Presents four sets of activities to develop the concepts of data analysis and graphing. Students estimate sample populations using beans, examine graphs from newspapers and magazines, predict the most popular color of cars, and simulate quality control in a manufacturing process. (MDH)

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…

Describes two investigations suitable for grades seven and eight that explore the properties of the figure created when the midpoints of an equilateral triangle or square are joined. (MDH)

Presents 5 school and home activities for the K-2, 3-4, 5-6, and 7-8 levels appropriate for beginning the school year that incorporate problem solving, collecting and analyzing data, and exploring patterns. Topics include a shopping spree, seat assignment, map-interpretation skills, and probability. Includes reproducible worksheets. (MDH)

Discussed is the place and teaching of trigonometry in a NCTM Standards-based mathematics curriculum. Presented is how these standards can be implemented in a technology-rich environment that encourages reasoning, communication, problem solving, and confidence building. Examples focus on functions, graphical sense, modeling, and identities. (KR)

Suggests that a discussion-based approach focused on experiences of actual environmental issues, encountered problematically, should characterize environmental education activities. An ecology exercise dealing with organic pollution of a river provides a context for the educational principles and ecological concepts included the study. (24…

The quadratic function can be modeled in real life by a suspension bridge that supports a uniform weight. This activity uses concrete models and computer generated graphs to discover the mathematical model of the shape of the main cable of a suspension bridge. (MDH)

Discusses the rationale and use of problem fields which are sets of related and/or connected open-ended problem-solving tasks within mathematics instruction. Polygons with matchsticks and the number triangle are two examples of problem fields presented along with variations in conditions that promote other matchstick puzzles. (11 references) (JJK)

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)

Presents a series of activities developed from the "Arithmetic Teacher's" regular feature entitled "Problem Solving: Tips for Teachers" to help students develop skills in each of the four steps of Polya's problem-solving process: (1) Understanding the Problem; (2) Making a Plan; (3) Carrying Out the Plan; and (4) Reflecting…

Presents three stories from mathematics history that can be integrated into classroom teaching: (1) the account of how Eratosthenes measured the circumference of the earth to discuss the concept of units in measurement, (2) ideas from Archimedes, Vite, and Descartes to introduce pi, and (3) the discovery of the Cardanic formula as an example of…

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…