In an accompanying study, Alibali et al. [Alibali, M. W., Ockuly, K. M., Fischer, A. D. (2009) "Learning new problem-solving strategies leads to changes in problem representation." "Cognitive Development, 24," 89-101.] present an important experimental result: introducing a new strategy can affect conceptual aspects of children's problem…

Effective teaching should focus on representational change, which is fundamental to learning and education, rather than conceptual change, which involves transformation of theories in science rather than the gradual building of knowledge that occurs in students. This article addresses the question about how to develop more efficient strategies for…

In two parallel one-year studies, solution strategies for subtraction number facts and achievement patterns of matched groups of first graders in two different instructional programs were examined. Significant differences between groups were found favoring the strategy approach. (Author/CW)

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

Based on a two-tiered epistemological model (preliminary physical concepts and emerging mathematical concepts), studied the construction of number among 91 kindergarten students in France, Canada, and the United States. Subjects' cognitive numerical structures were surprisingly similar despite differences in language and culture. (SV)

Student comments about having time in class to think and solve problems are presented. Stressed are teaching methods which allow students to familiarize themselves with the problem, think about solution processes, work through the solution process, and reflect while solving a problem. (CW)

An understanding of fraction addition can be thought to involve two quantitative ideas: (1) the understanding that adding to an original quantity increases its size, and (2) a sense of how much increase occurs. Both of these ideas should underlie or inform a child's approach to problems involving fraction addition and thereby constrain the class…

The author defines and discusses the cognitive theory of constructivism as it relates to teaching mathematics. It is suggested that the philosophical and theoretical view of knowledge and learning embodied in constructivism offers hope that educational processes will be discovered enabling students to acquire deep understanding rather than…

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)

Reported is a naturalistic study of the role of mathematical paradoxes in the preservice education of high school mathematics teachers. Findings indicate that the model of resolving paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive…

The main thesis of the paper is that geometry deals with mental entities (the so-called geometrical figures) which possess simultaneously conceptual and figural characters. The paper analyzes the internal tensions which may arise in figural concepts because of their double nature, developmental aspects, and didactical implications. (Author/MDH)

Presents two cognitive models that illustrate the commonalities between reading for meaning and solving mathematical problems with meaning. Discusses the importance of number sense in the prior knowledge component of the solving with meaning model and the implications of the models in teaching mathematics. (MDH)

Examined is the situation in which pupils invent mathematics on their own and teachers' reactions to this situation. The assimilation of students' original ideas into correct mathematical concepts is discussed. (CW)

Reviews the logic underlying mathematical induction and presents 10 tasks designed to help students develop a conceptual framework for mathematical induction. (Contains 20 references.) (MDH)