Teachers should develop detailed knowledge of the curriculum in order to break the mathematics down into small steps to develop mastery and address all aspects in a logical progression.
Small connected steps are easier to take than big steps
Having instant recall of number bonds to ten and within ten and being able to apply these to multiples (eg 40 + 20 = 60 and bridging ten 8 + 5 = 8 + 2 + 3 = 13 is crucial for mastery of the curriculum.
Learn the facts so that the mind is freed up to think about concepts.
Procedural Variation – calculations are connected and pupils use the relationships to find easy ways of calculating.
Conceptual Variation – representing the same concepts in different ways to draw out essential features and form a fluent and deep understanding of the concept.
Making connections between the different representations is important.
CPA all 3 are developed together – moving with fluency between the concrete and abstract.
Children and teachers need to think mathematically. This means to:
look for pattern,
and reason about relationships.
Representation and Structure
Teachers provide access to the mathematics through carefully selected representations.
Pupils represent concepts in different ways to demonstrate fluency and depth of understanding
Representations expose mathematical structure which encourages children to work systematically
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