The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

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…

A study documented 10 college students' understanding of the limit concept and the factors affecting changes in that understanding. Encouragement by the researchers for the students to change their common informal models of limit to more formal conceptions were met with extreme resistance. (Author/JJK)

Investigated was the learning of the mathematical uses of "more,""fewer," and "less" at a very early stage in the development of ideas. (CW)

Reports a study which identified different problem-solving strategies among Hong Kong high school chemistry students. Finds that student experts employed a recognition plus a working forwards strategy, whereas student novices attempted a means-end analysis to create a solution procedure. Comparisons were made with problem-solving in physics. (GG)

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)

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…

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…

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)

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

Argues that the dichotomy between domain-specific and general theories of cognitive development addressed in the "Merrill-Palmer Quarterly" special issue is unproductive. Suggests that polarities of generality and specificity exist in creative tension as seen through developmental processes. (Author/BB)

Identified is research related to concept formation; the chronology of identity and equivalence conservations; the relationship of mental age to performance on number concept tasks; perceptual, attentional, linguistic, and social factors; and the potential use of cognitive developmental criteria as measures of ability for both normal and retarded…

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)

Described are inconsistencies, definitions, and examples and their complex relationship which can be used to interpret students' reactions to the geometric tasks used to investigate inconsistencies in student thinking. Discusses the nature of definitions, the value of precise vocabulary, the use and limitations of prototypes, and the power of…

After observing secondary school students having great difficulty learning geometry in their classes, Dutch educators Pierre van Hiele and Dina van Hiele-Geldof developed a theoretical model involving five levels of thought development in geometry. It is the purpose of this monograph to present English translations of some significant works of the…