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An Inspector Calls – Advice for Leaders of Mathematics

Nicola Randall is a Primary Maths Adviser at Herts for Learning.  Here she sets out her advice for core subject leaders in surviving Ofsted inspections. 

All subject leaders know the anxiety caused by waiting for that call, looking for the tell-tale signs: the headteacher’s door closed with a ‘Do Not Disturb’ sign on, the mysterious and impromptu staff meeting to be held after school and the rushing around of office staff trying to get paperwork out to parents. I haven’t met anyone who enjoys an inspection, but in my experience, subject leaders tend to fall into 2 camps: those who feel the fear and those who say ‘bring it on!’ Continue reading “An Inspector Calls – Advice for Leaders of Mathematics”

The ‘Goldilocks Principle’ and Curriculum Design

Rachel Rayner is a Primary Mathematics Adviser at Herts for Learning.  The team are currently engaged in designing a mathematics curriculum for schools and teachers.  In this blog she considers how curriculum design impacts on learners.  This will be the first of a series of blogs on progression and design.

As a maths team we are currently writing every sequence of learning from Year 1 week 1 Autumn term to Year 6 final week Summer term. More on that later.  But I don’t mind telling you that it’s raised quite a few questions on the team about what a great curriculum for maths should look like.  Curriculum ‘14 for mathematics raised age-old debates – acceleration versus breadth and depth, knowledge versus engagement – let the twitter set debate. Furthermore, the new curriculum is being regularly referred to as a ‘mastery curriculum,’ heralding a bewildering array of products stamped with the ‘mastery’ brand all claiming to revolutionise your curriculum and behave rather like you might imagine a magic wand to work. And yet, and yet…still we battle to build a secure curriculum framework and schools are desperately seeking something (even after they have discovered concrete-pictorial-abstract).  One in which, age-related expectations become the norm for all pupils irrespective of their prior attainment – though we know there are a few children for whom added provision is ever needed irrespective of the curriculum. On top of that OfSTED are looking at how curriculum design supports learning for all pupils even beyond the mathematics lessons.  So where do we even begin? In this the first of a series of blogs I want to set out the current landscape as I see it (and sorry but no, I don’t possess even a modicum of fairy dust or a magic wand) before focusing in further in future blogs.  Continue reading “The ‘Goldilocks Principle’ and Curriculum Design”

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.


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My Trio of Messages – OfSTED tell us about the state of Primary Mathematics

Louise Racher is a Primary Mathematics Adviser for Herts for Learning

BetterMaths1

Having been lucky enough to be in the same room as the esteemed Jane Jones, Ofsted’s National Lead for Mathematics, I am going to attempt to order my thought succinctly. There were a lot of messages about Mathematics crammed into one day and many thoughts overlapped as is the tendency with this subject. At the end of the day when I looked back at my own scribbled notes I think I could see three general threads.  Overall, I was comforted that her messages aligned with my own and my colleagues therefore all of the training and subscription materials we are currently writing and producing to help and support teachers are steered towards the key messages. Continue reading “My Trio of Messages – OfSTED tell us about the state of Primary Mathematics”

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