.
People typically offer some combination of four reasons children should learn math: for everyday functions such as doing taxes, buying groceries and reading the news; for getting a job in an increasingly technologically advanced market; as a powerful way of thinking and understanding the world; to tackle high school or get into a good college.
Let's consider these one by one. To some degree, children naturally learn basic arithmetic just by spending time with people who use it, and by carrying out such tasks as setting the table, going to the store or sharing toys with friends. Research shows that even illiterate children can compute sums quite quickly and accurately in familiar settings (such as selling produce on the street). Babies are born with an intuitive knowledge of numbers. It wouldn't take much for schools to teach every child how to add, subtract, multiply and divide.
Those interested in highly quantitative fields such as technology, finance, or research are likely to have a natural inclination for math. They can obtain the knowledge they need later, in a much more effective and profound way, in college or beyond.
People who invent new industries are rarely using math they learned in school, and often aren't using any at all. Why drag all elementary school students through a compulsory curriculum that turns off as many as it prepares, on the off chance that a few might need it?
True, learning math can give us intellectual strengths different from the ones we get reading novels, studying history or poking around in a petri dish. But these kinds of thinking are not necessarily tied to numbers, certainly not at the novice level. Advanced mathematics requires students to reason logically, be patient, methodical and playful in trying out solutions to a problem, imagine various routes to the same end, tolerate uncertainty and search for elegance. They need to know when to trust their quantitative intuitions and when to engage in counterintuitive thinking.
But such abilities are usually precluded by the typical K-12 curriculum -- a dizzying array of isolated skills and procedures, which many college professors say they spend too much time getting students to "unlearn." Research has shown that many students who do perfectly well on math tests often can't apply a single thing they have learned in any other setting. We end up missing a chance to teach them what they would really need in order to go on to higher-level math or to think well.
Instead of a good score in algebra, children need three things:
Time: For the most part, children think concretely when they are young, and become more capable of abstract thought later. A huge industry has grown up around the idea that we can game the human system and teach children to think abstractly before they are ready. Such strategies haven't been very successful, and they preclude activities that would be much more compelling and useful to young minds.
Reading: Research has demonstrated that literacy is crucial to abstract thought. Children who read become capable of specific kinds of conceptual and logical thought not available to others. This opens the door to thinking about things that are not part of one's immediate tangible experience, a crucial aspect of higher mathematics.
Intellectual challenges: Children who are immersed in informal quantitative reasoning come to more formal math tasks, at a later age, with much greater ease. Similarly, children who are asked to give reasons for their thinking, or speculate about the past and future, are well positioned to learn various kinds of logic and argument.
So here's the plan.
Teach young children arithmetic, a task that would probably take 20 minutes a day through the end of third grade. Spend the extra time on reading, and on the kinds of play that involve abstract thinking and problem solving.
For young children, this could include building blocks, dominoes and playing store. For older children -- chess, Minecraft, cryptography and the mental puzzles that can be found in a few outstanding math books, as well as in the brain teaser section of many supermarkets. Ask students to come up with reasons and evidence for what they say, and engage in serious sustained arguments with one another.
By about ninth grade, those drawn to mathematics could take interesting, rigorous classes. Others could pursue subjects more suited to their interests and strengths. Teachers who love math could offer activities as a way of teaching good thinking rather than as an obligatory form of preparation for future math classes. Those who are adept at some other way of teaching good thinking would be free to do so.
Teachers and students alike would no longer be locked into a compulsory curriculum that is too much for some, too little for others, and leads very few children to true mathematical ability. We would give up little of worth, and make more room for truly valuable learning.
Susan Engel, a senior lecturer in psychology at Williams College, is the author of "The Hungry Mind: The Origins of Curiosity in Childhood."