The Maths-Twitter Blogosphere or #MTBoS is a network of maths teachers active on Twitter that seems particularly popular in the U.S. Recently, I’ve noticed a few #MTBoS tweets appearing in my timeline that follow a particular form – teachers thank the network for opening them up to a better way of teaching maths.
For many of those commenting, there appears to be two kinds of maths teaching. The first is a traditional, unthinking form of maths teaching with a focus on timed tests and the rote memorisation of facts and procedures. The second kind of maths teaching, the type promoted by #MTBoS, is more constructivist and inquiry orientated, and it often seeks to develop a growth mindset in students.
I think there are broadly two positions to take on maths teaching and they line-up pretty much this way. However, I wonder if the network is missing something important here that might better inform everyone involved in the discussion.
In characterising the alternative to constructivist maths as unenlightened, it appears as if teachers who teach fairly didactically are only doing so out of tradition and because they don’t know any better. At best, perhaps they struggle with the new ways. Yet there is a growing band of maths teachers who actively seek to teach in an explicit and structured way. They believe the best available evidence actually stacks up behind this approach.
The first tranche of evidence dates from roughly the 1960s. In these studies, researchers entered different classrooms and wrote down the behaviours of the teachers which they coded in various ways (the ‘process’). They then looks at correlations between gains in students’ maths scores (the ‘product’) and particular teacher behaviours.
Given that this was correlational research, we cannot be sure about cause and effect. For instance, imagine one of the behaviours that correlated with higher student gains was sharing the learning objectives with students. It could be that sharing these objectives causes better performance. Alternatively, an organised teacher may be more likely to share learning objectives and it might be the level of organisation that had the effect.
However, the number of studies was large and the similarity in findings was striking. Time and again, structured, explicit forms of teaching were correlated with the greatest gains. It is important to note that this was a whole system; a process of ‘I do’ then ‘we do’ then ‘you do’; a gradual release of control from the teacher to the students that is best summarised in an article by Barak Rosenshine for American Educator. A such, this is a whole system of teaching and you wouldn’t characterise a little just-in-time lecturing embedded within a problem-based learning environment as the same thing, even if you chose to also call this ‘explicit teaching’.
Correlational research really needs to be triangulated with experimental research if possible in order to remove any doubts about cause and effect. Such experimental work has been done. A number of studies were run to attempt to teach teachers to use the practices identified by product-process research and they were broadly successful in increasing student gains.
We now can add a more basic level of research from the field of cognitive science or educational psychology. Cognitive load theory is the area in which I am conducting research for my PhD and many of its experimental findings suggest the advantages of teaching in ways similar to those outlined by Rosenshine. One of the earliest discoveries was that novices learn more by studying maths worked examples than by solving equivalent problems, an effect that reverses once they gain more expertise. This fits with a model of the mind being composed of an extremely limited working memory through which all new academic learning must pass, coupled with an effectively limitless long-term memory.
The fit between these more fundamental experiments and explicit teaching more broadly compelled Kirschner, Sweller and Clark to publish their seminal 2006 paper on the concept, a paper they reworked for the teacher audience of American Educator.
There is a debate worth having
Clearly, given the nature of my research, you can infer that I am a fan of explicit teaching. But that does not mean I am right. You could, if you were so inclined, dismiss all of the evidence above on the basis that it is drawn from improvements in test scores and you do not value test scores. That is a valid argument, although I would counter with a question about how to measure the success of constructivist approaches. And that’s fine. That’s how a debate should proceed.
What I am not comfortable with is people in the #MTBoS network being under the impression that more explicit forms of teaching are somehow uninformed or unenlightened. That may be the case in many instances, but it may also be the case that teachers have read the research and have consciously chosen explicit teaching as the best available method.