Mastery Maths- a CPA approach (Concrete, pictorial, abstract)
Maths No Problem! Parent Workshop Aims of the session Curriculum overview Why Maths - No Problem What Maths - No Problem is
Mastery approach to mathematics Overview of Maths - No Problem How you can help at home A typical maths lesson at Heckington Aims of the National Curriculum 2014
The national curriculum for mathematics aims to ensure that all pupils: Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language. Can solve problems by applying their mathematics to a variety of
routine and non routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Curriculum coverage FLUENCY Being able to recall facts and solve calculations with speed. This also relates to solving simple word problems. REASONING Being able to explain the steps in a process, how an answer was found, or explaining mistakes or misconceptions in a process.
PROBLEM SOLVING Children are able to solve complex problems that require recall of facts, reasoning, and logical thinking. Children are also required to think about representing questions in different ways to help solve a problem. Why? Research Data
Ofsted report Lesson Study Local Maths Cluster Meetings CPD on the use of manipulatives in mathematics Education Endowment Foundation (EEF) 8 Recommendations for Improving
Mathematics in Key Stage 2 and Key Stage 3 Mastery Maths Specialist National Centre for Excellence in the Teaching of Mathematics (NCETM) Department for Education (DfE) confirmation that it is a high-quality text book to support the teaching for mastery + match funding provided Why Maths - No Problem? Children will have a greater conceptual understanding of number and calculation. They will be able to visualise and generalise more readily
due to a more in-depth understanding. All children will be fully supported through accessing concrete equipment and use of visual models to support understanding. Rapid graspers will be challenged through exposure to unfamiliar problems, development of reasoning skills and by exploring multiple ways to manipulate numbers and solve problems. All learners will access teaching of content which matches the expectations of the curriculum in England and be supported further, if
needed. The resources match the expectations for formal written methods set out by the government, alongside greater understanding in order to reach mastery. CPA approach Concrete, pictorial, abstract (CPA) is a highly effective approach to teaching that develops a deep and sustainable understanding of maths. The CPA approach is the mainstay of maths teaching in Singapore. doing seeing abstract
Types of understanding Instrumental Understanding Instrumental understanding can be thought of as knowing the rules and procedures without understanding why those rules or procedures work. Students who have been taught instrumentally can perform calculations, apply procedures but do not necessarily understand the mathematics behind the rules or procedures. Relational Understanding Relational understanding, on the other hand, can be thought of as understanding how and why the rules and procedures work. Students who are taught relationally are more likely to
remember the procedures because they have truly understood why they work, they are more likely to retain their understanding longer, more likely to connect new learning with previous learning, and they are less likely to make careless mistakes. (Richard Skemp) (rote and memorisation) vs (exploration and questioning) What is Maths No Problem? Maths No Problem! is a series of textbooks and workbooks written to meet the requirements of the 2014 English national curriculum. The MNP Primary Series was assessed by the DfEs expert panel, which judged that it met the core criteria for a high-quality textbook
to support teaching for mastery. As a result, the MNP Primary Series are recommended textbooks for schools on the mastery programme. Singapore approach to mathematics Singapore established a new way of teaching maths following their poor performance in international league tables in the early 1980s. Based on recommendations from notable experts, Singapore maths is a combination of global ideas delivered as a highly-effective
programme of teaching maths. The effectiveness of this approach is demonstrated by Singapores position at the top of the international benchmarking studies and explains why their programme is now used in over 40 countries including the United Kingdom and the United States. Singapore has become a laboratory of maths teaching by incorporating established international research into a highly effective teaching approach. With its emphasis on teaching pupils to solve problems, Singapore Maths teaching is the envy of the world.
Based on recommendations from notable experts such as Jerome Bruner, Richard Skemp, Jean Piaget, Lev Vygotsky, and Zoltan Deines, Singapore maths is an amalgamation of global ideas delivered as a highly-effective programme of teaching methods and resources. One of highest performing countries in terms of maths Teach the concepts of mathematics
Problem solving is at the heart of mathematics and should be the focus of what is taught in schools The focus is not on rote procedures, rote memorisation or tedious calculation but on relational understanding Pupils learn to think mathematically as opposed to reciting formulas they dont understand Is a way of teaching that allows students to develop a greater sense of number and how to use and manipulate numbers to solve a variety of
problems A highly effective approach to teaching maths based on research and evidence Pupils are encouraged to solve problems working with their core competencies, in particular: 1. Visualisation 2.
Generalisation 3. Make decisions Number sense Number sense is knowing what numbers mean by themselves and in relation to one another, the ability to partition (break apart numbers) into a variety of ways, and being able to manipulate numbers for different purposes. What is mastery?
Mastery of Mathematics Achievable for all Deep and sustainable learning The ability to build on something that has already been sufficiently mastered The ability to reason about a concept and make connections
Conceptual and procedural fluency Involves a longer time spent on key topics, providing time to go deeper and embed learning. Procedure has to be backed up by understanding Five Big Ideas Lesson design for Teaching for Mastery
Mastery Involves a development or three forms of knowledge: Factual I know that Procedural I know how Conceptual I know why We are aiming to provide children with opportunities to develop:
Deep and sustainable understanding of mathematical concepts Ability to reason about mathematics and make connections Facts and efficient procedures the mathematical tool kit Confidence and competence in using mathematics to solve problems Structure of Maths No Problem!
Concepts merge from one chapter to the next e.g. Chapter 1 Place Value Chapter 2 Addition and Subtraction Each chapter has a series of lessons to follow Children master topics before moving on How lessons are taught The parts to the lesson are:
Anchor task entire class work on problem to solve, use of talk partners and teacher/ TA guiding. The children are encouraged during this time to think of as many ways as possible to solve the problem and explain their ideas. Lets Learn look at methods from the text book together. Explain the method to your partner. What can we learn from this method? Guided practice practice new ideas with talk partners. Teachers/TAs assess understanding and support where needed.
Independent practice mostly independent, teacher/teaching assistant work with guided groups or specific children identified from guided practice. Once children have mastered the concept they use their reasoning and problem solving skills to develop their depth of learning. In Focus/ anchor task Guided practice Textbooks Ideas are developed systematically using learning theories and research as a basis, in particular, the work of Jerome Bruner (representations and spiral curriculum) and Zoltan Dienes (Informalstructured-practice progression as well as systematic and mathematical variation of examples)
Singapore spent a decade researching which questions to ask and in what order. The textbooks are based on this research. Workbooks Allow children to show their understanding of a concept by solving problems displayed in different ways The questions are set up to ensure children understand the concept forwards, backwards and inside out
For rapid graspers this consolidates any previous learning before they move onto greater depth challenges Children can work at their own pace through the questions Maths journals In focus
Guided practice Challenges How will children be challenged? Make links between previous learning Think about problems in different ways
Have opportunities to explain their reasoning Find and explain generalisations Use rich mathematical language when explaining ideas Solve complex problems which expand on their mathematical knowledge
Work with a range of manipulatives to consolidate their understanding Work with a mix of children in groups, pairs and independently Challenge Problem solving/ reasoning challenges Explain using drawing/ equipment
Explain orally/ through writing Write their own problem Invent a method/ game Create their own question Make connections
Identify rules/ generalisations Correct a mistake Odd one out Find something new
How are children supported? Make links between previous learning Think about the way they know to solve problems Have opportunities to listen to mathematical vocabulary from peers and use themselves
Be given more time to work on tricky concepts Work with a range of manipulatives to solve problems practically Work with a range of children in groups, pairs and independently Scaffold learning- extra clues and support How teachers support all learners
Move individual children on at their own pace throughout the lesson Set rich and sophisticated problem solving activities for rapid graspers Give time for all children to fully grasp and master concepts Provide visual stimuli for children to access a problem using CPA approach
Give children ownership in their learning Model making mistakes- maths is challenging Negative ideas that prevail about maths come from one idea, which is very strong, permeates many societies and is at the root of maths failure and underachievement: that only some people can be good at maths. The single belief that maths is a gift that some people have and others dont is responsible for much of the widespread maths failure in the world. Jo Boaler Mathematical Mindset (2016) Maths is challenging. Children need to expect to struggle - this is part of learning
How to teach number bonds How To Teach Number Bonds? | Maths No Problem! https://www.youtube.com/watch?v=D1hwopQLeCU Parent videos https://mathsnoproblem.com/en/parent-videos/ - 8 videos (3-6 mins long)
Dr Yeap Ban Har Column addition with regrouping Column subtraction with regrouping What the children think I like it. Its easier because I can see the maths in the textbooks. It is really helping me with my maths. I love maths now because its much easier than before. I like it because its fun.
I enjoy it because I am learning tricky maths. I like that I get to work with a partner. I like maths because it challenges me. I love Maths No Problem because I find out new methods to use that makes maths easier. Its cool. It is tricky but its fun.
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