buckinghamshire county council raising achievement, accelerating progress in mathematics amber...

Buckinghamshire County Council

Raising achievement,accelerating progress

in Mathematics

Amber Schools ConferenceMarch 2013

[email protected]


Characteristics of a Successful Learner

In Mathematics


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


How is mathematics viewed in your school?

• By pupils?• By teachers?• By parents / carers?


Particular problems?

• Teacher subject knowledge?• Teacher approaches?• Teaching Assistants?


Possible solutions

• Training

• Support

• Profile of Maths in the school


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


• Nuts and bolts vs. Challenge


By the end of Y3........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 = 20 + 34

• Addition and subtraction facts to 20 (not just to total 20)• Understanding of the four operations (before mental

strategies)• Problem solving


Challenge and Achievement

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


• 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!)


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


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)


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


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..............?


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


1

4


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)


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?


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….?


• 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’


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


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


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.


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


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


Teaching mathematical communicationStage 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


Which is larger 1 or 2 ?

3 5

Explain how you know.

_ _ _ _ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _ _


L3: 0% L4: 8% L5: 49% overall 18%


Opening Up


What would you choose?

5 or 9Why.......?


What would you choose?

or

..... why?


More complex tasks

• Combine concepts– Symmetry + other properties of shape

• Cross-curricular opportunities – ICT lesson


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


Key messages?

• So.... What will be your next steps? For you personally? For the school?

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