Parents and Carers Meeting Teaching for Mastery in Maths 25/4/18 Parents and Carers Meeting

Mathematics Curriculum Three aims of the National Curriculum: Fluency – Reasoning – Problem Solving. Fact: Understanding and skills are equally important. Myth: The curriculum is largely focused on rote learning and practise. 3 forms of knowledge: Factual – I know that! Procedural – I know how! Conceptual – I know why!

Growth Mindset It has become acceptable in society to be 'bad at Maths'. We need to find ways to actively encourage a positive growth mindset in our children. “In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. Carol Dweck

Achieving Mastery A longer time is spent on one idea, effective teacher questioning is used to challenge thinking, a scaffolded approach explores potential misconceptions and carefully chosen examples promote intelligent practice. Whole class interactive teaching, active learning. Ensure children are becoming fluent in number facts. Differentiation occurs in the support and intervention provided to different pupils. Challenge is provided through more demanding problems which deepen children’s knowledge of the same content. Same day intervention. Fast finishers are not accelerated into new content.

Achieving Mastery   A pupil really understands a mathematical concept, idea or technique if he or she can: • describe it in their own words; • represent it in a variety of ways; • explain it to someone else; • make up his or her own examples (and non examples) of it; • see connections between it and other facts or ideas; • recognise it in new situations and contexts. “I can do it and I can show it. Also I can draw it. I can explain it. I can help the person sitting next to me understand it” Knowing why as well as knowing that and knowing how Conceptual understanding and procedural fluency Making connections Precise use of mathematical language to communicate ideas Achieving mastery of particular topics and areas of mathematics. Mastery is not just being able to memorise key facts and procedures and answer test questions accurately and quickly. It involves knowing ‘why’ as well as knowing ‘that’ and knowing ‘how’. It means being able to use one’s knowledge appropriately, flexibly and creatively and to apply it in new and unfamiliar situations Understand reason explain challege Represent it in multiple ways Apply in unfamilar contexts Use maths concepts facts and procedures approriatelt flexiby and fluently Recall facts with speed and accuarcy derive unknown facts

Over the last three years Swallowfield has participated in a Teacher Research Group. We have introduced maths textbooks for teachers to support teaching for mastery. The textbooks have been researched in great detail and written by world-renowned authors which means that our teachers don’t have to spend time creating resources from scratch. The varied examples have been specifically chosen to stretch pupils into harder concepts, create depth and generate dialogue. It’s not just an Asian phonemon.

Mastery Specialists From September 2018 we will be supporting other schools in their Maths teaching. Advise on teaching strategies through a mastery approach.

Carefully Chosen Examples… The children carry out the procedural operation of multiplication, but through connected calculations have the opportunity to think about key concepts involving multiplication and place value. This leads to intelligent practice. The child is carrying out the procedural operation of multiplication, but through connected calculations has the opportunity to think about key concepts involving multiplication and place value This leads to intelligent practice If you can 2 x 3 I can do 30…..picked up on structure on maths…. More efficient fluent and can build upon it

Consider the strategies you used. Solve the following:  + 17 = 15 + 24 Consider the strategies you used. This illustrates how a conceptual method rather than a procedural method can lead to a quicker answers. 15+24=39. 39 – 17 =22 17 is 2 more than 15. If you simply take the two away from 24 makes 22.

CPA Approach One of the key learning principles behind the maths textbooks is the concrete-pictorial-abstract approach, often referred to as the CPA approach. This approach suggests that there are three steps necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

CPA Concrete representation Pictorial representation A pupil is first introduced to an idea or a skill by acting it out with real objects. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding. Pictorial representation A pupil has sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a picture of the problem. Abstract representation A pupil is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6.

Part whole relationships 4 is the whole. 3 is a part and 1 is a part.

Part Part Whole Model 5 apples and 2 apples?

The Bar Model 7 2 5 7 1.9 5.1 7.4 C 1.7 5.7 a b

Lesson Design at Swallowfield Explore Present problem to explore - chn try to solve it using manipulatives. Structure Teacher models chn’s methods on board and helps to organise their ideas. Focus on the method we want chn to pay attention to. Reflect Reflection supported by teacher. Chn practise skills, with talk partner – work through examples to move from concrete/pictorial to abstract. Practise - Independently Chn complete independent work – in Maths books.

The Answer is only the beginning……….. The teacher presents a maths problem and then asks: Describe the method/procedure you used Why does the method work, what relationships are involved, what generalities or rules can we glean? What is the answer?

Year 2 Lesson Addition Explore If the problem is about apples – they use apples etc

Year 2 Lesson Addition Structure If the problem is about apples – they use apples etc

Year 2 Lesson Addition Reflect If the problem is about apples – they use apples etc

Year 2 Lesson Addition Practise If the problem is about apples – they use apples etc

Year 2 Lesson Addition If the problem is about apples – they use apples etc

How can you help? Fluency Drive Number Bonds Number bonds refers to how numbers join together and how they can be split up. A lot of emphasis is put into number bonds from the early years so that children can build up their number sense prior to learning addition and subtraction. In the early stages pupils are introduced to number bonds with concrete experiences.

Multiplication Facts – end of Year 4 How can you help? Fluency Drive Multiplication Facts – end of Year 4 12 x 12

How can you help? Questioning Fluency Drive Questioning This can be done simply by asking children to explain how they worked out a calculation or solved a problem, and to compare different methods. Children quickly come to expect that they need to explain and justify their mathematical reasoning. They start to do so automatically – and enthusiastically!

Top tips for parents! Be positive about maths. Try not to say things like "I can’t do maths" or "I hated maths at school" - your child may start to think like that themselves. Point out the maths in everyday life. Include your child in activities involving numbers and measuring, such as shopping, cooking and travelling. Praise your child for effort rather than for being "clever". This shows them that by working hard they can always improve.

Any Questions?