Replacement and component rules in hierarchically ordered mathematics rule learning tasks.

Abstract

This investigation examined ordered and equivalence relations among hierarchically arranged fraction identification tasks. The study investigated whether hierarchical ordering among fraction identification problems reflects the replacement of simple rules by complex rules. A total of 456 middle-class second-, third-, and fourth-grade children were asked to identify fractional parts of sets of objects. Latent class techniques revealed that children applied rules that were adequate for simple problems but had to be replaced to solve more complex problems.

Prerequisite relations among inference tasks for good and poor readers.

“…Finally, reading comprehension processes are not directly observable, and optimal assessment remains a challenge. Recent work by Bergan, Towstopiat, Cancelli, & Karp, (1982); Bourque (1980); Garner, Macready, &Wagoner (1984), andHaertel (1984) have demonstrated that latent class modeling procedures provide a relatively new and useful framework from which to address issues related to order of trait acquisition. These modeling approaches are particularly viable because computer programs are now available for such analyses (Clogg, 1977;.…”

Rule replacement in the development of basic number skills.

“…The latent-class models relate to a domain structure model described by Bergan and Stone (1981). Within this model, domains, each of which is assumed to consist of well-defined classes of tasks, are ordered hierarchically.…”

“…The occurrence of prerequisiteness does not guarantee this state of affairs. The prerequisiteness criterion for two tasks can be met when tasks are identical (Bergan et al, 1982). The tasks would presumably not be identical if it were possible to perform one without also being able to perform the other.…”