Debbie Morgan - Edge Hill University

Report
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
2
TIMSS
HIGHER performance compared
with England
Participants performing at a
significantly higher level than in
England
SIMILAR performance compared
with England
Participants performing at a
similar level to England (not
statistically different)
LOWER performance compared
with England
Participants 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
Korea
Hong Kong
Chinese Taipei
Japan
Northern Ireland
[North Carolina, US]
Belgium (Flemish)
Finland
[Florida, US]
ENGLAND
Russian Federation
United States
Netherlands
Denmark
[Quebec, Canada]
Portugal
Germany
Ireland, Rep of
[Ontario, Canada]
Australia
Austria
Italy
[Alberta, Canada]
Sweden
Kazakhstan
Norway
New Zealand
Spain
606
605
602
591
585
562
[554]
549
545
[545]
542
542
541
540
537
533
532
528
527
[518]
516
508
508
[507]
504
501
495
486
482
Table 1.1 TIMSS 2011 performance groups: mathematics at ages 9-10
Source: Exhibit 1.3 international mathematics report
3
Key Reports
Good practice in primary mathematics: evidence from 20
successful schools (Ofsted November 2011)
Review of the National Curriculum in England What can
we learn from the English, mathematics and science
curricula of high- performing jurisdictions?
(DfE February 2012)
4
20 Successful Schools Report
This report evidenced that many
successful schools teach both fluency in
mental and written methods of calculation,
and understanding of the underlying
mathematical concepts.
5
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.”
(DfE RR178, 2011)
6
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.
7
The 3 Aims of the
New Curriculum in England
• Fluency
• Reasoning
• Problem Solving
8
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
9
The Interrelationship
between
Procedures and Concepts
Research examining the interrelationship between
understanding and computational skill (that is, between
knowledge of concepts, and knowledge of facts and
procedures in mathematics learning) has indicated that
both conceptual knowledge and procedural proficiency are
fundamentally linked with children’s mathematical
achievement and ability to apply mathematics flexibly in
different contexts
(e.g. Baroody, 2003;Gray & Tall, 1994; Rittle-Johnson & Siegler, 1998
cited in Voutsina 2011).
10
Factual &Procedural
Fluency
Conceptual
Understanding
INTEGRATION
11
The Knowledge Led Curriculum
3 Forms of Knowledge
Factual – I know that
Procedural – I know how
Conceptual – I know why
12
Is there evidence
of conceptual
understanding?
Is there
procedural
fluency and
efficiency?
13
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 ?
14
Lets do some Maths
How would you solve these?
 + 17 = 15 + 24
99 –  = 90 – 59
15
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
16
Raising Expectations
17
Provision of support and
resources
This new curriculum unlike the introduction
of the Numeracy Strategy (1999) has
much less resources accompanying it,
either in the form of training or
documentation.
However the NCETM are providing some
support
18
NCETM
19
References
DfE (2012) Review of the National Curriculum in England
What can we learn from the English, mathematics and
Science curricula of high- performing jurisdictions?
Ofsted (2011) Good practice in primary mathematics:
evidence from 20 successful schools
Voutsina, C (2011) Procedural and Conceptual changes in
young children’s problem solving Published online:
Springer Science & Business Media B.V.
20

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