Dr Jenni Back Host Schools Project Lead Arithmetic proficiency: achieving fluency with understanding in arithmetic Dr Jenni Back Host Schools Project Lead

Welcome and introductions The Host Schools Network 27 Host Schools and 152 Visiting Schools The HS Team Rachel Ball and Jenni Support from the NCETM Celia Hoyles, Jane Imrie, Debbie Morgan, Laurie Jacques, the Portal team Welcome to everyone Thrilled to have managed to start such a vibrant network of enthusiastic teachers from all over the country Key focus on arithmetic proficiency in years 3 and 4 and working together to support fluency and understanding for all learners Exciting day ahead and hope that you all get lots out of it both through the presented sessions and the opportunity to network with others in the network.

Building relationships in networks Alison Peacock Headteacher at The Wroxham School in Potters Bar Thrilled to welcome Alison Peacock. Effective head teacher and inspiring leader with experience of supporting and empowering people to change their professional practice through working in partnership with them. She is going to share with us some suggestions to help you to build effective and supportive working relationships in your networks.

The Host Schools Network An Introduction by Professor Celia Hoyles OBE, Director, NCETM Professor Celia Hoyles has been the Director of the NCETM over most of its existence and it gives me great pleasure to call upon her to fill in some more details about the Host Schools Network and how NCETM see it developing.

A Mathematical Task Exploring the key mathematical issues in years 3 and 4 Where do we start?

Strike it out

Rich tasks: low threshold, high ceiling Accessible to all at the start of the lesson Allows the most confident/ competent to go as far as they can and offers the opportunity to ask their own questions Plenty of supporting activity of those who will benefit from it Allows different types of thinking and different approaches Article on NRICH website at http://nrich.maths.org/7701 Rich tasks offer a meaningful context that provokes the students to learn in order to solve it

Progression from EYFS to KS2 and beyond Recognising number symbols to 10 – restrict the number line and use concrete apparatus KS1 Developing skills in addition and subtraction of numbers to 20 Lower KS2 Recording results systematically Conjecturing about possible choices Relating addition and subtraction facts Upper KS2 Building fluency with number bonds to 20 Predicting results, developing strategies Beyond KS2 Developing mathematical thinking: exemplify, visualise, generalise, do/undo, conjecture, prove

Calculation policy Need for a clear and consistent approach across the school Importance of communicating the policy at transition points Importance of fluency - only possible once the concepts make sense Moving away from procedures to conceptual understanding and reasoning

Key thresholds in mathematical development in arithmetic KS1 entry: conservation and counting KS2 entry: addition/subtraction, number bonds to 20, place value KS3 entry: multiplication/division, multiplication tables KS4 entry: proportional reasoning

The issues in years 3 and 4 Securing conservation and counting Additive reasoning, fluent recall and application of number bonds to 20, understanding place value Developing ideas of multiplication and division Intuitive understanding of proportional reasoning

The Big Ideas in arithmetic in Y3 & 4 Doing and undoing The number system and place value Securing and deepening understanding of addition and subtraction Building repertoire of known facts Developing understanding of multiplication

Models and images for multiplication Barmby et al’s Nuffield funded project ‘Developing the use of visual representations in the primary classroom’ CPD course on developing children’s understandings of multiplication and fractions through using a variety of models and images All resources have been made available to us for the Host Schools Project

Plates of strawberries

Beads on a rail

+6 +6 +6 +6 +6 +6 +6 6 12 18 24 30 36 42 Jumps on the number line

Array without spaces

Array with spaces

Area model of multiplication

TU x TU Grid method 10 8 10 6

10 5 3 10 TU x TU Grid method but splitting the units further 5 1

How can we teach them? Exploring the key educational ideas in teaching arithmetic in years 3 and 4 A number of statements about teaching arithmetic Discuss them in your groups and sort them according to their importance What would you include/ignore? Why? Make a poster showing your thoughts Share our findings as a group

Sharing experiences from across the Network Doncaster: Thorne Brooke Network Northampton: Great Bowden Network London: Eleanor Palmer Network Cumbria: Heversham St Peter’s Network

Using the Portal Getting your usernames to Rachel Each Network will have its own community There will be a national community to which all the Host Schools will have access Use it to communicate, to share resources and to ask us for input and advice Advantage that anything put up can be seen by all in your group.

Next Steps: questions and answers Debbie Morgan, NCETM Primary Director Admin: Rachel – purchase orders & complete lists of Usernames Completion of Questionnaires Date for Jenni’s visit should be fixed as soon as possible Resources

References Andrews, P., Sayers, J. & Back, J. (draft) The development of foundational number sense in England and Hungary: a case study comparison. Submitted for CERME 2013 Anghileri, J. (2000) Teaching Number Sense. London: Continuum Back, J. (2011) Maths without translation. Primary Mathematics 15(2) 19-21 Back, J. (2011) The Story of Six. Primary Mathematics 15(3) Barmby, P., Bolden, D., Raine, S. & Thompson, L. (2012) Developing the use of visual representations in the primary classroom: A Nuffield Foundation Project

Thank you for your hard work and attention. Dr Jenni Back jenni.back@ncetm.org.uk Telephone 07850100074