Research in the psychology of mathematics education has been confronted with the fact that people blatantly fail to solve tasks they are supposed to be able to solve correctly given their available domain-specific knowledge and skills. Also researchers in cognitive psychology have encountered such phenomena. In this paper, theories that have been…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…

This series of four studies investigated the abilities of children in grades five through eight to perform on a reasoning test written in both Ikonic and Symbolic form. An abstract reasoning test which had been shown to be highly correlated with success in mathematics was rewritten into Ikonic form. Children whose ages bridge the gap between the…

Over recent years, various theories have arisen to explain and predict cognitive development in mathematics education. We focus on an underlying theme that recurs throughout such theories: a fundamental cycle of growth in the learning of specific concepts, which we frame within broader global theories of individual cognitive growth. Our purpose is…

Piaget's constructs of concrete-operational and formal-operational stages are illustrated by quoting comments from Piaget and Inhelder (1958), summarizing the kinds of reasoning to be expected at each substage, and relating this reasoning to specific mathematical items. (DT)

The authors challenge some of the conclusions reached about Piaget by Brian Rotman in his book. (MK)

Examples of topics and problems which demand Piaget's formal operational thought at an early stage in the secondary school are provided. (DT)

Mathematics education is viewed as a process imbedded in social interaction. Alternatives to seven widely recognized modeling perspectives that provide conceptual foundations for mathematics learning are discussed. (MP)

A case for theoretical development of advance organizers that aid in the learning and transmission of knowledge is presented. (MP)

Examines some aspects of mathematical cognition at the highest level of formal functioning. Illustrates how the structure of a mathematician's output and its cognitive complexity can be characterized by the Structure of the Observed Learning Outcome (SOLO) taxonomy. Contains 28 references. (Author/ASK)

The ability of students in grades 1-12 to generate proofs of theorems in an unfamiliar, one axiom, abstract system was investigated. There were no significant differences in performance of two levels of secondary students; fourth- through sixth-grade students were also able to develop proofs, but needed more time. (SD)

The purpose was to determine whether different levels of education, race, and sex affect the degree of conservation of mass, weight, and volume attained by minimally educated adults. Subjects were 30 white and 30 black females and 30 white and 30 black males enrolled in Adult Basic Education classes, with 40 subjects each at grade levels 0-3, 4-6,…

Fifteen kindergarten children, who began the study with Piaget's stage II seriation capabilities (they could serial order sticks but could not insert a number of sticks into an already ordered set), were individually given 30 minutes of seriation training on three consecutive days. Cue fading and the manipulation of discrimination levels were used…