On the myths of mathematics instruction
A new research paper that draws a line under what works
My first couple of years in the classroom were a bit of a struggle. Not so much for me, but for my students. I had the curse of compliant girls, who were ready to learn. I designed ‘engaging’ lessons, they practised polite disengagement and everyone seemed happy. It wasn’t until the stakes were higher that I began to realise that my generally inoffensive and mildly entertaining lessons weren’t really producing much learning. I sometimes wonder whether my awakening would have come sooner if I had started my career in a school where students were not so polite and compliant - would I have been forced to discover explicit instruction sooner?
It’s easy to bob along as an English teacher, immersing students in the power of literature, inviting highly literate students to workshop their creative writing. But I did wonder why nearly every senior school teacher would suddenly ditch the fun stuff at Year 11. I was incredibly lucky in my third year of teaching to work on a team of Standard English teachers who happened to be some of the most competent teachers in the school who simply needed a year’s break from the Advanced English marking load. And guess what? They used explicit instruction, also derisively known as ‘spoon feeding.’
I started to develop views about ‘things that made sense’ and things that didn’t. I noticed that my students learned more when I told them about content and ideas, and could do more when I showed them. And then I discovered Twitter and found that the ‘things that made sense’ had a name: Science of Learning. In the early days, I assumed that some subjects were immune to progressivism. I mean, how can one ‘inquire’ their way to speaking French? Well, progressivism has crept into languages instruction. But surely mathematics was off the table? Surely students can’t be expected to essentially figure out mathematics on their own? Nope.
The Centre for Independent Studies has released a research paper about the myths that undermine the teaching of mathematics. It’s short, digestible and well-supported. I wouldn’t say that there are direct links to only progressive ideas and dispositions littered throughout the paper, but three things strike me:
It seems that a lot of the myths about the teaching of mathematics are built on poor to no evidence of their efficacy.
Quite a few of these myths are built upon student construction of knowledge and the idea that all students are equally ready to learn.
Many of these strategies don’t prioritise the direct teaching of skills and concepts.
The myths are summarised as follows, but I highly recommend you read the paper.
Myth: conceptual before procedural understanding (Truth: teach both!)
Myth: teaching algorithms is harmful (Truth: it’s not!)
Myth: inquiry learning is the best approach (Truth: learning should be scaffolded before moving on to problem-solving!)
Myth: productive struggle is important (Truth: it assumes a lot about motivation, prior knowledge and learning readiness!)
Myth: growth mindset increases achievement (Truth: there’s no evidence that this is a good use of instructional time!)
Myth: executive function training is important (Truth: there’s no evidence of far-transfer!)
Myth: timed assessments cause mathematics anxiety (Truth: done right, they don’t!)
I will say that this paper is very balanced. It avoids binaries, for example by suggesting the best methods for structuring inquiry learning. And I learned that there is even a method that teachers can use that puts a framework around supporting students to move from novices to novel problem-solving. Sometimes in my zeal for explicit instruction, I need reminding that eventually, the training wheels need to be taken off. Self-Regulated Strategy Development (SRSD) sounds like just the kind of scaffold I need!
Sometimes I feel like my newsletter is preaching to the choir. I wonder how many years it took you to figure out what works after your ITE set you up to ‘inquiry-learn’ your way to being a competent teacher. For me, it was two years too long, and even then, it’s been a slow road at times. So I’m going to give you a highly specific call to action - to send this newsletter to the newest mathematics teacher you know. Call out the myths and help them on their way to what works for their students.