stages of arithmetical learning - edubuzz.org
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Developing Numeracy Skills
Stages of Arithmetical Learning
Julie Davidson and Dianne MacKenzie
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Aims
• Significant shifts in learning
• Developing pedagogy
• SEAL - more than Early Level
• SEAL - not a resource
• Teachers need time to develop their
understanding of SEAL and consider the
impact this has on Learning and Teaching
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Learning and Teaching
in Numeracy
From the early stages onwards, children
and young people should experience
success in mathematics and develop the
confidence to take risks, ask questions
and explore alternative solutions without
fear of being wrong. They will enjoy
exploring and applying mathematical
concepts to understand and solve
problems, explaining their thinking and
presenting their solutions to others in a
variety of ways. Mathematics: Principles and Practice
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Let’s start with the children
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What does the research say?
• There are significant differences in the
numerical knowledge of children when
they begin school.
• Differences in number knowledge increase
as the child progresses through school
• There is a clear tendency for low attainers
in the early years to continue to be low
attainers.
If the research indicates this……
How can we give every child a
positive understanding and success
in early number?
How do we identify and support
development needs?
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Observing the learner
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The Stages of Early Arithmetical Learning
A model which highlights significant shifts in how children think about and
understand number
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Emergent
Figurative
Perceptual
Initial Number
Intermediate Number
Facile
Forward andBackward Number
Word Sequences
Numeral Identification
and Recognition
Number Structures
Multiplication and Division
Attempts to Count
Counts seen items
Screened / Count from 1
Counts on
Count down to/from
Range of Non-Count by ones
A - SEAL: Stages of Early Arithmetical Learning
B - FNWSs: Forward Number Word Sequences
BNWSs: Backward Number Word SequencesNumeral Identification
Also focus on knowledge of:
C - Structuring numbersC - Tens and Ones = conceptual place valueD - Multiplication and Division
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Because…..
“ ….there is no such thing as
arithmetical ability: only arithmetical
abilities. The corollary is that
arithmetical development is not a single
process, but several processes,
involving the development of different
components. “
Ann Dowker, The Development of Mathematical Skills
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Signposts
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Emergent Counting
What do you see…..
• Organisation
• Numeral Sequence
• 1-1 correspondence
• IMBY – It might be you!
Table 19 – person with longest hair
Murray
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Emergent Counting – What do I need?
• Copying and saying short number sequences forwards and backwards
• Using domino patterns and random arrays to develop ability to ascribe number
• Making Spatio-motor/Auditory patterns to match spatial patterns
• Making finger patterns – seen and unseen
• Copying and Counting temporal patterns and temporal sequences…including double patterns
Early Level - MNU 0-02a
I have explored numbers, understanding that they represent
quantities and I can use them to count, create sequences and
describe order
CfE
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What does this mean for our
teachers?
Research indicates that the quality of
instruction is an important factor
influencing student achievement in
mathematics…. We believe this quality of
instruction is critically important and is
directly tied to the teachers’ specialised
knowledge of the teaching and learning of
mathematics; that is, what is referred to as
pedagogical content knowledge.
(Shulman, 1986)Developing Number Knowledge
Wright, Ellemor-Collins and Tabor
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Perceptual Counting
Table 5 – person with the shiniest shoes
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Perceptual Counting - What do I need
• Saying alternate FNWS, BNWS• Saying the number word before and after• Sequencing/Identifying numerals 1-20• Counting two collections with one screened then two
screened• Counting items in a row with some screened• Partitioning visible and flashed patterns to 10• Combining patterns• Finger patterns; Five plus, partitioning 3-10, Doubles
plus 1, Partitioning 10 fingers• Describing equal groups, organising equal groups,
making equal groups, describing equal shares, organising equal shares, partitioning equal shares
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The Learning Cycle – What can SEAL offer?
Initial and on-going
assessment
Clear Learning
Pathways
Constructivist teaching with related
teaching activities
Problem solving
opportunities to challenge
current stage of
development
SEAL
Curriculum for Excellence –
Cumulative Growth
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Promoting discussion about strategies
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What do they need?
• Develop understanding of tens and ones
• Opportunities to explore the structure of numbers to
100.
• Combine and partition numbers in a variety of ways
• Tens and ones - creating and counting
• Developing jump strategies for addition and
subtraction
• Developing Knowledge and recall of equal shares
and groups
What do they NOT need?
Algorithms (not yet!)
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What are the key features of effective
learning and teaching in numeracy?
• Active learning and planned purposeful play
• Development of problem solving activities
• Developing mental agility
• Frequently asking children to explain their thinking
• Use of relevant contexts and experiences, familiar to children and young people
• Using technology in appropriate and effective ways
Numeracy across learning – Pg 2
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Curriculum for Excellence
‘Children and young people will most effectively develop their numeracy through cumulative growth in their understanding of key concepts and the application of their skills in new contexts.’
Numeracy across learning – Page 3
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Let’s finish with our teachers!
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Early Numeracy: Assessment for Teaching and Intervention
(Maths Recovery Series) by Mr Robert J Wright, Mr James
Martland and Ann K Stafford (Paperback - 5 Jan 2006)
ISBN: 978-1-4129-1020-0
Teaching Number: Advancing Children's Skills and
Strategies (Maths Recovery Series) by Mr Robert J Wright,
Garry Stanger, Ann K Stafford and Mr James Martland
(Paperback - 13 Sep 2006) ISBN: 978-1-4129-2185-5
Teaching Number in the Classroom with 4-8 year olds
(Maths Recovery Series) by Mr Robert J Wright, Garry
Stanger, Ann K Stafford and Mr James Martland
(Hardcover - 5 Jan 2006) ISBN: 978-1-4129-0757-6
Introducing SEAL,
Mhairi Stratton, 2011