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KS1 Mathematical Recording is not just for Ofsted.

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.

References:

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.


Herts for Learning is a not for profit organisation that provides a wide range of training and CPD courses, events and conferences to support teachers and school staff in their professional and also offers an extensive range of resources to support their offering through the HfL e-Shop.  Please visit the website for more information.

RUCSAC pack your bags, let’s hit the bar instead

Charlie Harber is the Deputy Lead Adviser for Primary Mathematics at Herts for Learning.  She has  researched the positive impact bar modelling has on pupils’ access to worded problems.

Recent analysis in many schools and discussion with subject leaders confirmed what many teachers have long suspected, that many children have the procedural skills but they  seemed to abandon all reasoning  when they need to apply them once they are embedded in a word/story problem. Many schools in the UK use RUCSAC to help the children, but have you considered why that doesn’t work? Is there a better way, one which just doesn’t prepare them to answer questions in tests, but also deepens operational understanding, exposes misunderstandings and develops reasoning – empowering the children to discuss the mathematics?

Simply put, yes I think there is a better way – bar modelling. Continue reading “RUCSAC pack your bags, let’s hit the bar instead”

Is mastery just a passing fad?

 

Nicola Randall, Mathematics Teaching and Learning Adviser at Herts for Learning

Before I even start to tackle this question, I think it is helpful to clarify what we mean by ‘fad’ and the best way I could think of doing this was to consider some examples.

  • Leg warmers worn anywhere other than inside a dance studio: fad
  • No make-up selfies: fad
  • Replacing actual laughing with the word “LOL”: fad
  • Dressing as clowns and scaring people: fad

Continue reading “Is mastery just a passing fad?”

Why dodecahedrons hate CPA.

Rachel Rayner is a Primary Mathematics Adviser for Herts for Learning

For a blog about the CPA approach click here.

Yes, teachers do label their fixed ability groups by shapes…still. Yes, pupils do end up in the circles group from the age of five and in some cases in the teacher’s head, younger.  And yes, it damages.  We are all by now familiar with the work of Carol Dweck and the idea of fixed and growth mindsets.  But in maths at least this fixed ability grouping or setting persists in Primary, despite the evidence that it can be detrimental to those pupils designated ‘circles’ or ‘triangles’.   Continue reading “Why dodecahedrons hate CPA.”

‘It’s differentiation Jim, but not as we know it!’

Nicola Randall is a Primary Mathematics Adviser at Herts for Learning

Over the past year I have worked with several schools developing a mastery approach to teaching and learning in Mathematics. The approach fits well with the new curriculum and enables both teachers and pupils’ depth of learning. From my conversations with teachers and leaders, one question that is on everyone’s mind is ‘what about differentiation?’ Continue reading “‘It’s differentiation Jim, but not as we know it!’”

Take One Resource: The Counting Stick

Deborah Mulroney is a Primary Mathematics Adviser for Herts for Learning

In this blog the resource that we are focusing on is the counting stick. It usually has ten intervals but the type with four faces and divided in several ways are most useful. The main use is that it can be thought of as representing a three-dimensional empty number line.

Numberline 1

Continue reading “Take One Resource: The Counting Stick”

CPA: using Cuisenaire to support pupils to develop fractional understanding

Louisa Ingram is a primary mathematics adviser for HfL

Identifying Fractions

To begin with, pupils need to become familiar with assigning a value to a rod and finding the fractional value of the other rods. A good starting point is to find the value of the white rod as this then allows you to find the value of all other rods. When the brown rod equals 1; the white rod is one eighth. Compared to dark green, the white rod’s value is one sixth. Against blue, it is one ninth and against orange one tenths etc. You can then start to apply this such as assigning the brown rod a value of 2. Through this you can also draw attention to fractions such as which rod is one half, one quarter, one third the length of etc. Continue reading “CPA: using Cuisenaire to support pupils to develop fractional understanding”

Maths across the curriculum (Pattern)

Nicola Randall is a primary maths adviser for HfL

In the aims of the new curriculum for mathematics, it states that a high quality mathematics education provides ‘an appreciation of the beauty and power of mathematics’. What better way to appreciate this beauty than to looking at nature? Continue reading “Maths across the curriculum (Pattern)”

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