Presents an activity that uses M & M's candy to initiate discussion about the mathematical concepts of empty set, zero, more than, less than, most least, and equivalent sets. Suggests extensions that could follow this activity. (MDH)

Describes three activities using dominoes, playing cards, and the calendar to give students mathematical experiences reinforcing basic skills and problem-solving strategies that involve patterns, relationships, and functions. Students discover mathematical relationships underlying the magic tricks used in the activities. (MDH)

Presents the hierarchical structure of quadrilaterals as an illustration of learning a geometric concept by moving from the levels of visualization and analysis to the level of formal deduction. The development discusses the classification of quadrilaterals, the inheritance of properties within the hierarchy, connections between algebra and…

Presents a hands-on mathematics task that can be investigated experimentally to produce a sequence of numbers. Describes ways to extrapolate values of the table of numbers by formulating and verifying a conjecture related to the pattern in the numbers. (MDH)

Course selection of 795 gifted adolescents in a summer residential program differed along traditional gender lines in mathematics, science, and writing/literature. Girls and boys performed equally well in all types of classes; main effects in achievement and motivation were found only for type of class. The Scholastic Aptitude Test served as a…

Reports the results of five contrasts between small-group learning and a more teacher-centered instructional style employed in junior high, high school, and college mathematics classes. In no case did the small-group class perform more poorly than the one led by a teacher; in one case, measuring long-term retention, the small-group class performed…

Presents a worksheet on graph paper that allows students to determine the perpendicular bisectors of given segments by folding the paper. Students then determine the slopes of the perpendicular bisectors and use inductive thinking to discover the relationship between the slopes of perpendicular lines. (MDH)

Discusses the first session and events from other sessions of a mathematics circle consisting of the author and four preschool children. Presents discussions that ensued with the children when asked to solve problems related to Piaget's stages of cognitive development. (MDH)

Describes the new development of mathematics education in the Peoples Republic of China. Explains changes that happened in the National Curriculum, teaching research, and the progress of our pupils. (Author)

Learning environment that facilitated the acquisition and expression of procedural skills in LOGO was set up for children in the 10- to 12-year range. Ten participants were placed in a series of situations that required them to manipulate programing procedures in LOGO. Analysis of children's behavior revealed their competence in manipulating…

Proposes a theory of cognitive processes in doing and learning place value arithmetic. Discusses a computer model that simulates the learning of multicolumn subtraction under one-on-one tutoring to measure the relative difficulty of two methods of subtraction. The model predicts that regrouping is more difficult to learn than an alternative…

Describes an activity in which students utilize mathematical communication and reasoning skills to develop a class constitution. Students brainstorm rules for their classroom in cooperative-learning groups, classify them into categories, and justify their decision to the class. (MDH)

This study investigated effects of a same-age tutoring procedure on academic and social behavior of eight behaviorally disordered middle school tutors and tutees. Results indicated increased scores on tutors' and tutees' math worksheets, improved attitudes toward math for both groups, and significantly improved social interactions between tutors…

This article traces the history of zero and its dual role as a placeholder, albeit of empty space, and as a number for computational purposes. The use of one symbol for both situations is shown to be tied to the adoption, and subsequent promulgation, of our modern numbering system. (JJK)

This review features new examples of using the computer relative to college-level mathematics to enhance pedagogy, solve problems, and model real-life situations. Included is a LOGO program that can be used to create and to stimulate subsequent investigations of spirolaterals, those figures generated by repeatedly drawing basic loops. (JJK)