| Abstract: | Examined replacement of simple rules by more complex variants in situations where 485 3–8.5 yr old children were confronted with tasks differing in rule application requirements. It was hypothesized that counting with and without objects would be equivalent tasks, that counting all would be subordinate to counting on, that counting on would be subordinate to counting down, and that counting on and counting down would be subordinate to counting by multiples. The restrictive knowledge perspective was compared to models congruent with the transition perspective assuming the existence of partial knowledge states. Latent-class models were used to test equivalence and ordered relations among the tasks. The results provide evidence that the development of counting skills is an evolving process in which parts of a relatively simple rule are replaced by features that enable the child to perform an increasingly broad range of counting tasks. The results also suggest that rule replacement in counting plays an important role in the development of other math skills. Support was also found for the restrictive knowledge perspective, lending credence to the stair-step learning theory. (26 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved) |
