Buckinghamshire County Council Raising achievement, accelerating progress in Mathematics Amber Schools Conference March 2013

Buckinghamshire County Council

Characteristics of a Successful Learner In Mathematics

Buckinghamshire County Council Desirable Learning Characteristics Enquire, explore and discover Be excited by their learning Find what they’re good at Ask questions Rise to a challenge Be curious, be happy, be confident Wonder and be amazed Be proud of their achievements Think for themselves Want to be part of a team Care about others Be themselves

Buckinghamshire County Council How is mathematics viewed in your school? By pupils? By teachers? By parents / carers?

Buckinghamshire County Council Particular problems? Teacher subject knowledge? Teacher approaches? Teaching Assistants?

Buckinghamshire County Council Possible solutions Training Support Profile of Maths in the school

Buckinghamshire County Council For whom in your school do you need to raise achievement or accelerate progress in mathematics?

Buckinghamshire County Council Nuts and bolts vs. Challenge

Buckinghamshire County Council By the end of Y key skills Ordering numbers – relative positions to the landmarks of multiples of 10 Counting on and back – initially in ones and tens, then other multiples Partitioning and recombining – into tens and ones but also other combinations e.g. 54 = Addition and subtraction facts to 20 (not just to total 20) Understanding of the four operations (before mental strategies) Problem solving

Buckinghamshire County Council Challenge and Achievement Challenge and Achievement for ALL children Making children think (for themselves) Independence, depth (not just acceleration) Opportunities for creativity Asking questions

Buckinghamshire County Council Taking risks Rising to new challenges Being willing to share and make mistakes Being imaginative Being innovative Being immersed in the subject Finding and exploring young children’s fascinations Qualities you might want for your pupils (and teachers!)

Buckinghamshire County Council Guy Claxton Building Learning Power Teach pupils to “know what to do when they don’t know what to do” The 4 Rs –Resilience –Resourcefulness –Reflection –Relationships

Buckinghamshire County Council Carol Dweck Mindsets – Fixed vs Growth “as educators we have a huge responsibility to support our students in developing a growth mindset which engenders a lifelong love of learning, not a short-term obsession with performance” Appropriate feedback and praise (examples)

Buckinghamshire County Council Classroom Organisation for Challenge Effective group work – Letting groups ‘go’ –Letting group members support each other –Guided group work Problem Solving focuses No Hands up Encourage appropriate self-differentiation Have extra challenge activities available (for all) Top-down planning Effective questioning

Buckinghamshire County Council Top-down planning How can we expect children to achieve work at a certain level (e.g. Secure Level 3 in Y4) if we never confront them with work at that level? So......give work at the appropriate level of expectation and then think what scaffolding will children need to achieve the outcome What would this approach look like in a lesson on ?

Buckinghamshire County Council Change the teaching approach Clare Gadsby techniques –E.g. Get the children to teach (“teach from the back of the classroom”) Challenge - Do’s and Don’ts

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What is the purpose of questions?  To check on prior knowledge (AfL)  To interest, engage and challenge  To focus thinking on key concepts and issues  To stimulate interaction  To challenge  To assess progress (AfL)

Buckinghamshire County Council Developing children’s thinking through questioning Numeracy Vocabulary book PLAN for appropriate questions –e.g. What could be the biggest possible answer when adding any two numbers less than 10 together? any four single-digit numbers together? And the smallest? –Give me any multiplication which will give a product (answer) which ends in 4 (or 0, 7, or 5, or 9) – what do you notice? –What happens when you add an even number to an odd number? Can you explain why this happens?

Buckinghamshire County Council Open-ended questions What do you think….? How do you know….? Why do you think that….? Do you have a reason…..? How can you be sure….? Is this always so….? Is there another way /reason/ idea…? What if…? What if… does not…? What is another example of …..? What do you think happens next….?

Buckinghamshire County Council Fewer but better questions, key questions must be planned Higher-order questions including generalisation Encourage and help children to ask their own questions (Handout 10) Give children time to think Provide scaffolding / partner work as appropriate Value the process rather than just the answer Value creativity and ‘having a go’

Buckinghamshire County Council More able children in mathematics may show all or some of the following: ability to generalise independence and perseverance capacity to learn, understand and apply new ideas and ways of working quickly effective communication skills ability to argue and reason creativity and originality ability to make connections between different concepts they have learned ability to take on more demanding tasks

Buckinghamshire County Council Mathematical processes Looking for patterns Working systematically Identifying relationships, making links Generalising Testing examples to find out whether the generalisation works Exploring the reason for the generalisation identified Communicating

Buckinghamshire County Council Always, sometimes, never true 1.Multiplication by a positive number makes positive numbers larger 2.A 4–sided shape with two parallel sides is a parallelogram 3.If you increase the price by 10% and then decrease the new price by 10%, you get back to the original price.

Buckinghamshire County Council Doing vs Undoing Find the Mean, Median and Mode for the given data set Invent a data set (at least 6 values)for which the mean, median and the mode are all the same e.g. 8

Buckinghamshire County Council Doing and Undoing Consider a task your class have worked on recently or that you have planned for the future Can you adapt the task in a similar way so that the children have to think more deeply

Buckinghamshire County Council Teaching mathematical communication Stage 1 –Thinking through the problem, noting anything that supports their own thinking (possibly no more than a memory prompt) Stage 2 –talking through the approach used and explaining to a partner Stage 3 –Recording the approach to the problem and its solution so that the partner can follow the approach and solution as communicated on paper (i.e. Using words, symbols and diagrams as appropriate

Buckinghamshire County Council Which is larger 1 or 2 ? 3 5 Explain how you know. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Buckinghamshire County Council L3: 0% L4: 8% L5: 49% overall 18%

Buckinghamshire County Council L3: 0% L4: 8% L5: 49% overall 18%

Buckinghamshire County Council Opening Up

Buckinghamshire County Council What would you choose? 5 or 9 Why ?

Buckinghamshire County Council What would you choose? or..... why?

Buckinghamshire County Council

More complex tasks Combine concepts –Symmetry + other properties of shape Cross-curricular opportunities – ICT lessonICT lesson

Buckinghamshire County Council Adapting maths lessons to provide appropriate challenge for all children Include opportunities for reasoning and generalising Teach communication skills Modify activities Plan questions Reduce scaffolding Modify organisation of teaching

Buckinghamshire County Council Key messages? So.... What will be your next steps? For you personally? For the school?