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…

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…

The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…

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)

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Some potential difficulties involved in using "real-life situations" in teaching problem solving are illustrated with a racing car problem. The importance of developing mental images and the ability to abstract in the solution process is indicated. (MP)

This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is…

Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)

This document is the second of three related volumes. They present the rationale, background, and framework for a comprehensive monitoring system being developed for the National Science Foundation. The system is being designed to gather information about the effects of national, state, and local policy actions designed to change the teaching and…

Illinois Central College's Development of Operational Reasoning Skills (DOORS) project, which is based on Piaget's developmental theory and learning cycle strategy, is described. The project provides a multidisciplinary freshman core program focusing on the improvement of student reasoning abilities. For each of the six DOORS courses--English,…