# MATHEMATICS AND NUMERACY

Contributed by:
VISION AND PHILOSOPHY:
1. Mathematics is a critical part of life and for the country’s economy.
2. Mathematics and numeracy experiences must be engaging, exciting, and accessible, as well as challenging.
3. To develop mathematical proficiencies, positive dispositions, and the four purposes of the curriculum.
1.
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
– 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
5. 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
•communication with symbols
•logical reasoning
•strategic competence.
6. 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 Progression step 3
•Calculate fractional quantities, •I have demonstrated my understanding
e.g. ⅛ of 24 = 3, that a fraction can be used as an
so ⅝ of 24 = 15. 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
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
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
• 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 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.
•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
•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