Investigated was student inability to understand mathematics across concepts, focusing on the processes by which students solve problems. In-depth clinical interviews were used with students during ninth-grade general mathematics. Mathematical abilities investigated were information gathering, generalization, reversibility, flexibility, and…

A simplified method is reviewed for analyzing any quadratic equation to determine whether or not the equation represents a nondegenerate conic. (MP)

A special calendar chart is presented that can be used to find out what day of the week any date falls on during the 1980s. (MP)

The use of a 25-pin lattice geoboard in a six-week course in middle school geometry is presented, with sample activity cards and test items. Two other ideas discuss the use of algebra in solving verbal problems and teaching negative exponents. (MP)

The use of a computer program written in BASIC to help prove a theorem in geometry is discussed. Ideas used in this example could be applied to writing programs for other geometric proofs. (MP)

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)