Described is a way to incorporate mathematics into such disciplines as social studies, English, science, and library skills. Emphasized is that connections must be made among various topics so that students can see how mathematical ideas are related and how one mathematical idea can help them understand others. (KR)

Examines what prospective elementary and secondary mathematics teachers understand about mathematics when they enter formal teacher education. Results reveal that the mathematics understanding of elementary and secondary teacher candidates tends to be rule-bound and inadequate. (BB)

A teaching experiment with six third graders to analyze their ways of operating while solving fraction tasks. Children's quantitative reasoning with fractions was based on their quantitative reasoning with natural numbers. Presents the constructive itinerary of one of the most advanced children in the group. (Contains 44 references.) (Author/MDH)

Citing examples from the author's third grade mathematics classroom, describes problems stemming from the use of concrete objects (e.g., fraction bars, base-10 blocks, and popsicle sticks). The vignettes show the fallacy of assuming that students will automatically draw the conclusions that their teachers want simply by interacting with particular…

Bilingual mathematics competencies and competency-coordinated activities are provided in the four sections of this curriculum guide for kindergarten (pre-operational) and grades 1-3 (concrete-operational) children. Topic areas for kindergarten include: classification (logic); comparing/ordering/graphing; quantitative; measurement; geometry;…

One of a series of pre-apprenticeship phase 1 training modules dealing with math skills, this self-paced student module covers the addition and subtraction of common fractions and mixed numbers. Included in the module are the following: cover sheet listing module title, goals, and performance indicators; introduction; study guide/check list with…

This book is intended to make common fourth-grade mathematical concepts both interesting and easy to understand. The text is designed to meet the particular needs of those children who have "accumulated discouragements" in learning mathematics. The reading level required of pupils has been reduced. Individual chapter titles are:…

This booklet is one of a set of five booklets which comprise the basic curriculum for "Mathematics Laboratories for Disadvantaged Students," a nationally validated Title III ESEA project. This publication provides evaluation materials and student materials related to fractions. Topics included in this booklet are meanings of fractions,…

Examines the use of a ratio table for developing students' conceptual understanding of rational number. The ratio table is an alternative to cross-multiplication and can utilize both additive and multiplicative strategies. It organizes numbers and keeps track of operations and results, which aids the teacher in assessment. (MLB)

Presents five activities for the family and K-2, 4-3, 5-6, and 7-8 levels that focus on the connection between mathematics and music. Activities examine the mathematical concepts of counting, estimation, measurement, statistics, fractions, and patterns involved in the topics of rhythm, beats in a measure, music preference, the music scale, and…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Uses work on children's counting schemes and a radical constructivist orientation to describe the development of computer microworlds for the teaching of rational numbers. Suggests that the design of complex software systems needs a strong theoretical background to provide direction for the design. Suggests that computer environments are the…

Uses the constructivist principle of active learning to explore the possibly essential elements in transforming a cognitive play activity into mathematical activity. Suggests that for such transformation to occur, cognitive play activity must involve operations of intelligence that, yield situations of mathematical schemes. Illustrates the…

Comments on the Fractions Project presented in this same issue. Discusses two major ideas: the construction of mathematics of children and its basis and playful actions as a basis for mathematical actions. Highlights the understanding of children's mathematical concepts and schemes as they grow and are organized in the context of computer…

Comments on the Fraction Project presented in this same issue. Examines the choice of appropriate perspectives on the phenomena induced and observed and the generalizability of the results. Investigates the phenomena as involving student attunement to constraints built into the computer-based learning environments and in terms of explicit…