Algebra Emerging In Preschool

Yesterday, I wrote about the great truth that nothing ever goes according to plan, especially if that plan involves people working together. This does not mean that all plans are doomed to failure, merely that in the process of collaboration, in the process of engaging actual human beings, the real project always emerges according to a timeline and in a form most suitable the the time, place, and people involved. That is, it does so when it is allowed to emerge. All too often, however, those "in charge" of planning, in their arrogance, demand that the plan take precedence and that's how we get ourselves into trouble.

A case in point: someone, somewhere has determined that all children will learn algebra in a certain manner at a certain time. As I recall, when I attended public schools in Corvallis, Oregon, that time was pegged at 6th grade, and the manner was to read from a textbook, watch a teacher solve for x on the blackboard, practice equations at home, then take a test. I learned the basics, at least enough and for long enough to score a passing grade, but it was a struggle. It was the first class I bumped into that caused me to join the chorus of generations bemoaning the "irrelevance" of what I was being expected to "learn" in school. These strings of number, letters, and operators were supposedly tools for understanding the real world, but since I had not been part of their emergence, since they had appeared before me as dictated by someone, somewhere at a certain place and time, they held little meaning for me and amounted to little more than picking up a few number tricks.

I know now that it wasn't a problem with me, but rather with the plan, a plan, in fact, that miscalculated when we were ready to start learning actual algebra by a good 6-8 years. 

In a just-published study in the journal Developmental Science, lead author and post-doctoral fellow Melissa Kibbe and Lisa Feigenson, associate professor of psychological and brain sciences at Johns Hopkins University's Krieger School of Arts and Sciences, find that most preschoolers and kindergarteners, or children between 4 and 6, can do basic algebra naturally . . . "These very young children, some of whom are just learning to count, and few of whom have even gone to school yet, are doing basic algebra and with little effort," Kibbe said.

The study authors are not talking, of course, about the tortured methods used to teach the mere ciphering that passed for "algebra" in my 6th grade classroom, but rather the algebra that is relevant because it emerges from the day-to-day lives of 4-6 year old children.

If this kind of basic algebraic reasoning is so simple and natural for 4, 5 and 6-year-olds, the question remains why it is so difficult for teens and others . . . "One possibility is that formal algebra relies on memorized rules and symbols that seem to trip many people up," Feigenson said. "So one of the exciting future directions for this research is to ask whether telling teachers that children have this gut level ability -- long before they master the symbols -- might help in encouraging students to harness these skills.

Now I shudder at what "planners" will read into the words "encouraging students," because for them that is too often synonymous with "compelling students," but the idea that these researchers have "discovered" is emergence, the phenomenon that stands at the heart of a play-based curriculum. It's something that those of us working with young children see every day as children engage their real world through the curiosity that drives play.

For those addicted to planning, the idea of emergence is too unreliable, but they are wrong. Indeed, if anyone is ever going to be successful with anything, it is because the plans were laid aside to make room for emergence. Emergence is among the most reliable phenomena in the universe and it's why play will always be the best more reliable way for humans to learn.

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