Siobhan King is a Mathematics Adviser at HfL. It’s probably fair to say teachers feel that have been hearing mixed messages about what pupils’ maths books should look like in Keystage 1. In this blog Siobhan gives teachers plenty to think about and argues that recording is a key mathematical skill at any age.
A question I often get asked, particularly by KS1 teachers, is…
“What should it look like in their books?”
I completely understand where this question comes from, as I know how hard teachers work to do the best for their pupils and over time, a misconception seems to have developed that books are all about providing evidence to external viewers. With this, teachers have felt a pressure to supply evidence of every learning activity that pupils have undertaken. In KS1, where fine motor skills and writing skills are being developed, this has sometimes translated into maths books full of photographs of children waving around plastic maths resources, which actually provide very little useful evidence of what has been learned.
Therefore, to start my answer, I might ask:
“What should it look like, for who? What is the purpose of the recording?”
Let us consider first who may use our childrens’ books and unpick what they really want to see. I will start with the easy one – Ofsted. If you are recording in a particular way for Ofsted, you need look no further than the Ofsted Myths clarification for schools (link here: https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/463242/Ofsted_inspections_clarification_for_schools.pdf ) or Sean Harford’s (National Director, Education) twitter account:
Ofsted Myth – Ofsted need photographic evidence of children’s work.
Ofsted Fact – We don’t. We’re happy to speak to children during an inspection about what they have learned. We’re very aware of teachers’ workload.
If Ofsted do not need maths recording in a particular way as evidence – and they don’t – why should SLT, or you for that matter? I guess what we all want is evidence that our pupils are learning and building an increasingly deeper understanding of what we teach them. Yes, books may be one source of evidence to support this, but there are others, not least (as Sean Harford says) talking to children.
Does this mean it is not worth recording anything in maths? Only if you consider the sole purpose of maths recording to be about providing evidence for an external body. I would argue that there are many reasons to record in maths, that mathematical recording is integral to our children building a deep mathematical understanding and that it can be useful for teachers too.
So why is recording in maths important?
Firstly, recording is a necessary part of building mathematical understanding. We know that depth of understanding is strengthened through transferring between concrete, pictorial and abstract models so recording alongside other created models supports deeper learning. It is through pupils representing their understanding that they explore and make sense of what they know. This is borne out in research by Carruthers & Wothington (2010) in which they noted children’s own recording supported, “deepened thinking about the mathematics in which they are engaged, and significantly, about their use of symbols and other visual representations to signify meanings. They enable children to build on what they already know and understand”.
In addition, recording while working on a problem can be helpful for pupils to reduce cognitive load by using jottings or identifying key facts, which may be used later. This type of recording may not be intended for anyone else to read, but can form a log of how pupils have worked a problem through and can be incredibly useful for teachers to identify misconceptions and the route of pupil mistakes.
Recording can be about developing a skill. For example, making use of abstract symbols and numerals, requires learning their formation and practice in using and recording them as well as learning about their meaning.
Recording can also sometimes become a mathematical tool in itself, helping pupils to explore problems and develop reasoning skills. Through recording, pupils can expose underlying patterns and structures, which lead to greater understanding or further questions to explore.
For pupils, recording can provide the opportunity to communicate with an audience. Being asked to explain and prove understanding to an audience provides an opportunity to develop precision in reasoning and again deepen understanding.
What is selected for recording can also affect pupil perceptions of how things are valued and support them to focus on different aspects of the learning they are undertaking. If pupils are asked to record how they tackled a problem rather than the answer to it, then they are much more likely to think, talk about and focus on these. By doing this, the teacher can show pupils the range of different approaches to the same problem and draw out discussions around different choices, evaluate strategies and consider the range of possibilities.
Going back to the original question: “What should it look like in their books?” It depends on the purpose of the mathematical recording. Is it to make connections between models, practice a new skill, record the journey through a problem, develop precision in reasoning, focus on reflection and evaluate strategies…? I can tell you one thing – it should not be simply to provide evidence for Ofsted!
In the Nrich article “Primary Children’s Mathematical Recording” (2013) there are some useful reflections as to how all teachers could think about making the most of mathematical recording:
Do we always make it clear to learners what the purpose of their recording might be and who it is for?
Do we value all types of recording and mathematical graphics?
Do we discuss a range of recording strategies, for example by asking, “How else might we record this?”
On reflection, I think the question many KS1 practitioners are actually asking is,
“How is it achievable to develop manageable, meaningful recording in KS1?”
and perhaps this relates to what we are expecting, but also to the opportunities we provide and how we are supporting its development. In my next blog, I will try to capture how current practitioners are developing pupil recording at KS1.
Carruthers, E. & Worthington, M. (2010) “Children’s Mathematical Graphics: Understanding the Key Concept”, Published on the Nrich website. Nrich Primary Team (2013)
“Primary Children’s Mathematical Recording” Published on the Nrich website.