The evolution of concept mapping has benefitted from the robust theoretical basis provided by Ausubelian learning theory. However, for concept mapping to maintain its relevance and to keep pace with the evolutionary changes in the educational context, it is vital that educational researchers and classroom practitioners can augment this theoretical…

The purpose of this thesis is to improve our understanding of sensemaking process as a basis for building better systems to assist sensemaking. Sensemaking is the task of creating an understanding of a problem or task so that further actions may be taken in an informed manner. Sensemaking is a pre-requisite for many other tasks such as decision…

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)

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…

As biological and socio-cultural beings, humans are encouraged and aspire to "see" not only what comes "within sight," but also what is not possible to see. Visualization is described as offering a method of seeing the unseen. These ideas are organized into sections that focus on seeing the unseen in data, seeing the unseen in…

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…

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…

Describes six divergent forms of constructivism in providing an overview of constructivist theory. Suggests a scheme for characterizing constructivist writing on the basis of its relative emphasis on personal versus social construction of knowledge, and objectivist versus relativist views of the nature of science. Contains 31 references. (DDR)

Argues that some forms of constructivism propose an epistemological idealism with a concomitant relativism, while other forms are explicitly opposed to such positions. Explains that all forms of constructivism are often presented as being relativistic. Contains 31 references. (DDR)

Examines central parts from the first two papers in this journal by Peter Slezak criticizing the "sociology of scientific knowledge". Considers some of the main philosophical issues raised by sociologists of science. Contains 87 references. (DDR)

This paper focuses on some main distinctions that are necessary to analyze mathematical knowledge from a learning point of view and explain how many students come up against difficulties at each level of the curriculum. From a learning point of view, visualization cannot be used as an immediate and obvious support for understanding, even though it…

Constructs the philosophical background and underpinnings of the Science Education Portfolio Instruction and Assessment (SEPIA) project. Explains that students must develop skills in order to participate in epistemic interchanges. They must also be provided opportunities and materials to develop those skills. Contains 29 references. (DDR)

Distinguishes between psychological constructivist and social constructivist groups. Explains the reasons for the growing acrimony in debates between the two groups. Discusses social constructivist accounts of the causes of belief in science. Contains 43 references. (DDR)

Presents three studies that demonstrate the efficiency of the kinesthetic conflict in promoting the understanding of three scientific concepts among children aged 5-12. Results support Piaget's theory which determines the origins of scientific thinking. Contains 26 references. (DDR)

Interest in mathematics learning that focuses on understanding, mathematical reasoning, and meaning-making underscores the need to develop ways of analyzing classrooms that foster certain types of learning. The goal of this paper is to show that the constructs of social and sociomathematical norms, which grew out of taking a symbolic…