Is the #MTBoS missing out on something important?


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.

Process-product research

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’.

Experimental work

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.

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5 thoughts on “Is the #MTBoS missing out on something important?

  1. As well as (or instead of) being research-informed, there’s also the possibility that many teachers have tried more constructivist approaches and, through experience, found them wanting. This is the case with very many working teachers, I suspect.

    Those who incessantly preach (and occasionally, although not always, practise) more constructivist forms of teaching tend to progress with prodigious speed into either senior administrative roles or academia, in my experience.

  2. As someone who considers herself a part of the #MTBoS, I think you’re looking for a problem that isn’t there. The #MTBoS definitely isn’t a monolith. As a teacher who applies CLT in my work and is pretty straightforwardly an explicit teacher, I don’t feel looked down upon by the group. In fact, a presentation at #TMC17 (Twitter Math Camp is the closest thing to an official #MTBoS conference) is what gave me the final push to dive into the research and commit to completely revamping my teaching style. I think the debate is happening, just perhaps not in places where you’d see it. Speaking purely for myself, I keep meaning to blog about what I’m doing and reading (I *really* need to do one on the ResearchED Philly conference) but I end up shelving it to deal with the day to day of teaching instead. I suspect that’s happening for other teachers as well.

    I think that some of the thanking the #MTBoS tweets that you see are less of a “thanks for showing me a better way” or more of a “thanks for sharing your resources and your thinking with me so I don’t have to recreate the wheel”. This is in no way a slight on my district but since the Common Core roll out and the push for more electronic resources in the US, high school teachers are given less and less physical resources to work with and are having to create their content out of thin air. The #MTBoS is overwhelmingly generous and if you post about your resources, you’re generally willing to share them with anyone who asks. When you’re sticking to prewritten worksheets because that’s all you’ve got, having someone share the awesome lessons (and the thought process being their development) they created is a life saver. I think that’s the “better way” that you’re seeing.

    My two cents, anyway.

  3. Hi Greg!

    I appreciate your concern that #MTBoS is not doing the research justice. I gave a talk on Task Design some months back that more or less is a peak into the world of #MTBoS. It is true that they don’t emphasize rehearsal or practice. However, I believe you would be hard-pressed to find teachers in the community who don’t lead their students in guided practice!

    I agree that explicit instruction has been implicated as the best available method. However, consider context. Have you ever taught at a school where: students, when asked to run a mile in gym shorts, walked one lap, in street clothes? Imagine how they might respond to “I do”, “we do”, “you do”…

    Now in some school networks (like Uncommon Schools in NY, NJ, MA) the entire culture provides the structure and discipline to enable this level of compliance. Yet most schools are not well-oiled machines and many teachers are looking for ways to engage their students and meet the varying needs of the 30 kids sitting in front of them with reading levels spanning 6 grade-levels.

    Here is a post on my talk if you are interested, https://evanrushton.blogspot.com/2018/09/cmpcpp-task-design.html

    There is also a question as to whether this kind of pedagogy is dehumanizing… a topic for another day.

    1. Yes – I have taught in challenging schools in London.

      My view is that you are presenting a false choice here. Ultimately, children value the learning process if they learn something and feel a sense of achievement. There is a reciprocal relationship in the research between maths motivation and self efficacy. We don’t need to use one approach for motivation and a different one to maximise learning, although I do favour variety and a pleasant, purposeful atmosphere generated by an enthusiastic teacher.

      As for dehumanising – it is almost the defining feature of humans that we have evolved to obtain and assimilate knowledge from other members our culture. Nothing could be more human.

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