| dc.description.abstract | The focus of this longitudinal case study was to investigate the progressive development
of unitizing in a cohort of students receiving reform-oriented mathematics instruction.
One-on-one videotaped mathematics interviews were conducted twice annually for 4
years from Grade 1 to Grade 4 with a varying number of participants from 61 to 45
respectively. Multiplication and quotative division questions were analyzed for
correctness, the physical model used to solve the problem, and the computation strategy
used to solve the problem. Multiplication and adding up for division models that required
the development of more sophisticated unitizing included modelling only one group,
modelling just the groups, modelling the groups with the composite numeral, and
modelling the new whole. Multiplication and adding up for division strategies that
indicated the development of a unitizing structure included rhythmic counting, starting
with a doublet, skip counting, regrouping to form a new composite, and splitting the
composite and then iterating the sub-composites to find the total. The varying levels of
simultaneity demonstrated by students were also noted as they pertain to the development
of a unitizing structure. A theoretical landscape of the development unitizing is proposed. | en_US |
