Three experiments examined the ability of 4- and 5-year- olds and adults to identify correspondences in spatial ratios. Results suggested that young children made accurate spatial proportionality judgments based on relational information and not on the exact form of the stimuli. Findings pose implications for theories of mathematical development…

Describes a study that explores secondary school students' conceptions of division by zero. Examines whether students identify expressions involving division by zero as undefined or tend to assign them numerical values. Studies students' justifications and analyzes the effects of age and level of achievement in mathematics on students' responses…

Presents a problem and its solution on generating the complete set of triples of given sides of a triangle. Determines that students who work through the problem stand to learn a great deal more than just which particular triangles fit the given requirements. (ASK)

Outlines the discovery of an advanced calculus class based on the generalization of the relationship between the volume of a right circular cone and the volume of a right cylinder with same height and base radius while studying solids of revolution. Relates the course of discovery and concludes with plans to use it to try to generate the same…

Discusses the rationale behind the technique of rationalizing the denominator in algebra. Argues that the importance of this technique is greatly exaggerated and is usually unnecessary. Examines an appropriate application of rationalizing the denominator. (ASK)

Argues that geometric models should be used to analyze, interpret, and solve problems from probability, algebra, and other areas of mathematics and that geometry should have a place among the major topics of emphasis in the mathematics studies of a middle school student. Presents responses from selected teachers to some questions about geometry.…

Explains how to code and decode messages using Hill ciphers which combine matrix multiplication and modular arithmetic. Discusses how a graphing calculator can facilitate the matrix and modular arithmetic used in the coding and decoding procedures. (ASK)

Suggests that the differences existing between the view of algebra as a mandated course at a specified grade level and the view of algebra as a way of mathematical thinking and reasoning developed gradually over time must be positively integrated to help students develop a genuine capacity for algebraic thinking and reasoning. (AIM)

Describes an exploratory teaching experiment carried out to test the hypothesis that it is feasible to develop a disposition toward more realistic mathematical modeling in pupils. The learning and transfer effects of an experimental class of 10- and 11-year-old students that were compared to the results of two control groups support this…

Provides examples of typical mathematics statements that elementary school teachers use when teaching mathematics, demonstrating how they are imprecise or incorrect. Suggests ways teachers can present ideas more clearly and precisely, noting that appropriate mathematical language should help students gain conceptual understanding, rather than…

Examined the impact of object boundaries on 3-, 4-, and 5-year-olds' quantitative reasoning. Asked subjects to choose between alternative collections that differed in number and size of cookies and in aggregate amount. Found that children were influenced by size of individual cookies at 3 years but were generally unsuccessful in aggregating size…

An education major enrolled in a mathematics education course ponders confusing definitions of "multiplication" functions in dictionaries and in a handout on Euclid. This student teacher wants to teach elementary students what multiplication really is, not just impart an algorithmic skill. (MLH)

Three studies investigated 5- to 8-year-olds' ability to solve partitive division problems when presented with a concrete model of a problem. Children found it easier to solve problems in Grouping-by-Divisor condition than in Grouping-by-Quotient condition, although there was evidence of developmental improvement in tasks. Findings suggest that…

This study compared 6- to 7-year-olds' knowledge of numerical fractions prior to school instruction in Croatia, Korea, and United States. Results suggested that the Korean vocabulary of fractions may influence the meaning children ascribe to numerical fractions and that this results in children being able to associated numerical fractions with…

Describes trigonometric calculations of the "fullness" (as viewed from Earth) of the outer planets as a function of their semi-major axes and their positions relative to Earth and the sun. (WRM)