This document provides guidance on improving numeracy teaching. It discusses the need to assess students' current abilities and establish clear learning goals. A good numeracy lesson includes 15-20 minutes of mental agility exercises followed by core teaching and a plenary session. Mental agility involves solving multi-step problems accurately in various ways. Quality instruction develops more sophisticated problem-solving strategies over time through activities like number talks and daily practice. Formative assessment informs flexible grouping and differentiation strategies to meet individual student needs. The document provides resources on progression frameworks and lesson planning approaches to support numeracy development.

1. Progressive Numeracy
2016

2. 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.

3. 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

4. Why do we need to improve?
How would you solve?
How would you support your
pupils to solve?
36 + 48 =

5. 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?

6. See Euan and Cameron video:
https://www.youtube.com/watch?
v=cZnkgpUM0RA

7. 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

8. 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

9. 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)

10. 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

11. 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.

12. 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?

13. 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.

14. Where are they now?
How would you solve…
6+5=11
Use counters or
other concrete
materials
Count from 1
Count on in 1s
from 6
Use a jump strategy 6+4+1
Use double/ near
doubles

15. 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.

16. How will they get there?
What does a good maths lesson look
like?
15-20 mins Mental Agility
Core Learning and Teaching
Plenary

17. 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

18. 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

19. 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

20. • See I agree Disagree video
https://www.youtube.com/watch?v=CdNn
VaTt7TE

21. 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

22. • See mental agility progression video
https://www.youtube.com/watch?v=PzyC
BM02XkQ

23. 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 open-endedness.
(Knowledge into Action Briefing 1- Differentiated Learning in Numeracy and Mathematics)

24. 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.’

25. Inverclyde Attainment Challenge
Elaine.McLoughlin2@inverclyde .gov.uk
@ACTcoachmodel