© Crown copyright 2009 Slide /10 Teacher CPD programme – primary mathematics Strengthening mental, reasoning and communication skills in mathematics Shirley Williams Poole LA Hazel Large Gloucestershire LA

© Crown copyright 2009 Slide 2 Programme for the day 9.00 Introduction Session 1- Exploring mental mathematics Break Session 2 Part 1-Fit-for-purpose pedagogy Lunch 1.00 Session 2 Part 2- Reflecting on mental mathematics and pedagogy 2.00 Break 2.15 Session 3 - Planning for mental mathematics 3.15 Close

© Crown copyright 2009 Slide 3 Programme aim and objectives Aim: To strengthen teaching and learning of mental mathematics Objectives: To deepen understanding of the range and depth of mental mathematics To explore fit-for-purpose pedagogy to support selecting the most effective approach to teaching and learning for particular learning outcomes and needs To secure understanding of how to embed mental mathematics within planning and teaching to ensure appropriate pitch and progression To explore to explore the negotiation of meaning through the use of practical resources, visualisation, models and images, language and dialogue, writing, jottings, symbols and notation To develop strategies to embed the development of reasoning and communication throughout teaching and learning

© Crown copyright 2009 Slide 4 Course outline Pre-course task Day 1: Developing mental mathematics – fit-for- purpose pedagogy School-based task Day 2: Developing mental mathematics – reasoning, communicating and negotiating meaning Follow-up activity

© Crown copyright 2009 Slide 5 Session One Exploring mental mathematics Aims To engage in mental mathematics and reflect on the key skills and attitudes involved To reflect on current practice in providing opportunities for developing mental mathematics To develop a shared understanding of mental mathematics and its implications for teaching and learning

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© Crown copyright 2009 Slide 12 Reflection What were you visualising? Did you enjoy this approach? Did you find it easy or difficult to visualise the numbers? Why might this be? What prior experience, knowledge and skills did you draw on? Did you want to jot anything down? If so, what and how did this help you? Did you find the shape visualisation easier or more difficult than the number visualisation? Why do you think this might be? What was the role of the sticky notes in supporting the activity? Would you say that you continued to work mentally?

© Crown copyright 2009 Slide 13 Pre-course task During the teaching week prior to Day One of the central CPD programme, we would like you to identify and note three opportunities when children in your class are engaged in working mentally in mathematics. Please record and bring to Day One notes on the learning focus, mathematical content and involvement of children in the activity. These notes will be used support shared discussion with other teachers about the nature and range of mental mathematics. Note the learning focus, mathematical content and involvement of children in the activity (were they visualising, jotting, working alone or talking with peers/the teacher, using apparatus…)

© Crown copyright 2009 Slide 14 Reflecting on the pre-course task – discussion prompts Learning focus When the activity took part in the lesson Context (whole-class, group, independent, one-to-one…) Differentiation Use of jottings and equipment Nature of talk

© Crown copyright 2009 Slide 15 What does working mentally in mathematics mean? What skills and attitudes to children need to be able to work mentally? What opportunities do children need in order to develop these skills?

© Crown copyright 2009 Slide 16 Time to reflect

© Crown copyright 2009 Slide 17 Session Two – Part One Fit-for-purpose pedagogy Aims To engage in a whole group mental mathematics and reasoning activity in order to reflect on both its effectiveness and its limitations To engage in a guided group activity to reflect on its effectiveness and how we can develop reasoning skills To begin to consider when it is most appropriate to work with a whole class and a guided group and why

© Crown copyright 2009 Slide 18 Whole Class Mental Mathematics Activity

© Crown copyright 2009 Slide 19 Reflecting on whole group activity How was the activity structured? What was the role of the teacher? What was the value of the activity for both the learner and the teacher?

© Crown copyright 2009 Slide 20 Mobile Key Pad How might you use a visualisation activity based on a mobile phone key pad with your own class? –What are the benefits of using these activities? –What difficulties are children likely to encounter and how would you help to overcome them?

© Crown copyright 2009 Slide 21 Annotated example What were the outcomes for the children in this class? Did they use similar methods to those we used? How did the activity develop their reasoning?

© Crown copyright 2009 Slide 22 Whole class activity - limitations In your table groups; Reflect on and discuss the limitations of this whole class activity; a)From the teachers point of view b)From the children's points of view

© Crown copyright 2009 Slide Three in a row Choose two numbers from the row of numbers above the grid. Find the difference between these numbers. If the answer is on the grid, cover that number with a counter. Guided Reasoning Activity

© Crown copyright 2009 Slide 24 Reflecting on guided group activity How was the activity structured? What was the role of the teacher? What was the value of the activity for both the learner and the teacher?

© Crown copyright 2009 Slide 25 Guided Group work in your class If you were leading a guided reasoning session with children in your class; a)What children might you select and why? b)What other strategies might you have used to help you develop children’s reasoning skills as effectively as possible?

© Crown copyright 2009 Slide 26 Plenary When would you work with the class to develop mental mathematics and reasoning skills and why? When would you work with a guided group to develop mental mathematics and reasoning skills and why?

© Crown copyright 2009 Slide 27 Session Two – Part Two Reflecting on mental mathematics and pedagogy Aims To gain further experience of visualisation and reflect on the role of representations To consider contexts for developing mental mathematics skills To reflect on aspects of fit-for-purpose pedagogy and identify next steps in developing practice

© Crown copyright 2009 Slide 28 Shape and Space Visualisation

© Crown copyright 2009 Slide 29 Fit-for-purpose pedagogy …involves the teacher in planning how best to construct a blend of teaching approaches that are selected and designed to match intended learning outcomes and needs, and to take account of the context and organisation of children.

© Crown copyright 2009 Slide 30 Reflecting on pedagogy How would you decide which children are struggling with the type of mental mathematics we have been exploring today? How do you know which children you need to stretch and challenge in their mental mathematics?

© Crown copyright 2009 Slide 31 Opportunities for identifying and supporting children in whole class Provide everyone with a common experience and include paired work but organise it in such a way to allow you to check on the particular response of a pair Focus on the feedback of identified individuals at different times to identify children who might need further investigation, intervention or challenge

© Crown copyright 2009 Slide 32 Opportunities for identifying and supporting children in a guided group Provide a targeted group of children with a simplified or more challenging activity to confirm the extent of their learning and any particular needs Provide a more open-ended task to invite children to share their visualisation skills that others might identify with and use Introduce mathematics language that children have not met or have struggled with Help children to describe or reason in a context where you can observe and listen to them more closely

© Crown copyright 2009 Slide 33 Developing reasoning in mental mathematics Question stems are a useful tool to develop reasoning in both whole class and group contexts. In groups write 3 different questions to share. Think about how they link to visualisation and mental maths.

© Crown copyright 2009 Slide 34 Session Three – Planning for mental mathematics To exemplify mental mathematics within one area of learning within a Block and explore appropriate activities for whole-class, guided and independent contexts To identify additional opportunities within the chosen Block to integrate mental mathematics and work together to plan for appropriate pitch and expectation for target year groups To explore further how to plan to integrate mental mathematics into every day teaching and learning

© Crown copyright 2009 Slide 35 Photograph of playground: ©Malcolm Bellamy. Used with kind permission

© Crown copyright 2009 Slide 36 Planning a guided reasoning activity What are the key features of this activity? How could the ideas and approaches used in the whole-class activity be extended? What mental reasoning and enquiry skills will this extended activity require? What is the teacher role during this activity?

© Crown copyright 2009 Slide 37 Resources available to support planning These include: Learning overviews from the relevant Unit Overcoming barriers in mathematics materials Pitch and expectations documents for the relevant year group Mathematical challenges book Primary Framework ICT resources and notes files

© Crown copyright 2009 Slide 38 Planning further opportunities Consider one or more of: 1.An activity that would enable children to draw on and rehearse their learning including the use of vocabulary and images 2.An activity that uses the properties of shape and develops the language that children can use to describe their observations about these shapes 3.An activity that develops reasoning skills about shapes

© Crown copyright 2009 Slide 39 School-based task Work with a colleague to plan, try out and observe one or more mental mathematics activities that were discussed and developed during the day, set within a whole-class and guided group context. In collaboration with your colleague, note and discuss responses and the impact on children’s learning highlighting any surprises in the children’s learning and responses or any key gaps in their language or reasoning skills. Capture ‘evidence’ in terms of notes about dialogue by groups or comments by individual children, the notes and jottings children make or visualisations they talk about, and images or resources used, and bring to Day Two

© Crown copyright 2009 Slide 40 Day 3 January 19 th Hamworthy Recreation Club