Kindergartners who received learning-set instruction on unidimensional classification, unidimensional seriation, and number conservation were retested at the end of first grade. Followup tests showed that the cognitive advantage and improved academic achievement gained from that teaching method was generally present 15 months later. However, a…

Addresses how the early childhood educator can develop mathematical concepts in the context of goals and standards set by the National Council of Teachers of Mathematics and simultaneously enhance literacy development. Includes suggestions for daily story time using children's books with strong mathematics and science connections, and for teaching…

This article presents a chart to illustrate learning paths for children ages 3 to 6 years and sample teaching strategies in the following areas: (1) number and operations; (2) geometry and spatial sense; (3) measurement; (4) pattern/algebraic thinking; and (5) displaying and analyzing data. (KB)

This annotated bibliography of recommended CD-ROMs that could form the basis of an early childhood multimedia collection makes some suggestions for linking them to books. Subjects include general early learning, math concepts, problem solving, reading readiness, and science. (DGM)

A study at a South African university investigated the mathematical reasoning ability of 314 first-year chemistry students and 69 mathematics students regarding ratios and proportions in non-chemistry-related problems. Results indicated students' mathematical readiness in these areas was only weakly linked to their previous achievement in…

Studies the developmental process of how the concepts of ratio and proportion do not develop in isolation, but rather are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. Follows one fifth-grade student as he attempts to schematize his…

Investigates students' understanding of the basic concepts of introductory set theory which are set, set element, cardinality, subset, and the empty set. Data was collected from preservice elementary school teachers. The project included experimentation with basic set concepts in an open computer-based environment using the mathematical computer…

This article presents a summary of considerations for teachers when assessing a student's understanding of division concepts. It discusses student products, student procedures and strategies, and student concepts and explanations at the preschool, elementary, and middle school levels. Examples of assessment activities and possible misconceptions…

Demonstrates the consequences of teaching rules without understanding using examples from two 3rd grade children. Suggests alternative instructional strategies. (KHR)

Four alternate versions of a 15-item general outcome measure (GOM) of mathematics conceptual understanding and applications were developed and administered to 117 eighth-graders. Results were correlated with scores on state multiple-choice mathematics achievement tests. Correlations ranged from .81 to .87 with no significant differences, offering…

Presented is a mean-value theorem that generalizes the Taylor-Lagrange formula. Discussed is the asymptotic behavior of the remainder term of the formula. Several numerical schemes are derived to approximate the solution to initial-valued first order differential equations. (KR)

Discussed are various models proposed for the Moebius strip. Included are a discussion of a smooth flat model and two smooth flat algebraic models, some results concerning the shortest Moebius strip, the Moebius strip of least elastic energy, and some observations on real-world Moebius strips. (KR)

Describes several ways to implement the NCTM Standards in technically enhanced classrooms. Presents examples from "Computer-Intensive Algebra." Provides suggestions for implementation. (YP)

Appropriate uses for graphics calculators in precalculus and calculus are discussed. The functions of Casio, Sharp, and Hewlett-Packard brand calculators are stressed. A "Stress Test" for graphics calculators designed to illustrate common errors and to furnish examples of tasks which cannot be completed on these instruments is provided.…

Describes two easily applied mathematical theorems, Budan's rule and Rolle's theorem, that in addition to Descartes's rule of signs and intermediate-value theorem, are useful in chemical equilibrium. Provides examples that illustrate the use of all four theorems. Discusses limitations of the polynomial equation representation of chemical…