Each child at Magill School is immersed in the conceptual framework called The Big Ideas in Number which supports development of understanding in number from early to advanced concepts.
Number sense relates to all Australian Curriculum: Mathematics strands through counting, magnitude and order. It allows students to deeply understand numbers by: having a sense of what numbers mean, understanding their relationship to one another, performing mental mathematics, and understanding symbolic representations using numbers in real situations.
Number underpins the numeracy general capability. It’s used across learning areas and in our everyday personal and professional activities. Number sense includes knowing the principles of counting and that: subitising tells us how many, an arrangement of a collection won’t change, and that the quantity of different arrangements are useful in solving problems. Number sense includes thinking and questioning the ways numbers are used in different contexts. It allows students to create mental objects that can be manipulated flexibly with understanding and confidence.
‘Just as our understanding of phonemic awareness has revolutionised the teaching of beginning reading, the influence of number sense on early maths development and more complex mathematical thinking carries implications for instruction’ (Gersten and Chard 1999).
The Big ideas in Number tools and advice outlines the 6 Big Ideas that develop a strong number sense.
‘For students to become numerate, concepts need to be experienced, strategies need to be scaffolded, and everything needs to be discussed for them to learn with understanding.’ (Siemon 2009 (PDF 186.6KB))
Di Siemon, Chief Academic responsible for The Big Ideas in Number framework, suggests that the concepts of ‘trusting the count’, ‘place value’, ‘multiplicative thinking’, ‘partitioning’, ‘proportional reasoning’, and ‘generalising’ are the checkpoints in number sense each student is required to pass through before progressing further in mathematics.
The Department for Education SA has released ‘Best Advice’ papers in mathematics aimed to assist educators in accurately teaching conceptual stages to students. The Big Ideas in Number supports conceptual thinking in the following way:
Building Belief: All Year Levels
Building Powerful Mathematicians: All Year Levels
Understanding Number and Algebra: All Year Levels