Considers how students' mathematical thinking evolves as a result of their actions and everyday experiences and from increasing reliance on introduced mathematical principles and representations. Exemplifies how 8- to 10-year-olds' personal representations come to face with representations involving algebraic concepts. Explores implications for…

Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)

Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

Illustrates a modeling approach used by Singapore educators to teach mathematical skills and concepts in a problem-solving environment. (Contains 11 references.) (YDS)

Describes how students can be guided to find an explicit rule for a pattern from a recursive rule. (YDS)

Presents action research in the classroom that involves a semantic feature analysis task to help students develop reasoning skills. (YDS)

Helps students develop new insights into mathematical relationships through alternative representations. Examines patterns, symbolic, and functions approaches. (Contains 11 references.) (YDS)

Investigates problems called "cranium crackers" and focuses on number sense, logical reasoning, data analysis, geometry, measurement, and algebraic thinking. (Author/NB)

Investigates ways to analyze change in various contexts. Focuses on computer technology providing contexts for children's investigations of patterns of change and helping to develop foundational ideas of algebra and calculus. Discusses relationships between patterns of change, fundamental algebraic notions as linear and nonlinear functions, and…

Presents a discovery lesson in which students investigate the limit of angle measures formed by repeatedly folding a strip of paper. (KHR)

Situations for which the researcher should use component analysis versus common factor analysis are discussed. Topics addressed include key algebraic similarities and differences, theoretical and practical issues, the factor indeterminacy issue, latent versus manifest variables, and differences between exploratory and confirmatory analysis…

Presents an example of a mathematical question to illustrate an approach to simultaneous equations. Provides an example with diagrammatic and numerical representations. Suggests some possible developments. (YP)

Presents an approach to Vieta's formula involving pi and infinite product expansions of the sine and cosine functions. Indicates how the formula could be used in computing approximations of pi. (MVL)

Presents a theory of the development of algebraic abstraction that extends Sfard's and Mason's ideas on learners' progress from operational or process-oriented thinking to the abstract or structural perspective. Analyzes secondary school students' approaches to classifying a set of complex equations. (Author/MKR)

Twelve adolescents with learning disabilities were trained to use a cognitive strategy in algebra problem solving. The two-phase strategy (problem representation and problem solution) was effective in improving algebra performance on algebra word problems, and maintenance and transfer of the strategy were evident. (JDD)