Discusses the process of mathematical iteration, its benefits as a problem-solving technique, and how to teach it. Presents a selection of mathematical ideas and problems that can be solved and explored using iteration, along with related BASIC computer programs. (MDH)

Twenty-four sixth-grade children participated in clinical interviews on ratio and proportion before receiving instruction in the domain. Student thinking was analyzed in terms of mathematical components critical to proportional reasoning. Two components, relative thinking and unitizing, were consistently related to higher levels of sophistication…

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…

Provided are three program listings which may be used to illustrate this fractal figure. Extensions of these algorithms and their use in the study of chaos and fractals are suggested. (CW)

Presented is an activity designed to develop a concrete linear model to assist students in estimating answers to percentage problems and developing an understanding of the concept of percentage. (CW)

This article explores the multiple representations (verbal, algebraic, graphical, and numerical) that can be used to study the golden ratio. Emphasis is placed on using technology (both calculators and computers) to investigate the algebraic, graphical, and numerical representations. (JAF)

Analyzed questionnaire responses of 152 prospective secondary mathematics teachers, 10 of whom were interviewed, to investigate their knowledge of the concept of function. Results indicated that many did not have a modern concept of function, a limitation that influenced their pedagogical approach. (Contains 45 references.) (MDH)

Describes how one second-grade teacher opened the way to an understanding of mathematical concepts for her students by opening some favorite children's books. Four specific titles along with the mathematical skills they focus on and suggested teaching ideas are presented. Additional resources are included for each title. (BB)

Presents a methodology of mathematical and technological principles as integrated components of the Design and Technology syllabus of the National Curriculum in the United Kingdom. The methodology is based on the syllabus area of product analysis and employs a structured problem-solving approach. (ASK)

Researching mathematicians is a way for students to gain an understanding of mathematical concepts applied in class. This article outlines an eight-day collaborative project in which librarians and math teachers guide eighth graders in researching and creating multimedia presentations on mathematicians. Lists selected Web resources, including one…

Explores the strategies used by prospective secondary mathematics teachers (N=13) to develop and validate functions as mathematical models of real-world situations. Uses a grounded hypothesis on strategy selection. Concludes that strategy choice was influenced by task characteristics and interactions with other student modelers. Contains 38…

Describes an action research project conducted in eighth-grade algebra and prealgebra classes. Suggests ways in which students can use their creativity to progress from a simple solution method to a method that produces a generalization and a formula. (AIM)

Discusses mathematical thinking and problems posed by seventh- grade students as part of a unit on the study of algebraic ideas. The unit involves showing how variables cause changes and also incorporates the solving of systems of equations by constructing line-graph drawings and combination charts. (AIM)

Analyzes the construction of mathematical concepts and techniques developed by high school algebra students in computer-assisted instruction; examines learning styles of the most inventive students; and discusses the use of student-generated mathematical techniques in the development of new software intended to cultivate mathematical inventiveness…