Amidst the undulating and unrelenting grimness of current events, I feel almost bad for being excited about my promotion to Director of Learning for Maths in September, and the fire that it’s lit in my, until now, rather limited CPD efforts. Almost as if it was slightly tacky, and I should instead be walking around with a permanently stoic expression, looking like an overcast November day.
Armed with Teacher Tapp and unspent petrol money, I’ve invested in a steady trickle of books from authors who I’ve long looked up to, and set about reading in every spare second I can prise in between childcare, job and general life admin. Honestly, it has reignited my love of teaching in a way that I simply had not anticipated. I knew I enjoyed teaching, but I simply had forgotten what it felt like to have the space and time to think about teaching. In the day-to-day of life, you work so hard just to keep going; with the lockdown the space opened up to step back and critically look at what exactly I was doing. As it turns out, there was a lot to critique: page after page, my self esteem and practice took heavy blows as I came to realise that, while my teaching was generally decent, there was just a vast amount of improvement to make.
This blog is an attempt to chronicle and make sense of that reading.
Rediscovering purposeful practice: or, how I learned to stop worrying and love the noise
So, the first of my revelations is the confluence of Mark McCourt’s Teaching for Mastery and Craig Barton’s How I Wish I’d Taught Maths and Reflect, Expect, Check, Explain. To get to it, first we need to be familiar with the idea of a progression of a learning episode (distinct from a lesson – because, of course, it takes different amounts of time to tackle different concepts). The progression begins with some sort of knowledge acquisition phase where students acquire inflexible knowledge – knowledge that is tied to the surface structure of how it is presented (all Pythagoras questions look like an explicit right angled triangle with just two sides marked, for example). That inflexible knowledge is then carefully worked with and increases in its flexibility – the ability of the student to identify its application to an ever wider set of problems, which may look very different to the practice in the knowledge acquisition phase.
The below, taken from Gary Lamb’s post on the Complete Maths website, follows Mark McCourt’s proposed progression – showing the knowledge acquisition phase (roughly speaking, the ‘Teach’ and ‘Do’ phases) and the knowledge development phase (again, roughly speaking, the ‘practise’ and ‘behave’ phases). The bar model illustrates the general principle that around 80% of a learning episode should be going through the Teach, Do and Practice phases, with 20% on the Behave phase (which is effectively an opportunity to interleave ideas taught some years prior into the current episode).
In Teaching for Mastery Mark suggests that the typical teaching follows a pattern of a chunk of ‘Teach’ then a sizable chunk of ‘Do’ followed by a little bit of ‘Practice’.
Reflecting on my own practice, I realise that I had fallen into a cycle of heavy dependence on the ‘Do’ phase and tricked myself into thinking that performance (correct answers on mini-whiteboards or in books) was the same as my students properly understanding the concept. While that false equivalence is a topic for a different post, the general idea was that I wanted my students to become fluent in a topic, and that held so much weight in my mind that the ‘Practice’ part was often relegated to extension material alone. After the lesson, or set of lessons, if a student hadn’t gotten onto the extension we simply had to move on. The wheels of education keep on turning, after all.
Obviously, this is not right. Part of what makes maths engaging and fun are, in the parlance of Craig Barton, purposeful practice activities. It’s the weird, obtuse tasks one can find on Don Steward’s website, or some of the wonderfully crafted resources on mathspad that encourage you to dig a little deeper and wade out of the comforting embrace of umpteen correct answers in a row.
This is not to say that I never used these resources – in fact, I made heavy use of mathspad – but quite often they seemed to only shine for the higher sets, and if I engaged lower sets with them then I did an eye-watering amount of scaffolding and support. Scaffolding purposeful practice tasks isn’t necessarily a bad thing, but too much and it somewhat robs the task of its desirable difficulty (to potentially misuse the phrase).
Why did I fall into this? I can trace it back to my PGCE and NQT years, which, at the time, felt as though I was cartwheeling through a firework factory while on fire. In my view, I would explain how to do a procedure, do a little bit of fluency work and then whoosh, onto this really fun activity! To my surprise, reactions tended to fall into three camps:
- “Huh, this is pretty cool”: a glowing endorsement by teenage standards, but also relatively rare.
- “I don’t get it, I can’t do it, I’m not doing it because I don’t get it and I can’t do it so I’m not-“: this was one of the more common responses in the classroom.
- “Can’t be bothered”: this was the other dominant reception.
There’s obviously a fair bit of disguised ‘2’ in reaction ‘3’, but the cumulative effect was that the classroom rapidly would become unmanageable. A sea of hands, a particularly anxious pupil rapidly asking a tonne of questions to ring out as much support as they could and a good deal of discussion about the week’s ‘birthday beats’ rota all combined to make the environment approximately as stressful as defusing a nuclear bomb.
“…the environment [was] approximately as stressful as defusing a nuclear bomb.”
After attempting these sort of tasks repeatedly and watching them fall apart in front of me was demoralising for both myself and the students. As I progressed in my teaching, I saw how fluency practice (the Teach-Do cycle) allowed me to build confidence and (perceived) competence quicker as well as ensure a more controlled, calm and productive environment. Indeed, Craig refers to the idea that success is motivating, and I saw how students switched on for fluency practice and switched off for purposeful practice. Naturally, being an inexperienced teacher in desperate need of a win, my lessons shifted more and more to securing fluency above all else. As the years rolled on, I slowly began doing more purposeful practice, but it definitely had an ‘optional extra’ quality to it, on the whole.
Now, securing fluency is incredibly important – without secure inflexible knowledge, there’s little chance of developing robust flexible knowledge – but it is only the beginning of the journey. Therefore, I can’t keep pushing purposeful practice out to the fringes of my students’ experiences, and I have to make it an integral part of the journey because it holds real intrinsic value for all learners, not just the top end.
Given all of that, then how can I embed purposeful practice in such a way that doesn’t give everyone in a 5 classroom radius mild PTSD? What was I doing wrong all those years ago?
- The first thing is that I’m simply a better teacher now than I was then. I have hundreds more teaching hours under my belt, and I can manage a classroom much better than I could do before. I shouldn’t be scared of the lesson going off the rails because I have the tools and skill to bring a lesson back from the brink in a way that I didn’t then.
- I also need to select the activity to be appropriate. What is it doing, and what do I want the students to get from it? Is it of an appropriate difficulty, or does it include concepts that we haven’t seen yet?
- Scaffolding the task is important, but a much better way of ensuring access (and therefore that motivating success) is to use formative assessment before the task to ensure that students can do all of the skills needed for the task. Such tasks often require knowledge outside of the novel concept that is the focus of the lesson, and it doesn’t matter how fluent they are in whatever we’ve just done if they then come apart when adding some fractions together.
- Finally, I need to actually do the task. Shamefully, I often did not fully do the tasks I set for students – snowed under as an NQT, I cut corners where I could assuming my maths was strong enough to wing it on the fly. I can disclose to you, that I definitely did not wing it on any sort of fly. But more importantly, doing the task in advance tells me where students are likely to struggle, what knowledge they really need to do it and also the questions and prompts I could give during the task itself to stretch or support students as needed.
Who knows what will happen when I first try it with my classes (now likely to be in a new school). Maybe it will be a disaster. But I can’t back down – I have to make this a meaningful and robust part of my practice. In time, with active reflection and adjustment, being consistent about my expectations and also making sure I plan very carefully, I’m sure I can bolster my teaching and enrich all my students’ learning.