Presents a refined form of a personal theory of learning that examines two distinct parts of the complex interaction between a learner's internal mental structures and his or her world of experience. (Author/MKR)

Via computational media, humans are entering a fifth stage of cognitive development leading to a virtual culture. This culture is seen as replacing the writing-based theoretic culture. Background information about the first four stages of mental evolution or cognitive development is provided. It is suggested that the evolutionary perspective needs…

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

Examines the nature of prior mathematical knowledge that facilitates the construction of useful problem representations in the domain of geometry. Indicates that high achievers build schemas that are qualitatively more sophisticated than low achievers, which in turn helps them construct representations that are conducive to understanding the…

This essay is based on observation and interpretation of the mathematical language of children while they engage in situations involving fractional numbers. This interpretation includes the consideration of various levels of language use, informal metamorphic and metonymic uses of fractional number language, and the interplay between language use…

Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…

This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

Presents background information about Vygotskian theories. Describes Vygotsky's Zone of Proximal Development (ZPD). Discusses a model of attitude development that incorporates the ZPD, meta-awareness, the components of an attitude, and factors influencing attitude development. Suggests educational implications. (45 references) (MDH)

Proposes a model for the growth of mathematical understanding based on the consideration of understanding as a whole, dynamic, leveled but nonlinear process. Illustrates the model using the concept of fractions. How to map the growth of understanding is explained in detail. (Contains 26 references.) (MKR)

This paper suggests that the systems of representations that we use in mathematics have a cultural origin and concludes that the knowledge produced with the help of these systems of representation likewise has a cultural origin. This assertion forces a reformulation of the issue of objectivity in terms that differ from those inherited from…

This yearbook contains essays that examine the construction of knowledge. The 10 articles, which are called "opinions," are divided into 5 sections, most of which examine the construction of scientific knowledge. An editor's introduction begins each section. Section 1, "Constructivism as an Epistemology and Philosophy of…

This paper explores the nature of content and language across the curriculum in relation to the Targets and Target-Related Assessment (TTRA) initiative. The TTRA is an assessment initiative designed to improve the quality of individual learning from Primary 1 to Secondary 5 in Chinese, English, and Mathematics in Hong Kong. A picture of content…

Reviews recent research in the area of mathematical understanding and compares and contrasts it with a model formulated for the growth of understanding. Uses the analysis of a transcript from an interview with an eight-year-old boy to illustrate the power of the model to describe and map the growth of his mathematical understanding. (18…

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

Distinguishes educational constructivism, which has its origins in the theories of children's learning, from constructivism in the philosophy of science and from constructivism in the sociology of science. Notes the evolution of educational constructivism and identifies some theoretical problems concerning constructivist teaching of science…