Inquiry maths is not the answer

I wrote this for an Australian newspaper but they decided not to run with it so I’m posting it on my blog:

New federal education minister Simon Birmingham recently announced nearly six and a half million dollars of government funding for the ‘Mathematics by Inquiry’ initiative for Prep to Year 10 students. Noting that, “when people think of maths they usually think textbooks,” he suggested, “These new curriculum and teaching materials will help make maths more meaningful and more attractive, to students by showing them how they use maths in their own experiences, careers and lives, in a range of everyday situations.”

What’s not to love about such a project? Participation in maths and science seems to be on the slide and teaching maths through real-world contexts sounds like an obvious way to make it more  interesting and relevant to students. The idea has the quality that the American comedian Stephen Colbert has termed ‘truthiness’. It feels right; from the gut.

Indeed it is such an obvious solution that it has been thought of before. As far back as the 18^th Century, the philosopher Rousseau was expressing similar ideas about how children should be taught but perhaps the most influential exponent of ‘learning by doing’ was the American academic, John Dewey. At the start of the 20^th century he did more than any other to popularise this idea and kick-start the progressive education movement.

Unfortunately, this is one of those grand ideas that sound plausible and appealing in theory but don’t work in practice. The benefit of large-scale educational research is that it can sift through the plausible to find the stuff that has real benefits. And inquiry learning does not appear to be such an approach.

For instance, Professor John Hattie of Melbourne University compared research into different teaching methods and concluded that, “the results show that active and guided instruction is much more effective than unguided, facilitative instruction,” such as inquiry learning. Moreover, a study by the American researchers, David Klahr and Milena Nigam, found that the few students who managed to discover a key scientific principle for themselves understood it no better than students who were explicitly taught the principle.

To understand why inquiry learning is not as effective as explicit instruction – where students are given carefully sequenced and structured lessons of increasing depth and complexity — apply the same idea to a trainee surgeon. Dull classes in anatomy and physiology would be cast aside. Instead, we would hand over the scalpel and see if our students could figure out what was wrong. This would never happen, of course, because people would die. Giving a novice maths student a real-world problem to solve is a similar affair. She won’t know what to focus on. Her lack of experience will mean that she cannot draw parallels with other problems. She might be lacking in the basic skills needed. Trying to execute these skills will take up most of her attention.

Cognitive science research has shown that the number of things that we can focus on at any one time is severely limited. A well thought out, sequential teaching sequence introduces new concepts drip by drip whereas an inquiry learning approach tends to overload students who are new to an area of study. We all experience being thrown in at the deep end from time-to-time and it is not pleasant.

We could counter-argue that inquiry learning should have a bit more scaffolding; a few hints and tips to send our student in the right direction. Even so, we are still not teaching skills in a systematic way that builds logically from one to the next. It’s a little like trying to learn to catch a ball by playing games of cricket. You might go through a whole match without having to make a catch.

The evidence may show that inquiry is not the best way to learn something new, but what if it turns more students on to maths? That has to be a bonus, right?

Let’s take this argument at face value and assume that a mathematics lesson that avoids the abstract in favour of the commonplace and mundane is something that kids really enjoy, even if they don’t learn a great deal from it. This still brings to mind a quote attributed to the American Entrepreneur Jim Rohn, “motivation alone is not enough. If you have an idiot and you motivate him, now you have a motivated idiot.”

The answer to declining mathematics and science performance and participation is not inquiry learning and not a dumbing-down of the curriculum. Those strategies are not going to help us outperform the Chinese. Rather, giving children sound basic mathematical skills on which to build provides them with a firm foundation and the confidence to tackle more advanced courses later in schooling.

This is a more long-term and challenging approach but it is more in keeping with what we know about learning than throwing money at a gimmicky scheme.

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