The framework of Tharp and Gallimore (1988) was adapted to form a ZPD (Zone of Proximal Development) Model of Mathematical Proficiency that identifies two interacting kinds of learning activities: instructional conversations that assist understanding and practice that develops fluency. A Class Learning Path was conceptualized as a classroom path…

Included are activities and guidelines which suggest ways to use large numbers in relative terms so that they can become more meaningful for elementary mathematics students. Several spreadsheet projects illustrate the incorporation of the recommendations from the NCTM Standards dealing with number sense. (JJK)

Introduces the idea of using computer microworlds--interactive software for exploration of specific concepts--for mathematics education, the theme of this issue's articles. Discusses their development and the advantages of their use. Suggests that they can be successfully used for interactive teaching or for interpreting mathematics textbooks,…

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)

Some specific uses of microcomputers in mathematics instruction are presented. Included are examples for generating data and patterns, checking, practice of various types, developing understanding, comparing results, simulation of experiments, introducing new ideas, solving problems, and extending into new areas. Brief computer programs are given.…

Presents eight points to emphasize when teaching the concept of place value. Contends that converting numbers from one base to another helps students understand the concept of place value and the importance of context in establishing meaning. Provides a BASIC computer program to make conversions. (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…

Comments on the Fraction Project presented in this same issue. Suggests that it has uncovered many implications for instruction. However, there are limitations as the proposed setting is restricted by the present school circumstances. Concludes that better learning will not come from finding better ways for teachers to instruct but from giving the…

Interprets and contrasts children's mathematical interaction from the points of view of radical constructivism and of Soviet activity theory. Proposes a superseding model based on the interrelations between the basic sequence of actions and perturbation and the interaction of constructs. Supports the model by describing how children used…

Proposes a new model of children's mathematics by composing aspects of the Fraction Project and critiques presented in the same issue. Argues that computer microworlds provide children with dynamic learning environments in which they are the primary actors and teachers with a medium for interact with children's mathematics while trying to maintain…

This instructor's guide contains materials for a 40-hour course designed to refresh math skills for current computer numerical control machine operators. The course uses two instructional methods: computer-based multimedia and traditional instruction. The course description lists target audience and general objective. The next section gives…

This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…