2 What is Maths? Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
3 Government agenda TIMSS (Trends in International Mathematics and Science Study) UK has been surpassed internationally in its mathematics performance. Singapore s students have consistently been top performers in the TIMSS assessment. Clearly, Singapore maths is effective.
4 National Curriculum Reform Post 2014 In mathematics there will be additional stretch, with much more challenging content than in the current National Curriculum. We will expect pupils to be more proficient in arithmetic, including knowing number bonds to 20 by Year 2 and times tables up to 12 x 12 by the end of Year 4. The development of written methods Including long multiplication and division - will be given greater emphasis, and pupils will be taught more challenging content using fractions, decimals and negative numbers so that they have a more secure foundation for secondary school.
5 New Primary Maths Curriculum The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on. National curriculum in England: Mathematics p3
6 Principles 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.
7 EYFS (Early Years Foundation Stage) Early Learning Goals (End of Reception) Number: Children count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing. Shape, space and measures: Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems. They recognise, create and describe patterns. They explore characteristics of everyday objects and shapes and use mathematical language to describe them.
8 Key Stage 1 - Years 1 and 2 The principal focus of mathematics teaching in key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the 4 operations, including with practical resources [for example, concrete objects and measuring tools]. At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency. Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
9 Lower key stage 2 - Years 3 and 4 The principal focus of mathematics teaching in lower key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the 4 operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. By the end of year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word-reading knowledge and their knowledge of spelling.
10 Upper key stage 2 - years 5 and 6 The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them. By the end of year 6, pupils should be fluent in written methods for all 4 operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils should read, spell and pronounce mathematical vocabulary correctly.
11 Two Beliefs about Intellectual Ability Innate Ability Effort-Based Ability
12 Belief in Innate Ability ASSUMPTIONS Ability is fixed You either have it or you don t BELIEFS Inborn intelligence is the main determinant of success OUTCOMES Poor Results Defeatism
13 Belief in Effort-Based Ability ASSUMPTIONS Effort = Development BELIEFS Consistent effort and effective strategies are the main determinants of success. OUTCOME Engagement Confidence Results
14 Changing Mindsets
15 A belief and a frustration Maths Mastery was developed by Ark schools who wanted a new taught curriculum to ensure that their aspirations for every child s mathematics success becomes reality, through significantly raising standards. Success in mathematics for every child Close the attainment gap
16 Mathematics Mastery Curricular principles Fewer topics in greater depth Opportunities are provided throughout Mathematics Mastery for pupils to use reasoning skills to make connections between prior knowledge and newly presented material. These connections will help foster a deeper understanding of the maths concepts. Mastery for all pupils Differentiation through depth, cumulative learning, AfL Number sense and place value come first Traditional algorithms meaningfully taught (Maths Meetings address the rest of the content) Problem solving is central Comprehension, calculation and problem solving developed simultaneously.
17 Achieving Mastery Understanding a skill conceptually and making links between topics Children should be able to show or explain a concept in a variety of ways Children can apply a concept in a new situation
19 Bloom s Taxonomy
22 Mathematics Mastery Key lesson features Mastering mathematical understanding Mastering mathematical thinking Mastering mathematical language Mastery for all: Structure of learning
23 Mastering mathematical understanding Concrete-Pictorial-Abstract (C-P-A) approach Jerome Bruner - three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations. Concrete- The DOING A child 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-The SEEING A child has sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. Abstract The SYMBOLIC A child is now capable of representing problems by using mathematical notation, for example: 12 2 = 6
24 Concrete representation
25 Concrete representation
26 Why use concrete manipulatives? Evidence from research shows: pupils who use concrete manipulatives develop a more precise and more comprehensive mental representations, they often show more motivation and on task behaviours, understand mathematical ideas and better apply these to life situations. (Anstrom, 2006)
27 3 x 4 = 12 Pupils can count the total Reinforces groups of It is clear that 4x4 would require another group/row of 4 (repeated addition)
28 Compare 31 and 35 Comparing numbers More or fewer Look at the tens and ones What s the same and what s different?
29 40 7 = 33 Understanding re-grouping Reinforcing place value
30 13 x 22 = 286 Supports counting in 100s, 10s and 1s Shows that every number is multiplied by every other number
31 Pictorial representation Drawing pictures of real objects Tallies, dots, circles
32 Pictorial representation Images of actual concrete manipulatives Explain the connections between the concrete and pictorial Don t remove or stop using concrete manipulatives
33 Abstract representation Symbolic stage Numbers, letters and symbols I did it in my head Most formal stage of mathematical understanding Efficient way of representing the maths
34 C-P-A benefits Provides pupils with a structured way to learn maths concepts Pupils can build a better connection when moving through the levels of understanding from concrete to abstract Makes learning accessible to all learners Research has proven this method is effective Able to use across year groups, from early primary through secondary school Helps pupils learn concepts before learning rules Can be used in small groups or the entire class Can be used to differentiate and to assess true understanding
35 Mastering mathematical thinking Whole class, paired, individual opportunities to: Compare (sort, organise) Modify (change, vary, reverse, alter) Generalise (pattern spotting, exemplifying, predict) Learning is generalisation. We want children to think like mathematicians. Not just DO maths
36 Eg: Addition at a deeper level P, Q, R, S and T represent single digits in this subtraction. What is the value of P + Q + R + S + T?
37 Mastering mathematical language Mathematics Mastery lessons provide opportunities for pupils to communicate and develop mathematical language through: Sharing essential vocabulary at the beginning of every lesson and insisting on its use throughout Modelling clear sentence structures using mathematical language Paired language development activities (toolkit lesson) Plenaries which give a further opportunity to assess understanding through pupil explanations
38 Mastery for all: Structure of learning Multi-part lessons Allow for cumulative, scaffolded learning where assessment is crucially feeding in to subsequent segments. Pupils are doing straight away. No time is wasted Do Now Task; New Learning; Paired Language Development; Develop Learning; Independent Task; Plenary
39 Mastery for all: Structure of learning Transitions Used to recall quick number facts or mathematical concepts through chants, actions and songs and to prepare children for learning.
40 Calculation Policy This policy outlines the different calculation strategies that should be taught and used in Years 1-4, in line with the requirements of the 2014 Primary National Curriculum.
41 Assessment Half termly end of unit assessments Against age related expectations Formative on-going assessment Gap analysis Responsive feedback Next step for depth stickers NCTEM materials
42 Age related expectations Interim Framework for Maths (End Yr 2 & 6) Target tracker steps.
43 Assessment: Target Tracker
44 Maths in Action You are now invited to look around the classes
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