Two education researchers in Australia, where I live, Jill Fielding-Wells and Kym Fry, recently argued that “inquiry-based learning” is the solution to get more students to enrolling in math courses in 11th and 12th grades. It is not.
The reasons why have implications beyond Australia and may be of interest in other countries where academics and school leaders are pushing pedagogical approaches that prioritize question-asking and exploration by students over direct instruction by teachers.
Fielding-Wells and Fry claim that a key reason students do not take math in Year 12 is because “they believe maths is too hard, too guarded by a rigid set of rules and not applicable to real life.” I agree with the first point. If students believe it is too hard then that requires us to ensure that we teach them by the most effective means possible. As they improve at mathematics, they will find it less hard and become more motivated. This logic is the inversion of the usual calls to make mathematics more engaging in order to motivate students so that they will then achieve.
Math really does have a rigid set of rules. If this is not to the taste of some students then we cannot do much about it. And why do we hold school math to a standard where it has to be relevant to the real world? The real world can be pretty mundane at times. How is art relevant to the real world? How is writing a story relevant to the real world? Should we insist seven-year-olds replace fairies and dragons with corrupt local politicians and broken washing machines? Should we tell children not to bother learning to draw because you can take pictures with your iphone? I suspect complaints about the relevance of math stem from the perception that math is hard and the way people rationalize the fact that they have not mastered it.
I definitely do not think that having a long and tedious discussion of how many pizzas are needed to feed the class, where everyone has a chance to express their opinions in the possible absence of mathematical understanding, is an effective way of achieving such mastery. Yet the authors argue this is a valid approach because, as they put it:
“Inquiry more closely aligns with the real work of mathematicians. In practice, mathematicians identify, or are approached with, a problem. They must decide on the maths they can use to solve it. Then they come up with a procedure, solve using the mathematics and monitor the outcome.”
School children are not professional mathematicians. There is a difference in the level of expertise here. Why would we assume that the most effective way of teaching math would be by trying to copy what expert mathematicians do? Paul Kirschner, a professor at Open University in the Netherlands, has written about this strange conflation, which he describes as confusing epistemology – how new knowledge is discovered about the world – with pedagogy – the best methods for teaching well-established knowledge to novices.
It does not matter which approach looks most like what professional mathematicians do. It matters which approach is most effective.
To demonstrate the supposed effectiveness of inquiry learning, the authors draw on a most unconvincing review article which, as part of its abstract, describes how, “references are given with explanations or possible reasons for the results that are not always consistent and, at times, even contradictory.”
These results are pretty easy to explain. You usually get a boost for any intervention when compared with a control because the control is usually business-as-usual. Teachers and students cannot be blind to whether they are getting something new or the same old same old and so you initially see some gains through a kind of placebo effect. And yet inquiry learning has been relatively inconsistent at pocketing even such modest gains.
This is because inquiry learning ignores what we know about the mind. It ignores that we have very limited working memories, that new academic knowledge has to pass through working memory and so we need to limit and control what we wish students to pay attention to in the first steps of learning. Otherwise we will overload them. This is why providing models and worked examples is effective. This is why confronting novices with an open-ended problem embellished with arbitrary and distracting real-world details is not effective.
Not only will such instruction be ineffective, it is likely to be frustrating and potentially demotivating.
This is probably why research into the practices of effective teachers shows that they tend to fully explain new concepts from the outset, model key processes, and initially guide student practice. This is also probably why data from the Programme for International Student Assessment, or PISA, shows that inquiry-type approaches correlate with worse PISA test scores in math and science.
In responding to comments on her article, Fielding-Wells conceded, “if you only taught using Guided Inquiry you would not be able to address all of the content in the curriculum as it currently stands …The teachers we work with typically teach one inquiry a term and will use other approaches such as explicit teaching (for example) during the inquiry process.”
Inquiry learning is not the solution. It would probably make things worse. That doesn’t mean that students shouldn’t ask questions or even that teachers shouldn’t sometimes ask students questions to which the students won’t immediately know the answer. But as a solution to education problems, “inquiry-based learning” is oversold.
Greg Ashman teaches physics and mathematics at an independent school in Ballarat, Australia and is the author of The Truth About Teaching: An Evidence-Informed Guide for New Teachers. He blogs at Filling the Pail, from which this post is adapted.
