Anne Watson AMET 2013 Purpose of study Mathematics is a creative and highly interconnected discipline that has been developed over centuries providing the solution to some of historys most intriguing problems It is essential to everyday life critical to science technology and engineerin ID: 468395
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Slide1
The new national curriculum: what is the role of the teacher educator?
Anne Watson
AMET
2013Slide2
Purpose of study
Mathematics is a creative and highly inter-connected 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 high-quality 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.Slide3
Purpose of study
creative
inter-connected discipline
history’s most intriguing problems
science, technology and engineering
financial literacy
ability to reason
beauty and power
enjoyment and curiosity
Slide4
Aims
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.Slide5
Aims
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.Slide6
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
perseveringSlide7
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 understandingSlide8
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.Slide9
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
. Slide10
The role of the teacher educator
To embed problem-solving throughout mathematics teaching and learningSlide11
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?Slide12
other roles of the teacher educator
Looking at the challenges for teachers in the new curriculum bearing in mind:
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.Slide13
creative
inter-connections
history
STEM
finance
reasoning
beauty & power
enjoyment & curiosity
practice increasingly complex problems over time
conceptual understanding
recall & apply
follow a line of enquiry
conjecture relationships
develop & communicate justification & proof
non-routine mathematical problems
mathematical models
perseverence
shift between representations
make connections
enrichment
consolidation
What will teachers find new/difficult?
same pace
progress based on understandingSlide14
Teacher educator focus
inter-connections (TE)
reasoning (TE)
beauty & power (TE)
enjoyment & curiosity (TE)
creative (web)
history (web)
STEM (web)
finance (web)Slide15
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?)Slide16
Teacher educator focus
shift between representations
make connections
enrichment
consolidation
same pace (SBTE)
progress based on understanding (SBTE)Slide17
The role of the teacher educator
To develop the teacher’s capability to ask important questions such as:
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?Slide18
More questions
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?Slide19
More questions
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?Slide20
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