mastery Maths with Greater Depth at Rosehill Infant SCHOOL

What is 'Mastery'? Essential idea is that ALL children need a deep understanding of the mathematics they are learning so that: Future learning is built on solid foundations and doesn't need to be re-taught Gaps in attainment are narrowed Fewer things are taught at a time, but in greater depth Sufficient time required to embed and sustain learning over time Stay with objectives and master those before moving on

Pedagogic practices (applying theory to practice) keeps the class working together on the same topic Expectation is that ALL children to master curriculum objectives Some will gain greater depth of understanding Long term gaps in learning are prevented through speedy teacher intervention

Difference between Mastery and Greater Depth Mastery – obtaining a greater level of understanding through deeper learning and being able to apply learning in different contexts. Greater Depth – learning can be transferred and applied in different contexts. Children can explain their understanding to others.

We need to get 'Mastery' to 'Mastery with greater depth‘ for best results!

Difference between Mastery and Mastery with greater depth A pupil really understands a mathematical concept when he/she can describe it in his or her own words represent it in a variety of ways (e.g. using concrete materials, pictures and symbols - the CPA approach)  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 recognises it in new situations and contexts make use of it in various ways, including in new situations 'Mastery with greater depth' Is characterised by those who can:  solve problems of greater complexity (i.e. where the approach is not immediately obvious), demonstrating creativity and imagination.; independently explore and investigate mathematical contexts and structures, communicate results clearly and systematically explain and generalise the mathematics .

Depth of Learning Longer time, smaller steps Intelligent practices Scaffolding children to make connections: If I know this then I know... Encouraging children to look for patterns. Variation, rather than repetition. Challenge Through effective questioning . Simple, then more complex problem solving . Expecting children to 'reason' their answer-'prove it', 'convince me'.

What does good counting look like? Making links to numbers and their values Recognising patterns Fluent Confident Mastery Expectation

Example : Teaching 'more' and 'less'   You highlight that when 'more' is added the number increases and that when finding 'less', the answer will be smaller. Can a number be both more than one number and less than another? Prove it ... Convince me..

Here are some examples of questions that have been changed into mastery and mastery with greater depth questions

Examples - FS2 Mastery at greater depth How many triangle can you see? What shape is this? Using a mastery approach What shape is this, how do you know? Mastery at greater depth How many triangle can you see? Children apply their understanding in a different context

Mastery at greater depth Examples – Year 1 Fill in the missing number 4 + 3 = 7 - = 4 Using a Mastery approach + = 12 Can you think of any more pairs? Mastery at greater depth I have this number 12 Can you think of different addition number sentences where the total is 12? Children apply learning of addition to find answers including addition on 3 numbers which is taught in Year 1.

Mastery at greater depth Examples – Year 1 Fill in the missing numbers 5, 10, ___ , 20, ___, 25 Using the mastery approach What number pattern is this? What would be the 10th number in this number pattern? Mastery at greater depth If you counted in 5s would you say 94? How do you know? Can you prove it?

Mastery at greater depth Examples – Year 2 Using the mastery approach Put a circle around the larger number. 1) 50 48 2) 77 81 Which number is bigger? 7 or 65? 13 or 57? Mastery at greater depth Write all the 2-digit numbers greater than 40 using these digits. 2 4 6 6 How do you know you have them all? Prove it.

Concrete - Practical - Abstract Skills taught through the use of CONCRETE objects Use of different resources Variety of representations

Concrete – Pictorial - Abstract Followed by PICTORIAL representations

Concrete – Pictorial - Abstract End with ABSTRACT learning 6 + 1 = 8 + 1 = 10 – 1 = 12 – 1 = 14 + 1 =

Problem solving Having practised different methods e.g. for 4 +3 through the CPA (concrete, pictorial and abstract) approach, children need to be given problems to solve where they are applying their skills and using them in a different context.

Lesson Content Every lesson should contain: Approx 5-10 - Verbal counting and fast pace starters the cover core mental maths skills. Approx 5 mins - Problem solving activity related to the lesson objective for children to attempt prior to the main teaching input. This will give teachers an insight into how to deliver the rest of the lesson. In focus approx 20 mins - Children focus on a single problem but look at it from multiple perspectives. They work in mixed ability pairs. Present the problem with visual representations, provide concrete resources, give children the chance to talk, explore, process their ideas and gain confidence. Approx 5 mins - Children explain their solution to the problem by presenting their different methods (HA variation of methods, LA focus on less methods) Approx 15 – 20 mins - Children practise for consolidation and fluency. Present children with similar problems which are slightly different each time. Encourage the use of different methods. Approx 5 mins - Give children reasoning opportunities and the chance to make up their own problems and identify misconceptions. This format can vary, depending of how children progress within a lesson.

What we will do first! Use the same mastery language across the school Explain it! Convince me! Prove it! Use it!

How will we use the language? Explain it! Can you explain it to me? How does this method work? Why does it work? Convince me! Who is right? Why is it not ___? How do you know that it is correct? Can you show me in a different way? Prove it! How many ways can you show me your answer? Can you check this to make sure it is correct by using another method? Use it! Can you solve a problem on your own? Can you show me that method again? Can you solve this problem using this method?