Learning progression toward a measurement concept of fractions

International Journal of STEM Education

Table 1 Description of mental actions

Mental action	Description
Partitioning	Projection of a composite unit into a continuous whole to create equally sized parts within the whole^a
Iterating	Repeating a unit of length or area to produce a connected whole^a
Disembedding	Taking parts out of a whole as separate units while maintaining their relationship with the whole
Splitting	Simultaneous composition of partitioning and iterating, as inverse actions
Units coordination	Maintaining relationships between the various levels of units within a mathematical experience; involves coordinating simpler actions, such as partitioning, iterating, and disembedding

^aA whole unit can be continuous or discrete, but the discussion in this article focuses on a continuous whole. Also note that splitting and units coordination, as coordinations of other mental actions, are more advanced and separated in the table