Discussed is the importance of incorporating calculators and computers into the primary grades. Number concepts, counting skills, place-value, basic operations, problem-solving, and higher order thinking skills can be reinforced by using calculators and computers along with manipulatives. (KR)

Children in grades four and five had instruction on fractions with a continuous manipulative aid to help transfer their knowledge to tasks with a discrete manipulative aid. Results suggest that discrete-embodiment tasks are more difficult than continuous-embodiment tasks. (MNS)

Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

Reported are the effects of a conceptually oriented unit on decimal fractions. The relationships between short-term changes in solving processes and the stability of these processes over time, performance of students, and entry achievement level and the long-term effects of conceptually based instruction are discussed. (KR)

The article presents strategies used by elementary teachers from around the country to promote mathematics learning in the classroom. Their ideas include using manipulatives, participating in cooperative learning, keeping math journals, collecting portfolios, and reading literature that relates to math concepts in real life. (SM)

Describes the typical eighth-grade geometry curriculum (with regard to teacher emphasis on content, time allocations, instructional methodologies, the use of manipulatives, and compared to current research models) of typical (n=109) and enriched (n=23) mathematics classrooms in the United States based on data from the IEA Second International…

Maintains that young children should be allowed to play with water and mud on the playground. Provides teachers with suggestions on ways to plan for such outdoor activities. (BB)

Reports results of interviews in which students were asked to illustrate three interpretations of fractions: a unit subdivided into equal-sized parts; a set subdivided into equal-sized parts; and a ratio. Two areas of difficulty in giving reasonable representations are discussed. Proposes teaching suggestions to overcome these difficulties. (MDH)

Features activities designed to enhance students' spatial reasoning ability combining geometry, language arts, and visual arts. (ASK)

Examines the mathematical sense-making of eighth-grade students as they use physical devices to learn about linear functions. Suggests the concept of transparency as an index of access to knowledge and activities rather than as an inherent feature of objects. Concludes that transparency is a process mediated by unfolding activities and users'…

This article discusses how children learn to understand the decimal system in very concrete ways, while having fun using beads. When counting the beads, the children learn 5,491 is not simply "five thousand four hundred and ninety-one" but actually 5 thousands, 4 hundreds, 9 tens, and 1 unit. They begin to understand that as they get 10 units,…

Activities and games which use dominoes to reinforce basic arithmetic skills are presented. Instructions and materials are provided for the activities and games, most of which involve addition and subtraction. Other skill areas which are covered include recognition and matching of domino patterns, multiplication, and division. A seven-item list of…

The purpose of this booklet is to help teachers design and select appropriate mathematical problems for the early childhood years. Organizing the classroom for problem-solving sessions is its secondary focus. The material was gathered in early 1970s and first appeared in the National Council of Teachers of Mathematics' Thirty-Seventh Yearbook,…

The articles in this collection of readings come principally from the last ten years of the "Arithmetic Teacher." The emphasis is on teaching mathematics in grades K-6, although some articles may include teaching ideas and activities for grades seven and eight. Articles on measurement geometry are not included; the focus is on the development of…

The Mathematics Pentathlon is a tournament of mathematics games held each spring since 1979 to promote the development of mathematical concepts and skills while fostering interaction among the educational community. There are five games in each of four divisions, for grades K-1, 2-3, 4-5, and 6-7. The focus is on active problem solving and…