The interpretations by first graders of mathematics illustrations designed to teach relationships between sets are reviewed. (MP)

Ways of using calculators to presents the concept and methodology of concurrent processing are discussed. Several problems that could be used to compare sequential versus concurrent processing are presented. (MK)

The computational difficulty of the word problem sections of eight standardized achievement tests was analyzed with respect to the variety of computational procedures and the number of digits per whole number computation. Analysis reveals considerable variation among the current tests in terms of computational procedure and difficulty. (Author/MK)

Argues the importance of teaching fractions and discusses examples of fundamental problems in students' conceptualization of common fractions and decimal fractions. (SS)

Describes how one logical scheme for the gearing for a multi-speed touring bicycle leads to a set of gear ratios which increase in an exponential function. (BT)

Explored the construction of mathematical proofs through a hidden figure task and a variant of "Mastermind" game with children ages 7-12 years old. Older children were better able to distinguish necessary moves and to recognize sufficient evidence. Modifying the original hidden figure task to reduce its information-processing demands improved…

Argues that any mathematical construct can acquire multiple referential meanings beyond its specific mathematical meaning as it is assigned several different mappings when applied to different real-world situations. Claims that the teaching of mathematics in schools is a vehicle for an ideology concerning mathematical activity and its outcomes.…

Highlights a mathematics program for gifted students (ages 6-8) in Beijing. Different components of the program are described, including using audiovisual geometry, emphasizing the combination of shape and number, stimulating imagination, applying the discovery method, and using the search-out model. Provides sample math problems. (CR)

Describes the Quantitative Understanding: Amplifying Student Achievement and Reasoning (QUASAR) national reform project aimed at studying and fostering the development and implementation of enhanced mathematics instructional programs. It is a framework for reflection based on mathematical tasks used during classroom instruction and the ways in…

Discusses the process and the usefulness of translating empirical logic puzzles into mathematical problems which may be more easily solved, then translating the answer back into the context of the original problem. Presents nine logic puzzles devised by Lewis Carroll, with answers. (AIM)

Illustrates how many key algebraic concepts can be informally developed within the number and operations strand taught in the primary grades. Discusses expressions and equations, properties and conventions, relationships between operations, and variables from this perspective. (ASK)

Presents a model of what it means to understand mathematics followed by examples of exercises designed to develop understanding in specific ways. Presumes that understanding is more likely to develop if it is the direct focus of exercises. (AIM)

Describes an episode involving conditional statements and the notion of logical equivalence that occurred in a 10th-grade college-preparatory geometry class. Illustrates some of the confusion that can arise in connection with this topic, for both students and teachers. (ASK)

Focuses on culture examined in the unique context of South Africa. Makes visible both conceptual difficulties in its formulation and also difficulties with respect to its interpretation into educational practice. Also explores a critique of ethnomathematics using the South African situation and conceptual tools of a critical mathematics education.…

Explores the relationship between learners' actions, visualizations, and the means by which these are articulated. Describes a microworld called Mathsticks which is designed to help students construct mathematical meanings by forging links between the visual and symbolic representations they develop and their actions. Presents a case study of two…