We provide evidence of validity for a newly developed diagnostic competence model of operation sense, by both (a) describing the theoretically substantiated development of the competence model in close association with its use within a large-scale formative assessment and (b) providing empirical evidence for the theoretically described cognitive…

EARLY FORMS OF NUMERICAL REASONING WERE INVESTIGATED BY EXAMINING THE ROLE OF A SET OF VARIABLES IN THE DEVELOPMENT OF CONSERVATION OF NUMBER. CONSERVATION OF NUMBER WAS DEFINED AS THE RECOGNITION THAT THE NUMBER OF OBJECTS CONSTITUTES AN AGGREGATE WHICH IS NOT CHANGED MERELY BY REARRANGING THEM. EXPERIMENT ONE WAS CONDUCTED WITH CHILDREN FROM…

Children completed three types of equivalent cardination tasks which assessed the influence of different stimulus configurations (linear, linear-nonlinear, and nonlinear), and density of object spacing. Prior results reported by Siegel, Brainerd, and Gelman and Gallistel were not replicated. Implications for understanding cardination concept…

Presents results of 46 randomly selected children's performance measurement and partitive division problems when remainders are zero, nonzero but not used in the solution, and nonzero and used in the solution. Results indicate that children demonstrate an understanding of division prior to formal instruction. (MDH)