2. 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.
3. The rationale for change
• Research about mathematics performance:
– Estyn
– international
– PISA.
• Too much reliance on procedural fluency (technique/tricks).
• Not enough conceptual understanding.
4. 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’.
5. 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.
How is it different?
6. A change in emphasis from ‘What’ to ‘What and How’ will influence
pedagogy and result in teaching for conceptual understanding, as
shown below.
How is it different?
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.
7. 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.
8. 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.
9. 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.
10. 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
11. 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
12. 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?
Editor's Notes
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.
Not enough conceptual understanding:
depth of understanding
alternative strategies
problem solving.
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’.
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.
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).
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.
Extensive research of best practice and international approaches.
Designing a curriculum.
Pedagogy.
Mathematics and numeracy best practice – mastery, etc.
Extensive research of best practice and international approaches.
Designing a curriculum.
Pedagogy.
Mathematics and numeracy best practice – mastery, etc.
What does the evidence tell us? – extensive material utilised.
Expertise utilised to inform:
approach to financial literacy
pedagogy
Welsh dimension
wider skills
Foundation Phase
progression
achievement outcomes
etc.
