Mastery in Maths
Mastery is an approach where all children can achieve at a
high standard in mathematics. It is a teaching and learning approach: challenge
is provided by going deeper rather than accelerating in to new content. It
means being able to use knowledge appropriately, flexibly and creatively and to
apply it in new and unfamiliar situations, through problem solving, questioning
and deep mathematical thinking. It is important that children have the time and
opportunity to master facts, procedures and concepts in mathematics. As a
result, teachers will prioritise areas of weakness through their teaching and
target time appropriately. Mastery of mathematics is not a fixed state, but a
continuum where children are always striving towards something new. It is built
continually throughout school and is a valuable tool for life.
Features of a Mastery Curriculum
Curriculum Design

Longer units of work, prioritising key topics

Lesson Design

Carefully structured lesson (vary where appropriate) to develop detail
and depth in concepts, knowledge, skills and application

Pupil Support

Quick Intervention – picking up and addressing misconceptions

Teaching Resources

Carefully chosen examples and activities; varying resources – right
resources for the right job (models and images)

Teaching Methods (differentiation)

Keeping the class together; teaching the same topic and aiming for
depth of understanding through questioning

Practice

Practice where needed; appropriate consolidation

How it is Taught
·
Effective questioning – for deep thinking and
for enquiry
·
Practice and rehearsal of key skills and
knowledge
·
Exploring contexts beyond the maths lesson (real
life contexts or cross curricular links)
Levels of Teaching/Questioning
·
Instructional (use of models/images, key
vocabulary, demonstration teaching)
·
Qualifying (applying knowledge, making choices)
·
Deep/Challenge (different contexts, levels of
challenge, reasoning)
Expectations
·
All/Most children will achieve at least ARE
·
Deep structural knowledge (LINKS TO FLUENCY IN
NUMBER)
·
Examples to make connections between topics
·
Keeping the class together (teaching the same
content)
·
Using longer time for key topics
Key Threads
1)
Arithmetic (LINKS TO FLUENCY AND UNDERSTANDING
OF NUMBER CONCEPTS – AIM 1)
·
Concepts and skills for efficient calculation
·
Understanding – properties and manipulation of
numbers
·
Rules and laws of arithmetic
2)
Algebra (LINKS TO PROBLEM SOLVING AND REASONING
– AIMS 2 AND 3)
·
Missing numbers/number boxes
·
Number balances  equality
·
Using letters to represent numbers
·
Solving equations – linking to problem solving
Reasoning
Reasoning is a key aim of the New Mathematics Curriculum. It
is not only important in its own right, but impacts on the other two aims. For
example, reasoning about known facts to work out what is unknown will improve
fluency. The ability to reason also supports application to new contexts and
solving problems. Reasoning is an important factor in a pupil’s success in
mathematics: it supports deep and sustainable learning and allows connections
between topics and areas to be made.
Strategies
·
Spot the
mistake / Which is correct?
·
True or
false?
·
What comes
next?
·
Do, then
explain
·
Make up an
example / Write more statements / Create a question / Another and another
·
Possible
answers / Other possibilities
·
What do
you notice?
·
Continue
the pattern
·
Missing
numbers / Missing symbols / Missing information/Connected calculations
·
Working
backwards / Use the inverse / Undoing / Unpicking
·
Hard and
easy questions
·
What else
do you know? / Use a fact
·
Fact
families
·
Convince
me / Prove it / Generalising / Explain thinking
·
Make an
estimate / Size of an answer
·
Always,
sometimes, never
·
Making
links / Application
·
Can you
find?
·
What’s the
same, what’s different?
·
Odd one
out
·
Complete
the pattern / Continue the pattern
·
Another
and another
·
Ordering
·
Testing
conditions
·
The answer
is…
·
Visualising
Progression in Reasoning
Supporting Materials
Links with calculation policy (DEVELOP FLUENCY)
·
Develop
children’s fluency with basic number facts
·
Develop
children’s fluency in mental calculation
·
Develop
children’s fluency in the use of written methods
·
Develop
children’s understanding of the = symbol
·
Teach
inequality alongside teaching equality
·
Don’t
count, calculate
·
Look for
pattern and make connections
·
Use
intelligent practice
·
Use empty
box problems
·
Expose
mathematical structure and work systematically
·
Move
between the concrete and the abstract
·
Contextualise
the mathematics
·
Use
questioning to develop mathematical
·
Expect
children to use correct mathematical terminology and speak in full sentences
·
Identify
difficult points