1. Primary Mathematics 2014: embracing the opportunity
Genuine problem solving through deep conceptual understanding, mathematical reasoning and fluent procedures

2. Starting point
Establishing a rationale for the learning of mathematics
Why do children learn mathematics?
What do we mean by ‘mathematics’?
Mathematics is a way of seeing the world that enables people to solve problems. It is part of a cultural endeavour that opens windows to order, pattern and creativity.

3. The 2014 primary curriculum
Key messages
Recognises the importance of:
problem solving, for which children need fluency and reasoning
Integrated use of multiple concrete, pictorial and digital representations
communicating mathematical ideas
conceptual understanding in parallel with procedural skills

4. The primary mathematics classroom
A community of adults and children who:
“Have imaginative ideas
Ask questions
Make mistakes and use them to learn new things
Are organised and systematic
Describe, explain and discuss their work
Look for patterns and connections
Keep going when it is difficult”
Leone Burton (2004)

5. Problem solving
Solving problems is how and why we learn mathematics, and includes:
unfamiliar problems, open-ended investigations, and connections from and to existing ideas
in a variety of meaningful contexts, within mathematics, across and beyond the curriculum
where pupils choose and use appropriate knowledge and approaches

6. Representations
Children experience mathematical concepts through a variety of concrete, pictorial and digital representations
Important models for -
The number system: (empty) number line;
Place value: Dienes or similar;
Number bonds: tens frame or similar
These underpin and lead to deep understanding of abstract mathematical concepts

7. Central role of talk
Negotiating meanings: sharing ideas and deepening understanding – teacher with child and child with child
Communicating in a variety of ways (oral, written, electronic), with increasing rigour of language
Children use increasingly precise and flexible mathematical language to develop and share mathematical reasoning

8. Conceptual understanding and procedural fluency
These are best developed in parallel:
Procedural fluency without conceptual understanding can result in:
Computation without meaning
Inability to adapt skills to unfamiliar contexts
Difficulty reconstructing forgotten knowledge or skills
Conceptual understanding without procedural fluency can result in:
Computation which is slow, effortful and frustrating
Inability to focus on the bigger picture when solving problems
Difficulty progressing to new or more complex ideas
These can both limit progress

9. The importance of number
Deep knowledge of the number system is a principal focus throughout the curriculum. It requires:
Fluency in calculation
Ability to solve number problems in a variety of contexts
Use of multiple representations
Communicating with words and symbols for numbers and operations
This underpins understandings of measurement and, later, algebra, and complements work in shape and space.

10. Key Stage 1
Represent numbers to 100 and beyond using concrete objects, pictures, and ICT, and with numerals and words.
Know and use number bonds to 20
Use and understand the place value of tens and ones
Use practical objects to represent the four operations

11. Lower key stage 2 Understand and represent whole numbers and fractions
Use measuring instruments with accuracy
Use and understand place value, including decimal
Memorise multiplication tables up to and including 12x12
Calculate efficiently using mental and written methods

12. Upper key stage 2
Make connections between multiplication and division with fractions, decimals, percentages and ratio
Begin to use the language of algebra
Fluent written methods including long multiplication and division
Calculate fluently, including mentally, with fractions, decimals and percentages

13. The role of the teacher
The teacher is the lead learner in the mathematics classroom, and models interaction with mathematics for children
Getting stuck, or not knowing, is part of mathematical challenge, and an opportunity to learn: be confident to model that
Curiosity, enthusiasm, and resilience are infectious: enjoy the challenge!