The evidence paradox that is holding innovative education back – from contributor Conrad Wolfram

As we continue to explore how an enablement mindset could help foster more experimentation in government, it seems clear that the reliance on firm evidence can sometimes be a barrier to innovation – which requires room for failure. Mathematician and technologist Conrad Wolfram explores what a reliance on evidence can do to stymie maths education.


I’ve long been interested in how technology and computation can move our lives and economies forward, and over the years I’ve realised that the school subject of maths has become almost totally detached from its real-world application. As a result, I’m involved in many debates about the teaching of maths in schools.

The question of evidence and its role in driving innovation comes up regularly, and I’m often struck by the fact that we confuse two very different “importance of evidence” conversations. One with which I completely concur, and one with which I vehemently disagree. I call the two evidence uses innovation-led evidence and evidence-led innovation.

The difference is whether you build your “product” (e.g. phone, drug, curriculum) before you test it, using those tests for iterative refinement or rejection, or whether formal evidence that exists from previous products determines any new products you build.

Innovation-led evidence is highly productive in achieving outcomes, although care must, of course, be taken that those outcomes reflect your objectives. Evidence-led innovation almost by definition excludes fundamental innovation, because it means you only build stuff that past evidence said would work.

When you build something significantly new, it isn’t just a matter of formally assembling evidence from the past in a predictable way. A leap is needed, or several. Different insights. A new viewpoint. In practice, these will often derive from a mixture of observation, experience and what still appears to be very human-style intelligence. But wherever it comes from, it isn’t straightforwardly “evidence-led”.

I strongly agree with the late physicist Richard Feynman, who explained neatly in one of his famous 1960s Caltech lectures how the scientific process works. In summary, he said: guess, make a theory, test it, and compare the results with that theory.

Evidence-led innovation stifles major innovation because it locks out the guess, yet I firmly believe that it’s what most of “evidence-led” education is talking about – with painfully little innovation-led evidence applied. I believe this exposes the failure of many in charge of education to understand how major innovation normally happens and how “evidence” can often stifle innovative leaps rather than encourage them.

I’ve faced this repeatedly when advocating a major reform to maths education, called Computer Based Maths (CBM). I’m often asked, “do you have evidence it works?” My answer to that is, “where’s your evidence that today’s traditional maths education works? Have you done randomised controlled trials?”

One problem with the evidence-led innovation crowd is that they often have no idea how hard it is to build something completely new. They think you can do micro-innovations, then test, then micro-innovate, then test.

It’s been amazing to me just how different every aspect of the maths curriculum becomes when you don’t need to assume hand-calculation. Equally amazing is how deep everyone needs to dig into their own understanding to uncover those differences, particularly since those involved have learnt maths in the traditional way. A narrow reliance on the existing evidence won’t get us where we need to be. We need to be innovation-led.

You might ask whether now is the time for a new maths curriculum – can we really take the risk? As guesses go, the idea that maths education should be the same subject as maths in the real world, i.e. using mechanised computation rather than the current hand-calculation proxy, is extremely sure-footed. The risk of not being in step with the real world poses a very significant danger.