Taking small steps: the process of atomisation

With returning to teach classes post-lockdown we have all had to adapt our approaches somewhat to match the situations we find ourselves teaching in. For me it has made me revisit aspects of Explicit Instruction (see this article here) and also Rosenshine’s Principles of Instruction. I want mainly to be able to teach “from the front” to avoid too much movement around the room, yet I still want to know how all my students are doing and make sure that none of them get left behind.

A specific aspect I have been thinking about recently is Rosenshine’s Principle no.2:

“Present new material in small steps: Only present small amounts of new material at any time, and then assist students as they practise this material.”

This also ties in with the National Centre for Excellence in Teaching Mathematics (NCETM)’s 5 Big Ideas of Teaching for Mastery: “Small steps are easier to take”.  From this comes the process of atomisation*:

Atomisation – separating something into fine particles. atomization, fragmentation. division – the act or process of dividing.

In order to support all of my class in moving forward together, I have been trying to use the process of atomisation to break down each topic into really small steps and then to teach each one of these explicitly. As teachers we have the Curse of Knowledge – we sometimes make the assumption that an aspect of a concept is obvious to students because it is obvious to us and it takes a bit of thinking on our part to overcome this.

For example, I am about to teach rearranging formulae to my lower attaining year 8 group. Questions are often phrased as “Make x the subject of the formula…” which in itself is quite a complex sentence, so I am going to begin my lesson just by identifying what the subject of a formula is, and then getting students to tell me when x is the subject of the formula, and when it isn’t, so that they are really clear about what they are going to be asked to do. My small steps for this topic might be:

  • Identify what the subject of a given formula is
  • Identify when x is the subject and when it isn’t
  • Understand inverse operations
  • Perform inverse operations in one-step equations
  • Be able to perform inverse operations in the correct order in multi-step equations
  • Perform a check that the formula now has the correct subject

It is a really useful activity for a department meeting to try to identify the atoms of a particular process or topic at first individually, and then by comparing with colleagues. It can also be helpful to “write a line, miss a line” and then try to fill in the blank spaces with atoms that might have been missed first time around, and hence break the process down into smaller and smaller atoms.

The process of atomisation really helps me as a teacher to consider the micro-decisions that I am making every time I solve a problem and to make sure that I am supporting my students in making these as well. I can then use formative assessment in the classroom to find out as I am teaching which atoms my class are already fluent in, and which I need to give them more practise in before we move on. This small-steps approach should mean that I bring all the class along with me, addressing gaps and misconceptions on the way.

*Term coined by Bruno Reddy. Further reading: Naveen Rizvi, Kris Boulton and Ben Gordon have written extensively on atomisation, as has Craig Barton in both of his books and Emma McCrea in Making Every Maths Lesson Count.

Deb is a maths teacher at Durrington High School. She is also a Maths Research Associate for Durrington Research School and Sussex Maths Hub Secondary Co-Lead and will be delivering our training on the EEF Guidelines for KS2 and 3 Maths.

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