The Cognitive Acceleration (or Let's Think) approach to mathematics teaching is a Piagetian programme drawing on Vygotsky's research, developed at King's College London over 30 years ago, along with its associated professional development (PD) programme. This project sought to replicate the original studies conducted 10-15 years earlier and before…

This paper focuses specifically on the reasoning skill called proportional reasoning. Areas addressed include: (1) a definition (providing examples of direct and indirect proportional reasoning); (2) the development of proportional reasoning (discussing survey results of students logical reasoning abilities); (3) planning for the future (proposing…

The purpose of this paper is to review the relevant evidence concerning the relationship between knowledge and its effect on learning, with an end to answering the questions: (1) How important is knowledge to learning? and (2) How does the relative importance of knowledge change with development? The paper is divided into three main sections:…

The contribution of decentration as an underlying component of discrimination learning and discrimination shift behavior was investigated in this study. In addition, the effect of verbal labeling and the relationship of academic achievement to discrimination learning and decentration was considered. The subjects were 120 first grade students who…

Attempts to express a group of children's understanding of inversion, retrograde, and retrograde-inversion as it applies to musical composition and color schemes. The children, ages six to nine, displayed idiosyncratic approaches to the problems. Discusses the possible implications for symbolic language and cognitive development. (MJP)

Defines M-demand as the maximum number of schemes that the subject must activate simultaneously in the course of executing a task. Discusses the effect of M-demand on problem solving. Uses algorithms to reduce M-demand. Describes the role of algorithms in problem solving. (MVL)

This book is a collection of essays forming a mosaic of theory, research, and practice directed at the task of spreading mathematical knowledge based on the learning theory of constructivism. The authors collectively address questions raised by the observation that current practice frequently generate in the student an aversion to mathematics.…

The Threshold Project focuses on the language and learning difficulties that children in Southern African schools experience when they change from their mother tongue to English as a medium of instruction in their fifth year of schooling. This report discusses Threshold Project research relating to the nature of pupils' cognitive capacities and…

The teaching of critical thinking is discussed, based on the view that methods of teaching critical thinking vary from discipline to discipline. After covering basic concepts related to teaching critical thinking, a framework to examine the process of critical thinking is presented, based on cognitive science and developmental theory, especially…