THE NEW NATIONAL
CURRICULUM: WHAT IS THE ROLE
OF THE TEACHER EDUCATOR?
Anne Watson
AMET
2013
PURPOSE OF STUDY
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Mathematics is a creative and highly interconnected discipline that has been developed over
centuries, providing the solution to some of
history’s most intriguing problems. It is essential
to everyday life, critical to science, technology
and engineering, and necessary for financial
literacy and most forms of employment. A highquality mathematics education therefore
provides a foundation for understanding the
world, the ability to reason mathematically, an
appreciation of the beauty and power of
mathematics, and a sense of enjoyment and
curiosity about the subject.
PURPOSE OF STUDY
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creative
inter-connected discipline
history’s most intriguing problems
science, technology and engineering
financial literacy
ability to reason
beauty and power
enjoyment and curiosity
AIMS
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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 the
ability to recall and apply appropriate knowledge
rapidly and accurately.
reason mathematically by following a line of
enquiry, conjecturing relationships and
generalisations, and developing and communicating
an argument, justification or proof using
mathematical language
can solve problems with increasing sophistication
including non-routine problems expressed
mathematically or requiring mathematical modelling,
by breaking them down into a series of steps and
persevering in seeking solutions.
AIMS

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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 the
ability to recall and apply appropriate knowledge
rapidly and accurately.
reason mathematically by following a line of
enquiry, conjecturing relationships and
generalisations, and developing and communicating
an argument, justification or proof using
mathematical language
can solve problems with increasing sophistication
including non-routine problems expressed
mathematically or requiring mathematical modelling,
by breaking them down into a series of steps and
persevering in seeking solutions.
AIMS
practice
 increasingly complex problems over time
 conceptual understanding
 recall
 apply
 following a line of enquiry
 conjecturing relationships and generalisations
 developing and communicating an argument
 justification or proof
 non-routine problems expressed mathematically
 requiring mathematical modelling
 persevering

ALSO
move fluently between representations of
mathematical ideas
 make rich connections
 majority of pupils will move through the
programmes of study at broadly the same pace.
 progress based on the security of understanding
 pupils who grasp concepts rapidly should be
challenged
 those who are not sufficiently fluent with earlier
material should consolidate their understanding
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OFSTED SUBJECT SURVEY VISITS
Teaching is rooted in the development of all
pupils’ conceptual understanding of important
concepts and progression within the lesson and
over time. It enables pupils to make connections
between topics and see the ‘big picture’.
 Problem solving, discussion and investigation are
seen as integral to learning mathematics.
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Constant assessment of each pupil’s
understanding through questioning, listening
and observing enables fine tuning of teaching.
Barriers to learning and potential
misconceptions are anticipated and overcome,
with errors providing fruitful points for
discussion.
THE ROLE OF THE TEACHER EDUCATOR
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To embed problem-solving throughout
mathematics teaching and learning
PROBLEM SOLVING – THREE KINDS
Procedural: Having been subtracting numbers for three
lessons, children are then asked: ‘If I have 13 sweets and
eat 8 of them, how many do I have left over?’
 Application: A question has arisen in a discussion about
journeys to and from school: ‘Mel and Molly walk home
together but Molly has an extra bit to walk after they get
to Mel’s house; it takes Molly 13 minutes to walk home
and Mel 8 minutes. For how many minutes is Molly
walking on her own?’
 Conceptual: If two numbers add to make 13, and one of
them is 8, how can we find the other?
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OTHER ROLES OF THE TEACHER EDUCATOR
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Looking at the challenges for teachers in the new
curriculum bearing in mind:
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Their likely school experience – varied but including
procedural text-focused work
Their recent work towards the 2007 curriculum –
more problem-solving, functional mathematics
Current pressures in school – test-focused,
acceleration, grade-trade
New intentions – same curriculum for all, increased
conceptual challenge
Habits in school – levels, three-part lesson etc.
creative
inter-connections
history
STEM
finance
reasoning
beauty & power
enjoyment & curiosityWhat
practice increasingly
complex problems over
time
conceptual understanding
recall & apply
follow a line of enquiry
will teachers
conjecture relationships
find new/difficult?
develop & communicate
justification & proof
shift between representations
non-routine mathematical
make connections
problems
enrichment
consolidation
mathematical models
perseverence
same pace
progress based on understanding
TEACHER EDUCATOR FOCUS
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inter-connections
(TE)
reasoning
(TE)
beauty & power
(TE)
enjoyment & curiosity (TE)
creative
history
STEM
finance
(web)
(web)
(web)
(web)
TEACHER EDUCATOR FOCUS
 practice
increasingly complex problems over
time
 conceptual understanding
 recall & apply
 follow a line of enquiry
 conjecture relationships
 develop & communicate justification & proof
 mathematical models
 perseverance (SBTE?)
 non-routine mathematical problems (web?)
TEACHER EDUCATOR FOCUS
 shift
between representations
 make connections
 enrichment
 consolidation
 same
pace (SBTE)
 progress based on understanding (SBTE)
THE ROLE OF THE TEACHER EDUCATOR
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To develop the teacher’s capability to ask
important questions such as:
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How does this idea connect to the rest of the
curriculum?
What kinds of reasoning are required/made
possible by this mathematical idea?
How does this idea make learners more
powerful?
What sources of curiosity are lurking in this
idea?
MORE QUESTIONS
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How can questions become more complex over time?
What timescale – hours, days, weeks, years?
What does it mean to understand this idea?
What has to be recalled and how?
What has to be noticed to know when to apply this?
What can be enquired about/conjectured and how?
What needs justifying/proving and how?
What does this idea contribute to a modelling
perspective?
What needs perseverance and over what time period?
MORE QUESTIONS
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What representations are useful and how do
they relate?
How can this idea be presented so that it
connects?
What deeper understandings/applications are
possible?
What aspects of this idea might need
consolidation?
What is a reasonable learning goal for everyone,
and how will enrichment and consolidation be
managed?
IMPLICATIONS FOR MATHEMATICS
TEACHER EDUCATION
Subject-specific focus
 Working on mathematics
 Range of experiences to reflect on
 Questioning habits to plan and evaluate teaching
 Distinguishing between what is learnt by being
told; what is learnt by watching others do
mathematics or teach mathematics; what is
learnt by doing mathematics; what is learnt by
teaching mathematics
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