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)
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)
Infinity within and on a number line
Negative as a reflection of positive
Standardised units for measurement
Place value (particularly mid-primary/elementary)
Mixed numbers and Improper fractions
Decimals/Fractions/Percentages (the relationship)