The Primary Mathematics Curriculum in the UK

with a particular focus on England

Debbie Morgan Director for Primary Mathematics

Background

• 1988 The First National Curriculum • 1999 National Numeracy Strategy• 2000 Revised National Curriculum• 2006 Primary Strategy• 2014 New National Curriculum

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TIMSS

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HIGHER performance compared with EnglandParticipants performing at a significantly higher level than in England

SIMILAR performance compared with EnglandParticipants performing at a similar level to England (not statistically different)

LOWER performance compared with EnglandParticipants performing at a significantly lower level than England

6 countries [and 1 benchmarking participant], with their scale scores

6 other countries [and 1 benchmarking participant], with their scale scores

37 countries [and 5 benchmarking participants] including…With their scale scores

Singapore KoreaHong KongChinese Taipei JapanNorthern Ireland[North Carolina, US]

606605602591585562[554] 

Belgium (Flemish)Finland[Florida, US]ENGLANDRussian FederationUnited StatesNetherlandsDenmark

549545[545]542542541540537

[Quebec, Canada]PortugalGermanyIreland, Rep of[Ontario, Canada]AustraliaAustriaItaly[Alberta, Canada]SwedenKazakhstanNorwayNew ZealandSpain

533532528527[518]516508508[507]504501495486482

Table 1.1 TIMSS 2011 performance groups: mathematics at ages 9-10Source: Exhibit 1.3 international mathematics report

Key Reports

Good practice in primary mathematics: evidence from 20successful schools (Ofsted November 2011)

Review of the National Curriculum in England What canwe learn from the English, mathematics and sciencecurricula of high- performing jurisdictions?(DfE February 2012)

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20 Successful Schools Report

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This report evidenced that many successful schools teach both fluency in mental and written methods of calculation, and understanding of the underlying mathematical concepts.

Review of the National Curriculum Report

“... there is a wider consensus amongst mathematics educators that conceptual understanding, procedural and factual fluency and the ability to apply knowledge to solve problems are all important and mutually reinforce each other.......... Within this there is also broad consensus that automatic retrieval of basic facts facilitates the solving of more complex problems.”

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(DfE RR178, 2011)

The Aims of The New Curriculum in England

The national curriculum for mathematics aims to ensure that all pupils:

• 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 are able to recall and apply their 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.

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The 3 Aims of the New Curriculum in England

• Fluency• Reasoning• Problem Solving

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Research: the conceptual / procedural debate

Whereas past research and theory have focused predominantly on determining whether procedural or conceptual knowledge develops first (Byrnes & Wasik, 1991; Rittle-Johnson & Siegler, 1998; Siegler, 1991; Sophian, 1997), the acknowledgement that mathematical competence requires both knowing what to do and why has directed the focus of more recent research onto exploring the integration, and relations between, procedural and conceptual knowledge within mathematics learning and instruction.Voutsina 2011

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The Interrelationship between Procedures and Concepts

Research examining the interrelationship betweenunderstanding and computational skill (that is, betweenknowledge of concepts, and knowledge of facts andprocedures in mathematics learning) has indicated thatboth conceptual knowledge and procedural proficiency arefundamentally linked with children’s mathematicalachievement and ability to apply mathematics flexibly indifferent contexts (e.g. Baroody, 2003;Gray & Tall, 1994; Rittle-Johnson & Siegler, 1998cited in Voutsina 2011).

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Factual &Procedural Fluency

Conceptual Understanding

INTEGRATION

The Knowledge Led Curriculum

3 Forms of Knowledge Factual – I know thatProcedural – I know howConceptual – I know why

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Is there evidence of conceptual understanding?

Is there procedural fluency and efficiency?

Sally knows all her tables up to 12 x 12

When asked what is 12 x 13 – she looks blank

Does she have knowledge of facts, underpinned by conceptual understanding ?

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Lets do some MathsHow would you solve these?

+ 17 = 15 + 2499 – = 90 – 59

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Other Principles underpinning the New Curriculum

• Close the gap and raise attainment• Providing access to mathematical

concepts for all children• Pupils should make connections in

mathematics• Use representations to support learning• Deep rather than superficial learning• Calculating with confidence• More and longer time on fewer topics•

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Raising Expectations

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Provision of support and resources

This new curriculum unlike the introductionof the Numeracy Strategy (1999) hasmuch less resources accompanying it,either in the form of training ordocumentation. However the NCETM are providing somesupport

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NCETM

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References

DfE (2012) Review of the National Curriculum in EnglandWhat can we learn from the English, mathematics andScience curricula of high- performing jurisdictions?

Ofsted (2011) Good practice in primary mathematics:evidence from 20 successful schools

Voutsina, C (2011) Procedural and Conceptual changes inyoung children’s problem solving Published online:Springer Science & Business Media B.V.

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