Rule replacement in the development of basic number skills.

Abstract

Four hundred and eighty-five 3-to SVa-year-old children participated in a study to examine the development of rudimentary numerical skills. Replacement of simple rules by more complex variants was examined in situations where the individual was confronted with tasks differing in rule application requirements. Hypotheses were generated to reflect the assumption of hierarchical ordering associated with rule replacement. In addition, restrictive knowledge and variable knowledge perspectives were evaluated. Latent-class models were used to test equivalence and ordered relations among the tasks. The results provided 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 suggested that rule replacement in counting plays an important role in the development of other math skills. The results also give support for the restrictive knowledge perspective, lending credence to the stair-step learning theory.

Prerequisite relations among inference tasks for good and poor readers.

“…Results from the preliminary analysis of item equivalency within item types revealed that for each inference item type, individuals could be classified as either Acquirers or Non-acquirers of the trait. This is consistent with Haertel's (1984) findings of “homogeneous” multiple-choice inference items, and it suggests that views of “partial acquisition” (see Bergan, Stone, & Field, 1984) may not be tenable for inference production skill.…”

Latent class models for knowledge domains.

“…This state would be followed by a second transition leading to mastery of both skills. Bergan and his colleagues developed models that reflect this possibility (Bergan, 1983; Bergan, Stone, & Feld, 1984). In the case of two hierarchically ordered skills, these models include five latent classes: a nonmastery class, a transition class involving inconsistent performance on the subordinate task accompanied by nonmastery of the superordinate task, a class involving mastery of the subordinate task and nonmastery of the superordinate task, a second transition class characterized by mastery of the subordinate task and inconsistent performance on the superordinate task, and finally a class involving mastery of both tasks.…”