Aspects of the source of power of mathematics and the ways in which mathematics works are discussed. The author discusses various philosophies about mathematics, presents several unusual "real world" problems, and reviews the social consequences of the "imposition of mathematics" on humanity. (MP)

Incorrect answers on an arithmetic test given to 83 first-year students at Aberdeen College of Education in the United Kingdom are reviewed. The nature of wrong responses and the likely reasons for the given responses are discussed. (MP)

The relationship between logic and mathematics is examined. Four basic concepts inherent in symbolic logic that are typically included in ninth- and tenth-grade mathematics programs are reviewed. Symbolic logic is advocated for all students who will study algebra and/or geometry. (MP)

A new approach to teaching the division of common fractions is described. The approach is related to the multiplication operation and involves children working with concrete materials. (MK)

Presented are suggestions for teaching absolute value using five different definitions of the concept. (MK)

The format of digits in liquid crystal displays (LCDs) on calculators and watches can motivate some simple investigations appropriate for school mathematics. Several sample problems or investigations are provided. (MK)

Reviews the author's research on students' conceptions of mathematics and suggests ways to overcome or prevent misconceptions. (MP)

Three levels of mathematical concepts and three theoretically corresponding levels of cognitive development were posited. Children's test results were consistent with predictions for each age group, leading to the conclusion that, for concept attainment at each level, a minimum information-processing capacity is a necessary, but not sufficient,…

Methods are suggested for using equivalent fractions in the introductory stages of teaching fractions. (MK)

Five-year-olds were found to give more conserving responses to small number versions than to a large number version of a test of identity conservation. Superiority of performance with small number versions was reduced but not eliminated when the opportunity to requantify was removed. (Author/SJL)

The authors suggest a few games for which programmable pocket calculators are used to create an environment in which mathematical concepts can be experienced more easily by students. (Author/MK)

Defends new math by stating that most new math programs were never correctly implemented, that scores on the Scholastic Aptitude Tests and other aptitude tests were lower not only in math but in verbal ability as well, and that math concepts have not been learned in either new math or traditional curricula. (CS)

The concept of "baby research" signifies a playful investigation that takes place at a child's initiative, carried out with freedom and joy, without specific knowledge of preconceived ideas of where it will lead. A joyous firsthand experience with Cuisenaire rods is described by a teacher who once disliked teaching mathematics.…

Combine history and current events with graham crackers and crepe paper in a Washington model. (Editor)

Describes how students in a third-grade classroom were given opportunities to practice measurement activities on their school playground. Argues that the school buildings and playground can be rich sources of ways to help students make connections and extend their spatial thinking and reasoning beyond the confines of the classroom. (ASK)