I’ve been reading a fascinating paper by a group of maths education researchers with the title, “Positioning Mathematics Education Researchers to Influence Storylines.” It is interesting for what the researchers do and don’t say. It was published in March in the house journal of the U.S. National Council of Teachers of Mathematics (NCTM) and represents the work of the NCTM’s research committee.
The committee seem to be concerned that a group of Canadian parents and mathematics professors have influenced the debate in the Canadian media about maths teaching methods and they propose the use of ‘positioning theory’ by maths education researchers as a way to fight back and avoid this situation arising in the U.S. This involves infiltrating bodies that make decisions on maths education and manipulating ‘storylines’ about maths in the media.
They identify three storylines that they disapprove of. They are:
1. There Are Two Dichotomous Ways of Teaching Mathematics
2. Mathematics Education Research Is Not Trustworthy
3. The Main Goal of Mathematics Education Is to Produce a STEM Workforce
The first two of these ‘storylines’ are essentially true.
There are broadly two distinct ways of teaching mathematics. There is an explicit approach where all concepts and procedures are fully explained and there is the constructivist alternative where students are asked to figure certain things out for themselves, with varying amounts of guidance. Maybe they are not dichotomous: It may be true that at any one time you can only be teaching maths one of these ways but that doesn’t mean you can’t mix these approaches over the course of a unit of study. But I don’t think anyone is claiming that you can’t use a variety of methods. The argument in Canada, as I understand it, is that a shift in the balance towards relatively more constructivist maths has coincided with a decline in the performance of Canadian maths students.
Oddly, the article praises Jo Boaler’s attempts to reach out to the wider public through her blog and other activities and yet Boaler herself has done much to promote the idea that there are two dichotomous ways to teach maths. In her famous UK study, she compared one school, ‘Phoenix Park’, that followed an approach described as ‘project-based’ and ‘open-ended’ to another school, ‘Amber Hill’, that followed a more ‘traditional’ one. This methodology was broadly repeated in the U.S. where the ‘reform-oriented’ school, ‘Railside’, was compared with two other schools which each offered a mix of maths courses.
And this particular approach to research might help explain some of the scepticism that exists about its trustworthiness. We are talking about very small samples of schools here: Two in the U.K. and three in the U.S. We might have simply chanced upon particularly effective examples of constructivist teaching and particularly ineffective examples of more explicit teaching. In fact, I reckon I could produce the opposite finding – a win for explicit teaching – by carefully researching teaching methods and then selecting schools on the basis of their reported results prior to running such a study. It is therefore quite reasonable to caution about drawing too many conclusions.
When you look at the broad mass of research conducted by maths education researchers then the picture becomes even less clear. Many studies don’t even study the effectiveness of a teaching method. Instead, they report an initiative where teachers are trained in a constructivist maths teaching method and then report whether this training led to sustained changes in teaching practice (e.g. here, here, here, here , here and here). The teaching method is simply assumed to be superior, even though this is not tested as part of the study.
And this is not an argument between maths researchers who possess research evidence and others who just possess a feeling in their bones. There is plenty of evidence to support the argument of those Canadian parents and maths professors. The effectiveness of explicit instruction has been well documented, from the process-product studies of the 1960s and 1970s – including Project Follow Through – to experimental studies and cognitive science research. And this is all supported by a strong theoretical framework.
Even my recent investigation of PISA data showed that student-oriented forms of instruction seem to be less effective. I don’t think this is particularly conclusive on its own but it is interesting to note that PISA has not highlighted this relationship, nor have the maths education researchers who have written columns about this data, preferring instead to focus on less significant correlations that are more supportive of their theories.
Turning to the third storyline, I have to share the disapproval of the committee. Teaching maths is not about producing a STEM workforce; this is simply a happy byproduct. We teach a curriculum in order to pass on culture and cultural artifacts to the next generation. We cannot predict what the future will bring for individuals or which knowledge they will eventually find useful or fulfilling and so we choose the content on the basis of that which has endured: powerful ideas that have explanatory value, that have proved useful in the past and that are therefore likely to be useful in the future. We don’t exclude anyone on the basis of not being academic enough or because we assume that they are destined for a particular type of career. The fruits of civilisation are our common heritage and should be available to all.
Yet I have some empathy for STEM enterprises that watch the fall in mathematics standards, worry about it and start to become more vocal in response.
What don’t the committee say? They never address the fact of the declining maths scores that convinced the Canadian parents and maths professors to start arguing the case for more explicit teaching in the first place. They never state the kind of mathematics education that they would like to see more of in schools. We can perhaps infer this from the output of the researchers who they highlight. Instead, the committee are focused on applying the sociological notion of ‘positioning theory’.
My advice to these researchers is very simple. Trust the public with the facts of the debate. Come out vigorously, explaining your positions on maths teaching, the evidence for these positions and what you think needs to be done. These will be challenged but that is to be welcomed as part of a democratic debate. The demos can then make up their own minds about which education policies to vote for at the ballot box.
We don’t need all this sneakiness.