Students' development of place value understanding in primary school.

Understanding place value (e.g., how digits represent tens, hundreds, and thousands) is a key foundation for children's later success in mathematics. However, many children struggle to fully grasp how the base-ten system works. Developmental trajectories can inform formative assessment and structure instruction of place value understanding. In this paper, the longitudinal validity of a hierarchical model of typical steps in children's development of place value understanding was challenged. Students' development of place value understanding was assessed during a longitudinal study across one school year (N = 195; 87 girls; Grades 3 and 4) at three measurement time points. Significant gains in place value understanding over the course of 1 year were found at the group and individual level. Individual development was visible in terms of raw scores as well as the level of place value understanding in terms of a development model. Whereas prior knowledge had no effect on the development of place value understanding, intelligence was positively associated with a steeper development. Individual developmental trajectories emphasize the heterogeneity of place value development. The results support the utility of the model as a developmental progression of place value understanding for guiding instruction and assessment.