Ever since we discovered that the Earth is round and turns like a mad-spinning top, we have understood that reality is not as it appears to us: every time we glimpse a new aspect of it, it is a deeply emotional experience. Another veil has fallen.
Carlo Rovelli, “Seven Brief Lessons on Physics”
Educators have assumed that the minds of young children are insufficiently well-developed to take in abstract ideas that challenge the intuitions of adults. But what if flexible young minds were to be exposed to counter-intuitive concepts from an early age? Do not intuition-bending concepts as multiple infinities, quantum uncertainty, and evolution by natural selection have something in common with the imaginary worlds and beings that are the fabric of a child’s life?
Instead of indoctrinating children in the apparent concreteness of the world-as-it-seems, might it not be possible to at the same time to provide glimpses of the true weirdness of the world-as-it-is?
Consider as an example this typical maths curriculum from Ontario. For 7 full years, from JK to grade 5, the existence of negative numbers is hidden from students. Only numbers greater than or equal to 0 are to be mentioned, a fiction that sets firmly in a child’s mind that these are all the numbers there are. Then in grade 6, when negative numbers are finally revealed to them, students must unlearn what they understood to be a basic fact of numbers – their “positiveness” – before working with negatives. This creates a feeling of cognitive dissonance that some students will never completely overcome, and probably contributes to the anxiety, and sometimes hatred, of maths that is epidemic in our society.
And yet negative numbers can be as real and as compelling to young children as their invisible friends. Negative numbers (as well as multiple infinities, complex numbers, infinitesimals, fractals, etc.) are “unreal” invented concepts as fascinating as wizards, ghosts, or magical lands above clouds or under the sea. Even the youngest student could be given glimpses of these wonders for three reasons:
- introducing these ideas gradually over the course of many years will make it easier for children to embrace them when time comes to actually work with and manipulate these numbers.
- it will go a long way to instill the idea that the maths are creative subject, one that demands and welcomes insight and imagination as well as discipline and precision. Much of current maths instruction involves dry mastery of rote routines and rules that is boring and distasteful to most people. This in turn leads to adults who are ill-equipped to use mathematical concepts to manage their finances, safety, and participation as engaged citizens.
- one of the most seductive things an adult can say to a child is “there’s something more, but you aren’t quite ready for it, wait til you are older”. This is true of books, movies, roller-coasters, sports, magic tricks, and alcohol. Properly handled it can be true of maths as well, tempting some (many?) students to seek out this “hidden” knowledge on their own, and as a result to associate maths with pleasure rather than fea
Humans seem to be addicted to narratives, so it is helpful that Maths come with some intriguing (and occasionally) bloody stories: the deadly heresy of the square root of 2, how a chessboard bankrupted an Indian king (or maybe queen), how an “imaginary” number first identified in ancient Egypt led to the smart phones.
The above example is about maths, but it applies to every type of knowledge – the fuzziness of quantum mechanics, the multiple perspectives of history, the ways our brains misperceive reality, the complex dynamics of societies. All have versions that are accessible to young children at a time when their core understandings of the world are formed.
They will grow to inhabit a world of unforeseeable challenges and dramatic changes. Bizarrely, we have told our schools to present young students with a grey 2-dimensional static picture of the world.
In order for our children, when they are adults, to successfully manage what will confront them, we must help them build from an early age a deep intuition about the richness, fluidity, and mystery of the world.