Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

Previous research has shown that sequences in which instances from the same category appear successively facilitate performance in concept attainment. This could be due to subjects adopting strategies which involve comparisons of instances from within the same category. However, if subjects were to adopt a strategy involving comparisons of…

Nine students (ages 7 to 11) with math disabilities were effectively taught using an instructional sequence that moved from the concrete to the semiconcrete to the abstract. Subjects needed between three and seven lessons using manipulative devices and pictures before being able to do abstract-level problems. (Author/DB)

The criterion problem in the neoPiagetian cognitive-developmental literature is reviewed. This problem has provoked debate in the context of three empirical questions: concept age norms, concept training effects, and concept invariant sequences. It is argued that only the question of invaniant sequences in same-stage concepts is theoretically…

Defines five levels between concrete and formal operation in the development of the concept of controlling variables. The sample, methodology and research on which the work is based is described in SE 519 500. (CP)

This study tested certain implied predictions regarding conceptual learning at each of four sequential levels of development: concrete level, identity level, classificatory level, and formal level. For this purpose, scaled batteries to assess the level of conceptual development of children, kindergarten through high school, were constructed and a…

This article presents the "concrete semiconcrete abstract" (CSA) teaching sequence for teaching basic math skills to students with and without learning disabilities. Guidelines include providing a minimum of nine instructional lessons (three at each level), each with four lesson steps. Validation of the CSA sequence and lesson format with 15…

Research conducted at the Institute of General and Pedagogical Psychology of Moscow, and based on the premise that the development of thought processes is a direct product of the social environment, is described. As a corollary to this premise, Piaget's view that the development of the thinking process occurs in orderly fashion is questioned.…

The major results and conclusions of a program of research concerned primarily with the relationship of cognitive abilities to learning are summarized. The major purpose of this research was to develop theorems of instruction related to the interaction of task variables and individual difference variables and to develop them in a manner relevant…