Table 1 Summary of key stages investigated
Stage | Key characteristics | Possible indicators | |
|---|---|---|---|
INS | • Numerical thinking • Use of numerical composites | • Counting on • Reliance on figurative material to keep track of composite quantities | |
TNS | eTNS | Construction of composite units during problem-solving activity | • Constrained to equi-segmenting operations when partitioning • Need to construct composite units in new problem situation before they can be used |
aTNS | Anticipatory use of composite units | • Simultaneous partitioning operations • Ability to mentally work with composite units • Difficulty keeping track of multiple quantities in a problem situation | |
ENS | • Construction of iterable units of 1 • (Reversible) disembedding • Coordinating three levels of units in activity | • Equi-partitioning operations • Construction of fractional schemes • Ability to relate multiple levels of units mentally | |