Psychologist and author of the book Changing Our Minds, Naomi Fisher, once told me that her three-year-old son took an early interest in numbers. One day as they walked together through their neighborhood, he noticed of the house addresses. "Did you know," he asked his mother, "that there are lonely numbers and friendly numbers?" He had, she said, "discovered odd and even numbers."
I doubt there is an educator on earth who would "teach" this mathematical concept in these terms. Indeed, most school curricula don't introduce the idea until first or second grade when children are twice Naomi's son's age, and even then it's typically done using the dry convention of numerals and ciphering, rather than the rich, relevant metaphor of lonely and friendly numbers on a street of houses.
As a preschool teacher, I've known hundreds of children who discover mathematical, scientific, literacy and other concepts well before they're "supposed" to. Parents have been taught by our educational system to treat this as a matter for pride in their obvious genius, to jump on it, to get them enrolled in advanced enrichment programs. The truth, however, is that sometimes their youthful proclivities foretell an abiding passion, as was the case with Dr. Fisher's son, but generally their epiphanies are indicators of nothing more than a typically curious child taking note of their world.
As a teacher in a cooperative school, my entire classroom career has been spent in the company of both children and their parents, and often even grandparents. I recall having a conversation with one of these grandparents who was visiting for a week. She wanted me to know that her grandson's obvious brilliance was the product of his mother's genes, who had, she assured me, been a genius child. She also let me know that she loved her daughter, but was disappointed that she had "wasted" her genius on such commonalities as stay-at-home motherhood. If she had anything to do with it, she was not going to allow the same thing happen to her grandson Max, which is why she was saving up to pay for expensive private schools. She also let me know, kindly but firmly, that she disapproved of our play-based curriculum. Perhaps it was good enough for the rest of these more common kids, but her grandson, she assured me with a wry nod, needed something more.
It was both sad and touching, mainly because I knew the mother (her daughter) and she was fully onboard with her son spending his childhood at play. In fact, she was considering avoiding school altogether, opting instead for a self-directed version of homeschooling called unschooling. "Max has already taught himself to read," she shrugged. "He's shown me that he's his own best teacher."
Not every child is a literacy or mathematics prodigy, of course, but they all, if allowed to be their own teachers, are driven to discovery. I've rarely met a parent who was not, rightly, blown away by their preschooler's capacity to learn in this way. "Children who don't go to school," explains Dr. Fisher, "live in a state of alert awareness because they're not expecting to be told what to do and not expecting to be evaluated." It frees them up, she says, to look for patterns and make connections. A child who has not yet been taught the dubious lesson that they need adult instruction and approval for their learning instead comes to rely upon their own curiosity, which is what play-based, or self-directed, learning is all about.
In his book The Search After Truth, rationalist philosopher Nicholas Malebranche writes, "The mind does not pay equal attention to everything it perceives. For it applies itself infinitely more to those things that affect it, that modify it, and that penetrate it, than to those that are present to it but do not affect it." This is the idea behind not just self-directed learning, but learning in general up until the relatively recent advent of what we today call school. "Schools are the new bit," says Dr. Fisher. "Sadly, society thinks that self-directed learning has to end at seven."
Yes, Max had taught himself to read, but his driving interest during his grandmother's time with us was working with his buddies to construct devious traps. They would spend their days snickering and scheming, using scrapes of wood, fabric, old mesh produce bags, and whatever came to hand to create contraptions that they were certain would ensnare a classmate or two. His grandmother was appalled, whisper-begging me to guide them into more useful endeavors. Then one day, a trap made of rope was sprung on his grandmother, who found her ankles tied together as she tried to traverse the playground. As the boys cackled, I helped extricate his grandmother who was laughing along with them. I couldn't help remarking, "Pretty genius, huh?"
It's hardly likely that Max will grow up to be a professional trap maker, but that's beside the point. The beauty of play-based learning is that it is always relevant to the learner and that is what's important if are goal is live a life of alert awareness.
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This concept of "alert awareness" stands at the center of why play-based learning, or self-directed learning, is the gold standard. Every child thrives in a self-directed environment because every child deserves the right to pursue their own special genius, especially in the early years. It's not just a foundation for life, but a way of life. If you're interested in providing provide this kind of childhood for the children in your life, then you'll want to look into my popular 6-week course, Teacher Tom's Play-Based Learning. It's designed for early childhood educators, childcare providers, parents, and grandparents who know that there is so much more than mere academics. To learn more and to register, click here. 
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