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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)

  • Unitising 

  • Equality/equivalence

  • Moving from cumbersome strategies to automatic recall of number facts

  • The field axioms (laws of arithmetic)

  • Multiple answers/possibilities

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

  • The Cartesian plane

  • Ordinality

  • Infinity within and on a number line

  • Negative as a reflection of positive

  • Standardised units for measurement

  • Place value (particularly mid-primary/elementary)

  • Fractions/Decimals

  • Mixed numbers and Improper fractions

  • Regrouping

  • Equivalent fractions

  • Decimals/Fractions/Percentages (the relationship)

  • Ratio

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