In his
2010 TEDglobal talk, “Teaching Kids Real Math with Computers” Conrad Wolfram, strategic director of Wolfram Research, proposed a novel approach to mathematics and education: let the computers do the computation so the students can learn how to do math.
“We've got a real problem with math education right now.” Said Conrad, speaking to an audience at Oxford, “Basically, no one's very happy. Those learning it think it's disconnected, uninteresting and hard. Those trying to employ them think they don't know enough...”
If students feel that the math they learn in high school, college and even in primary school is “disconnected”, as Conrad suggests, they may be right. In classrooms across the US and UK students are taught to do long-hand computations of everything from simple division to complex differential equations. The phrase, “Show your work” has frustrated students across the globe for decades leading them to ask the, very relevant, question, “Why?” Is this what math in the real world looks like? Long columns of painfully hand calculated variables and equations? Not really. In the real world, as Conrad affirms, math is done by geologists, engineers, biologists and all sorts of people who aren't career mathematicians. They use complex computer programs to generate models of biological or geological trends. The computation is done by the computers, and the experts spend time developing the equations and hunting down the data. This is what math in the real world looks like.
“But in education it looks very different -- dumbed-down problems, lots of calculating..” Wolfram Notes, “I estimated that, just today across the world, we spent about 106 average world lifetimes teaching people how to calculate by hand... [and] they didn't even have fun doing it.”
Calculus is "Damn Hard"
Wolfram suggests teaching calculus in primary schools. Hitherto we haven't attempted this because, as Wolfram admits, “Its damn hard.” But, using simple examples such as “What happens to a polygon as you add more sides? It eventually becomes a circle.” he shows how you can begin teaching the complex 'form' of calculus, even if kids aren't yet ready to handle the demanding calculations.
As Chomsky would have us say, we should teach phonemics and morphology of math before we consider things such as semantics. Teach the form of math first and the number crunching later. And why not? Children naturally learn morphology before semantics. If someone suggested we try to teach a two year old proper spelling and had them memorize the dictionary before they could even speak a basic sentence we'd think they were crazy. Yet this is exactly how we teach math- the syntax, number crunching, before the grammar.
Why Children Can Learn Calculus (Hint: They Can Learn English!)
In
The Symbolic Species biological anthropologist Terrence W. Deacon discusses why children can speak before they can tie their shoes (try learning a new language and learning to tie a knot and see which is more difficult, then imagine a two year old doing the same).
Linguists have always marveled at how children can acquire language proficiency when, as Deacon states, they are “Far less sophisticated in their analytic abilities”. In
Syntactic Structures Chomsky makes the compelling argument that, as Deacon writes, “logical structure of grammars [is] more complex and difficult to specify than anyone previously suspected,” but, “normal speakers of a language seem to know an enormous number of complex grammatical rules and applications without an explicit knowledge of what they know.”
So how can children, who's brains are biased against memorization and the assimilation of novel concepts, learn language? Simply: Children love patterns. Or, as Deacon says, “...a child's initial discovery of the [pattern] relationships underlying language is only the beginning..” When children hear language they focus only on the patterns they hear, not the specific meaning or use of syntax for which they have no context. Given this, when their brains become more receptive to memorization and novel concepts, they have a framework within which to place syntax. This is why we teach children to speak before we teach them to spell. Imagine if we left a child in the crib with a dictionary and expected them to come out as scholars!
As with language so with math. Wolfram is preaching that we should teach children the patterns and grand schemes of math more than the grueling and almost-irrelevant-in-the-real-world computations. He wants us to teach our children the form of math before the syntax.
