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# THRESHOLD CONCEPTS

## In "Thinking Deeply about Primary Mathematics" we explore threshold concepts in the primary mathematics classroom. With a hierarchical subject such as mathematics it is extremely difficult to pin down precise threshold concepts, which is why I was reticent to commit a list to print. Instead, what follows is a fluid list comprised of those concepts and ideas which our pupils will find particularly difficult to navigate and which will demand some serious consideration on our part.

## The principles of counting (stable order, 1:1 correspondence, cardinality, order irrelevance, abstract principle)

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## Unitising

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## Equality/equivalence

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## Moving from cumbersome strategies to automatic recall of number facts

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## The field axioms (laws of arithmetic)

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## Multiple answers/possibilities

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## Abstract symbols can represent a multitude of underlying structures (aggregation, augmentation, additive comparison)

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## The Cartesian plane

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## Ordinality

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## Infinity within and on a number line

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## Negative as a reflection of positive

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## Standardised units for measurement

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## Place value (particularly mid-primary/elementary)

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## Fractions/Decimals

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## Mixed numbers and Improper fractions

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## Regrouping

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## Equivalent fractions

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## Decimals/Fractions/Percentages (the relationship)

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## Ratio

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