Mental computation is a window to students' understanding of important mathematical ideas, particularly in number and algebra.
The following are the key ideas that underpin fluent and flexible calculation strategies.
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Counting
Meaningful counting requires understanding of important principles, including cardinality.
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Place value
The understanding of place value progresses from a way to abbreviate counting initially, to a multiplicative system based on powers of ten.
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Reliance on counting then adding and subtracting
Increased sophistication with number operations means moving from counting to additive thinking to multiplicative thinking.
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Division as sharing and measuring
Students need to understand that division can be viewed as two actions – sharing and measuring – and that the numbers in the same division equation can involve different types of units.
