Mathematics Mastery is a complete curriculum programme from Ark Curriculum Plus, which includes all the teacher and student-facing resources needed for high-quality mathematics lessons, assessments and insights, planning support and guidance, curriculum-aligned subject-specific PD, and bespoke school support.
Here, Principal Development Lead, Clare Hill, discusses how a more collegiate approach to lesson planning offers high-quality PD and develops greater consistency across your maths team.
John Hattie, ‘Visible Learning for Teachers’, 2012
Have you ever had a colleague that you know you can rush to at the last minute when you’re struggling to work through a problem when you’re unsure where to start with a topic? You might know the infamous Frog problem on Nrich. This was my nemesis when I first started teaching, and I valued my trusted colleague who supported my various panics when I just couldn’t ‘see’ how to even start it!
It would have been transformative for me as a new teacher – or even as an experienced teacher working through the task for the first time – to have the chance to talk through these tasks with a colleague. The opportunity to sit down with my colleagues, do some maths together, talk through how we might approach a task, consider how our students may think about it, and the misconceptions they may have, would help me and my team to develop a collective and agreed approach as a department towards the task or topic – and even our subject of maths.
At Mathematics Mastery we give this process a name – Departmental Workshops (DWs). For the whole team, completing a Departmental Workshop together is one of the highlights of our week. It’s an opportunity for us to ‘do the maths’ - our favourite phrase! It is also an opportunity for us to learn from each other, challenge each other’s thinking and assumptions, and can also provide the curriculum designer with a chance to think through and maybe present the task in different ways.
A Departmental Workshop focuses on a specific task from the upcoming week’s teaching materials, and the DW comes with its own prompts and guidance to prompt discussion across a team. It is a chance to discuss firstly the substantive knowledge of the task – i.e. the content of the curriculum that we teach as established fact – and then the disciplinary knowledge of our subject, which we call the dimensions of depth – conceptual understanding, language and communication and mathematical thinking. When we bring together curriculum content and pedagogical approaches like this, we really see the transformative impact of Mathematics Mastery, and DWs are one of the best places to see this in action.
My colleague and I recently had the privilege of running a Departmental Workshop with 40 of our colleagues from Ark Schools, and their comments show just how powerful these sessions can be in helping cultivate a collegiate approach to teaching maths:
‘DWs are a great place for a discussion. As a team we look at different ways of sequencing a unit. We look at different methods then agree a method for consistency.’
Another colleague said they
‘discuss different approaches to teaching the topic. Then we agree the ‘best’ approach which as a department we use in teaching.'
In our Departmental Workshop with Ark teachers, we examined the introduction of double-sided counters to support students’ understanding of subtracting a negative number. As always, we started off by ‘doing the maths’!
For many teachers in the room, this was their first experience using manipulatives to develop a conceptual understanding of positive and negative numbers. Across the room, we heard teachers collectively making sense of why and how they would use counters. This teacher was trying out the second calculation:
Once I laid down my four positive counters I asked myself, ‘Does it actually matter how many zeros I put in’? So the questions we were looking at were, one: how does the student know how many zeros to actually put in, and two: does it actually matter? When we moved onto the third question we developed that conceptually further.
What a rich, mathematical discussion! In a very short time, teachers had not only completely reconsidered their thinking on how to teach addition and subtraction of negative numbers but also started to plan how to introduce manipulatives as representations of numbers into other areas in the curriculum.
Now imagine how difficult these insights, realisations and revelations would be to achieve as an individual teacher, planning in isolation from their team. Would they feel confident in implementing this approach? What level of consistency would you see across a department? Would their students benefit from the collective, harnessed knowledge of a whole department?
Hattie, J., 2012. Visible learning for teachers: Maximizing impact on learning. Routledge.
Owen, S. (2005) ‘The Power of Collegiality in School-Based Professional Development’. Australian Journal of Teacher Education.