Download Inverclyde Numeracy Training

Progressive Numeracy
2016
Numeracy- Learning
Intentions
• Consider why we need to improve
the learning and teaching of
numeracy in our schools
• Explore the guiding principles
underpinning quality learning and
teaching of numeracy and SEAL
which supports these.
• Investigate quality resources.
Success Criteria
• Appreciate why we need to improve
• Identify guiding principles and consider these in
relation to our own practice
• Begin to develop progressive mathematisation
in our classrooms.
• Locate NNPF, Numeracy Maths Hub and LoP
and investigate how they may help with
learning and teaching
• Identify the structure of a good lesson
• Integrate a variety of mental agility approaches
and resources
Why do we need to improve?
How would you solve?
How would you support your
pupils to solve?
36 + 48 =
Euan and Cameron
• Are Euan and Cameron at the
same point in their learning?
Listen to the language they use and the strategies
they employ.
• What helps you to establish where
each child is in their learning?
See Euan and Cameron
video:
https://www.youtube.com/w
atch?v=cZnkgpUM0RA
Euan
• Finds it difficult to understand the problem
when presented verbally
• Does not apply number bonds
• Is reliant on an algorithm to solve the task
• Adopts a count-by-ones strategy
• Requires to track counts in ones on his
fingers
• Applies a process that he has been taught
• Uses mathematical language in the wrong
context
Cameron
• He understands the problem
• Applies number bonds to 20
• Uses a jump strategy to add and
subtract
• Has quick recall
• Applies a strategy that he has
developed
• Has language that enables him to
explain his thinking
The Guiding Principles of Learning and Teaching of Numeracy
Inquiry –based learning
Learning is inquiry based. Children are routinely
engaged in thinking hard to solve arithmetical
problems
Initial and on-going assessment
Learning is informed by ongoing assessment
Zone of Proximal Development
Learning is focused just beyond the cutting edge of
children’s current knowledge
Quality crafted lessons
Learning approaches are carefully selected to
meet the needs of the child
Developing more sophisticated
strategies
The teacher understands the children’s numerical
strategies and deliberately engenders the
development of more sophisticated strategies
through mathematisation
Observing and fine-tuning
learning
Observation of learning informs micro-adjustments
within lessons
Symbolising and notating
Children talk about their strategies and learn to
notate their thinking and formalise this over time
Sustained thinking and reflection
Wait time is valued and given
Intrinsic satisfaction
Through distancing settings and self checking their
thinking children understand they are making
progress
Based on Developing Number Knowledge; Wright R J, Ellemor-Collins D, Tabor P D, SAGE Publications Ltd 2012 (pp20-19)
Progressive Mathematisation
The development over time of the mathematical
sophistication of students’ knowledge and reasoning
with respect to a specific topic, for example addition.
Structuring numbers
Extending the range of numbers
Decimalising towards Base-ten
thinking
Unitising and not counting by ones
Distancing the setting of materials
Notating
Formalising and generalising
What is SEAL?
• SEAL sets out a progression of the strategies children use in early
number situations which are problematic for them.
• It consists of a clear progression through stages in children’s
development of early arithmetical strategies.
• Teachers are recognising the potential that SEAL has. It provides
a framework that helps profile an individual’s numerical
knowledge and offers clear guidance in teaching approaches
that nurtures their understanding.
• SEAL focuses on children’s own understanding of number thus
developing sound counting strategies that are based on
understanding rather than processes.
There is a clear tendency for low attainers in the early years to
continue to be low attainers.
Share:
In your classroom,
how do
you and your
pupils establish•
•
•
•
Where they are now?
Where you/ they want them to be?
How they will get there?
How you/ they will know when they are
there?
Where are they now?
• It is essential for a teacher to
determine the extent of each
child’s knowledge.
• Consider what you are assessing
and how they should be assessed.
Where are they now?
How would you solve…
Use double/ near
6+5=11
doubles
Count from 1
Use counters or
other concrete
materials
Use a jump strategy 6+4+1
Count on in 1s
from 6
Where do you want them to be?
• There is a need to establish clear
objectives.
• It is important to have a sound
mathematical knowledge and an
understanding of how children’s
mathematical learning progresses.
Think critically about the learning and teaching in your classroom
and consider the current levels of knowledge.
Consider how well you understand the aspects you are responsible
for and if you could undertake professional development to raise
your mathematical knowledge.
How will they get there?
What does a good maths lesson
look like?
15-20 mins Mental Agility
Core Learning and Teaching
Plenary
How Will They Get There?
Mental Agility is..
…the ability to carry out multi-step mental questions
accurately, either without writing anything down or
without a calculator.
SSLN Professional Learning Resource:
Numeracy and Mathematics Skills
Mental Agility: Why?
Mental agility is an essential skill. As adults, we need to
estimate and calculate every day. This skill must be
developed from the early stages.
SSLN Professional Learning Resource:
Numeracy and Mathematics Skills
How will they get there?
Mental Agility is…
• Efficiency
finding the most efficient, shortest way to solve a problem
• Accuracy
understanding number relationships and relationships between
operations, sound understanding of number facts
• Flexibility
understand that there are many ways to solve a problem, can use a
different way to check solution
• Fluency
all of the above combined
How will they get there?
Talking About Number
problem centred
encourage use of a range of
strategies
provide opportunities to
justify, describe, compare,
explain
errors are welcomed
• See I agree Disagree video
https://www.youtube.com/watch?v=
CdNnVaTt7TE
How will we get there?
Number Discussions –
• 5 to 15 minutes
• Daily routine
• Designated area in classroom
• Vocabulary
• Use concrete materials and visuals
• All answers are accepted
• Poker face
• Teacher records
• Children share thinking – HOW
• Answers and strategies are discussed
great posters on
http://displays.tpet.co.uk/#/ViewResource/id982
• See mental agility progression video
https://www.youtube.com/watch?v=
PzyCBM02XkQ
How will they get there?
• Whole class learning and teaching
• Flexible or fluid groupings to meet
individual needs
• Mixed ability groupings
Certain approaches to differentiating the learning using ability groupings,
i.e. using setting or streaming, may actually widen the attainment gap for
children from disadvantaged backgrounds.
Teachers use a range of differentiated strategies with all children, including
flexible grouping, ongoing assessment to ascertain next steps, as well as a
variety of daily numeracy activities that vary in complexity and openendedness.
(Knowledge into Action Briefing 1- Differentiated Learning in Numeracy and Mathematics)
Evaluation
(teachers’ views)
• The numeracy training improved teachers’
perception and beliefs about their own abilities,
especially in establishing at which numeracy stage
a child is at the moment to plan future actions.
‘This was excellent for helping me assess and plan for the
children in my class who have gaps. It has also validated
some of my practice.’
• Almost half of our teachers expressed the need for
sharing the knowledge, encouraging other teachers
and providing whole school numeracy training.
‘There's something for every ability stage + progression levels
are clear. Wish every teacher could get the training.’
Inverclyde Attainment
Challenge
Elaine.McLoughlin2@inverclyde .gov.uk
@ACTcoachmodel