Mathematics education experts

Have we had enough of them?

So, I posted a tweet:

It caused a bit of fuss.

Three points before I address the substance.

Firstly, I find it amusing how much huffing and puffing was generated from what was something of a throwaway tweet - it was the fourth tweet in a thread about an excellent report on research relevant to designing a mathematics curriculum by England’s education regulator, Ofsted.

Secondly, you can bet the same group of people, including various academics and an organiser of education conferences in Australia, will soon be tweeting about how unimportant and insignificant I am while still obsessively stalking me on Twitter.

Finally, the fact that I am a researcher myself - I am completing a PhD part-time which you can read about here - is not a contradiction. I carefully sought out one of the few areas of research that I found promising and valuable.

So, let’s get to the main thrust of this. Have I outed myself as a populist philistine? Not quite.

It was Michael Gove, at the height of the 2016 Brexit campaign in Britain, who infamously suggested, “people in this country have had enough of experts”. For many, this demonstrated the anti-intellectual impetus behind the Brexit campaign and helpfully distinguished intelligent, cultured Remainers from ignorant, deplorable Leavers.

However, the full quote is, “I think the people in this country have had enough of experts... from organisations with acronyms saying that they know what is best and getting it consistently wrong.” It’s worth noting that Gove’s dismissal of experts is contingent on them ‘getting it consistently wrong’. I would be the last to claim that Brexit has been a success, but it is a fact that many of the predictions of experts in the run-up to the vote, such as the IMF’s claim that a vote to leave would lead to a house price and stock market crash, were plain wrong.

Without relitigating Brexit, this is, ultimately, the point. It does not particularly matter whether someone is labelled an expert or not, it matters whether they are right or wrong.

In some fields, such as medicine and law, the discipline is stable enough and accreditation standards are high enough that it makes sense to trust in expertise, most of the time. In other areas, such as economics, the underlying system is so unpredictable that, through no fault of the experts themselves, their predictions need to be treated far more cautiously. When it comes to education in general, and mathematics education in particular, there are systematic flaws that mean most of our experts, most of the time, are wrong. This is due to the epistemology of education - how we seek truth and validate claims.

For example, research often starts with a set of conclusions (drawn from ideology, theory or some other non-empirical source) and works from there:

If a mathematics education expert researches the question of how to make teachers adopt certain practices, but never actually tests whether those practices are more or less effective than the alternatives, then why should you trust their view of what constitutes an effective practice?

When mathematics experts do make the effort to empirically test different practices, they are set a pretty low bar. Professor Jo Boaler, the most prominent maths education expert of all, is probably best known for two studies, one from the UK and one from the US.

The methodology of both studies was similar. In the case of the UK, two schools were selected, one using textbooks and traditional teaching methods and the other using open-ended activities (there were three schools in the US study). Both schools had their idiosyncrasies and the results were not clear-cut. Regardless, this is effectively a sample size of just two. I am not for a minute suggesting Boaler did this, but if I wanted to demonstrate that Approach A was more effective than Approach B, and I had all of the schools in London to choose from, I’m pretty sure I could find two that would fit the bill.

You cannot conclude anything much from such research, no matter how earnestly and faithfully it is conducted. And so ideological stances tend to predominate.

Contrast these established methods with the way that, over the past ten years, teachers have used social media to seek out evidence from the fields of education and cognitive science and communicate that to each other. We are beginning to professionalise. Experts are part of that, but not all experts are equal. We are picking and choosing, creating and applying a new standard as we learn more.

In 2012, Daniel Willingham released his book, When Can You Trust The Experts?, in which he outlined his criteria for assessing educational claims. For mathematics education, I would add the heuristic: most of the time you cannot.

But all is not lost. We probably don’t need them much any more.