Vision and philosophy Mathematics is a critical part of life and for the country’s economy. Mathematics and numeracy experiences must be engaging, exciting and accessible, as well as challenging. To develop mathematical proficiencies, positive dispositions and the four purposes of the curriculum. Mathematics is an international discipline, and numeracy – the application of mathematics – plays a critical part in our private, social and civic lives, and in the economic health of the nation. It is imperative that Mathematics and Numeracy experiences are as engaging, exciting and accessible as possible for learners, while also ensuring that learners develop mathematical resilience (being able to embrace challenge as a positive aspect of learning). Development of the mathematical proficiencies and the development both of positive dispositions and the four purposes of the curriculum is the vision of the Mathematics and Numeracy Area of Learning and Experience. In the early years, play forms an important part in the development of mathematics and numeracy, enabling learners to solve problems, explore ideas, establish connections and collaborate with others. In later years learners need to have opportunities to work both independently and collaboratively to build on the foundations established in the early years. For all ages, real-life examples drawn from the local, national and international environment help learners make connections between the concrete and the abstract. Real-life contexts can be used to introduce and explore mathematical concepts, as well as to consolidate them. Indeed, teaching which introduces a reasoning and problem-solving approach to all mathematics and numeracy experiences supports the development both of positive dispositions and of the four purposes of the curriculum, as well as supporting the development of the mathematical proficiencies. 

The rationale for change Research about mathematics performance: – Estyn – international – PISA. Too much reliance on procedural fluency (technique/tricks). Not enough conceptual understanding. Not enough conceptual understanding: depth of understanding alternative strategies problem solving.

How is it different? Organised around five mathematical proficiencies. Gives learners opportunities to use manipulatives and represent concepts in a variety of ways. Use verbs such as ‘explore’ and ‘derive’ to ensure balance between ‘breadth’ and ‘depth’. The Mathematics and Numeracy curriculum is organised around five mathematical proficiencies explained in later slides, which have been used to shape the achievement outcomes. All learners should have opportunities to use manipulatives and represent a concept in a variety of ways, including verbal, concrete, visual, digital and abstract representations. Verbs such as ‘explore’ and ‘derive’ are used to ensure a suitable balance between ‘breadth’ and ‘depth’.

How is it different? Mathematical proficiencies These inter-dependent proficiencies used in developing the descriptions of learning are central to progression at each stage of mathematics learning. Numeracy involves applying and connecting these proficiencies in a range of real-life contexts. The five mathematical proficiencies are: conceptual understanding fluency communication with symbols logical reasoning strategic competence. Conceptual understanding: Mathematical concepts and ideas should be built on, deepened and connected as learners experience increasingly complex mathematical ideas. Learners demonstrate conceptual understanding through being able to explain and express concepts, find examples (or non-examples) and by being able to represent a concept in different ways, flowing between different representations including verbal, concrete, visual, digital and abstract.  Communication with symbols: Learners should understand that the symbols they are using are abstract representations and should develop greater flexibility with the application and manipulation of an increasing range of symbols, understanding the conventions of the symbols they are using.  Strategic competence (formulating problems mathematically in order to solve them): Learners should become increasingly independent in recognising and applying the underlying mathematical structures and ideas within a problem, in order to be able to solve them.  Logical reasoning: As learners experience increasingly complex concepts, they also should develop an understanding of the relationships between and within these concepts. They should apply logical reasoning about these relationships and be able to justify and prove them. Justifications and proof should become increasingly abstract, moving from verbal explanations, visual or concrete representations to abstract representations involving symbols and conventions.  Fluency: As learners experience, understand and apply increasingly complex concepts and relationships, fluency in remembering facts, relationships and techniques should grow, meaning that facts, relationships and techniques learned previously should become firmly established, memorable and usable. 

How is it different? A change in emphasis from ‘What’ to ‘What and How’ will influence pedagogy and result in teaching for conceptual understanding, as shown below. Current curriculum (Product) New curriculum (Process) Year 5 Calculate fractional quantities, e.g. ⅛ of 24 = 3, so ⅝ of 24 = 15. Progression step 3 I have demonstrated my understanding that a fraction can be used as an operator, or to represent division. I understand the inverse relation between the denominator of a fraction and its value. Emphasis is on the pedagogy – this will be key to making it different.  Allows time for depth of understanding. Authentic context; hands on/practical, using manipulatives, real-life, in meaningful contexts relevant to learners. Foundation Phase principles throughout.  Principles of progression/refined content of progression steps – it has gone from a concept-based curriculum to a process curriculum.  Conceptual understanding; Communication with symbols; Strategic competence; Logical reasoning; Fluency. Links with other areas of learning and experiences. Embedded National Literacy and Numeracy Framework (LNF).

What Matters in Mathematics and Numeracy The number system is used to represent and compare relationships between numbers and quantities. Algebra uses symbol systems to express the structures of relationships between numbers, quantities and relations. Geometry focuses on relationships involving properties of shape, space and position, and measurement focuses on quantifying phenomena in the physical world. Statistics represent data, probability models chance, and both support informed inferences and decisions. The group considered ‘big ideas’, e.g. patterns, estimation, etc. Plenty of research but no country has used them to structure their curriculum. The principles of progression helped shape our progression steps.   More about the how than the what. The different areas of mathematics are highly inter-connected and dependent on one another, concepts are built up over time, drawing on prior knowledge and learning, often from more than one area of mathematics.   Granularity – wanted to get enough detail to support teachers in implementing the curriculum without directing too specifically (remit from Curriculum and Assessment Group), we felt that more detail was needed in mathematics than other areas of learning and experience due to the specific, hierarchical nature of mathematics. Achievement outcomes – constant review to get a balance between the detail in achievement outcomes and planning for learning, again needed enough detail to be supportive without being too prescriptive. Foundation Phase pedagogy – following meetings with Foundation Phase experts, we made sure that the principles and language of the Foundation Phase is clear in achievement outcomes. Algebra, geometry and statistics cannot be fully understood without a prior understanding of number.  Numeracy – the use of mathematics to solve problems in real-life contexts. 

How did we get here? Approach and expertise Research Curriculum reform Designing a mathematics curriculum – Indonesia, issues around mathematics curriculum reform. Evolution of Singapore’s school mathematics curriculum. Mathematics curriculum in Pacific Rim Countries – China, Japan, Korea, and Singapore. Finland curriculum structure and development. National Mathematics Advisory Panel, US, 2008. Excellence in Mathematics – Scotland (report from the Maths Excellence Group). Interdisciplinary Programs Involving Mathematics – India. Extensive research of best practice and international approaches. Designing a curriculum. Pedagogy. Mathematics and numeracy best practice – mastery, etc.

How did we get here? Approach and expertise Research Curricula and associated pedagogy Wales – Foundation Phase, Key Stages 2–4 programmes of study, National Literacy and Numeracy Framework (LNF), Task and Finish Report (Nov 2015), LNF – A Strategic Action Plan (2016). England – Key Stages 1 and 2, Key Stage 3, Key Stage 4, Formal Written Methods. Scotland – Curriculum, Pedagogy, Numeracy Experiences, Numeracy Framework Republic of Ireland – Primary Curriculum and Teacher Guidance, Secondary – Project Maths (programme to bring more problem solving in secondary schools). Singapore – Primary, Secondary. Finland – Curriculum (P. 158-167), Problem Solving. Ontario – Primary , Secondary. Quebec – Primary, Secondary (embedded in Maths/Science/Technology subject area). Mastery approach being promoted in England – mastery, video1 video2 and maths hubs. Extensive research of best practice and international approaches. Designing a curriculum. Pedagogy. Mathematics and numeracy best practice – mastery, etc.

How did we get here? Approach and expertise Evidence: Estyn Mathematics Good Practice in mathematics Key Stage 3, 2015 Good Practice in mathematics Key Stage 4, 2013 Best practice in mathematics for pupils aged 3 to 7 years, June 2009 Numeracy Numeracy in key stages 2 and 3: an interim report, November 2014 Numeracy in key stages 2 and 3: a baseline study, June 2013 Numeracy for 14 to 19-year-olds, July 2011 Improving numeracy in key stage 2 and key stage 3, April 2010 Evidence: Others Does Financial Education Impact Financial Behavior, and if So, When? Should all students be taught complex mathematics? (OECD Library Publication) 10 Questions for Maths Teachers … and how PISA can help answer them. (OECD publication) Achievement of 15-Year-Olds in Wales: PISA 2012 National Report What does the evidence tell us? – extensive material utilised.

How did we get here? Approach and expertise Expert input and feedback includes the following. Estyn. Qualifications Wales. Marie Joubert (NNEM researcher), various. Anne Watson, Emeritus Professor, Oxford University, ‘Pedagogical guidance for mathematics’: Excellent pedagogy and the twelve generic pedagogical principles from Successful Futures and ‘Digital technology and the new Welsh mathematics curriculum’. Professor Matthew Jarvis ‘AoLE Implementation of the ‘Welsh Dimension and International Perspective’’. Tom Cox, ‘Wider Skills and the Areas of Learning and Experience (AoLE): An audit and analysis with proposals for future work’. Learning Partnership. Foundation Phase Expert Group. Progression: CAMAU team Expertise utilised to inform: approach to financial literacy pedagogy Welsh dimension wider skills Foundation Phase progression achievement outcomes etc.

Considerations for schools How will your leaders, practitioners and networks be able to prepare for the next phase of co-construction and provide meaningful feedback? What, if any, are the resourcing implications (national and local)? How could you approach whole-school and/or inter-departmental approaches to both: – knowing about the new curriculum? – understanding how to do the new curriculum?