Over half a century has passed since Bruner suggested his three-stage enactive-iconic-symbolic model of instruction. In more recent research, predominantly in educational psychology, Bruner's model has been reformulated into the theory of instruction known as concreteness fading (CF). In a recent constructivist teaching experiment investigating…

There is growing interest in implementing reform-based lab courses in undergraduate physics that are student driven rather than instructor driven. In these courses, students develop and carry out experiments while simultaneously reasoning about their hypotheses, data collection procedures, collected evidence, and the relevant physics content.…

The authors point to systemic-theoretical instruction (STI), which underscores the importance of abstract conceptual knowledge in schooling, and dynamic assessment (DA), in which mediators and learners function cooperatively, as examples of the theory-practice relation envisioned by Vygotsky (1987). This article proposes an interactional framework…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

Problem Statement: The interest in raising levels of achievement in math and science has led to a focus on investigating the factors that shape achievement in these subjects. Understanding how different learning styles might influence science achievement may guide educators in their efforts to raise achievement. This study is an attempt to examine…

Based on an M.A. thesis (Snow) submitted to McGill University.

Proposes a model of mathematics conceptual development consisting of two phases: abstraction and generalization. Illustrates model by references to the development of multiplication and angle concepts. (19 references) (MKR)

One of the most typical ways in which people learn is by inferring general rules from examples. In recent years, significant progress has been made toward understanding how learning from examples can occur, determining when it does occur, and identifying conditions that promote it. This paper reviews these results and then suggests a program of…

Examples are given illustrating a facet of early learning involving insights into abstract thinking. Several learning theories examined fail to account for this phenomenon. (MP)

Analyzes the meaning of Piaget's concept of abstraction and provides discussion of some of its shortcomings. (HM)

Induction refers to categorizing sensory experience and substitution to interchanging similar objects. If similar items are functionally identical and near the focus of attention at nearly the same time, similarity impedes learning (interference). If either condition is not fulfilled, similarity aids learning (transfer). (DD)

A colliding spheres type of experiment is used with several hundred 4-12 grade students to test for knowledge of the concept of controlling variables. Results support the contention that the concept is developed gradually during the concept stage but not fully attained until around 14 years of age. (CP)

This paper analyzes common practice and the difficulties children encounter and outlines an entre to mathematics learning which may make the child's task easier. (Author)

This study considers two problems related to cognitive development: "Is development hierarchical?" and "If so, what are the mechanisms involved in the process of development?" Analysis of the results of an experiment lead to differentiation of stages of development, and problem-solving strategies at each level are discussed.…

From a review of the literature on modeling processes, observational learning, social learning theory, and vicarious concept learning by young children, the author draws guidelines for the teaching of abstractions to preschoolers. (SJL)