Noting that assumptions about the teaching and learning of early childhood mathematics have changed substantially since the 1970s, this chapter examines recent research that may inform curriculum development in early childhood mathematics. The chapter begins with a consideration of the theoretical perspectives for defining an appropriate…

Provides two activities. Discusses the use of a computer and a calculator for the activities. Presents BASIC and LOGO program for finding Pythagorean triples. Seven references are listed. (YP)

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)

Illustrates and discusses one class of strategies to solve word problems referred to as "number-consideration strategies." Contrasts actions and goals of students who focus mainly on number considerations with those of students who focus mainly on problem understanding. (MDH)

Shares an experience from a mathematics methods course for elementary teachers that used concrete materials to teach the concept of rounding in different bases. Discusses how this experience modeled recommendations by the NCTM "Professional Teaching Standards" in creating classroom climate and conducting discussion. (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)

Introduces a cultural perspective in the teaching of mathematics. Describes the mathematical practices of African peoples and of the indigenous peoples of the Americas in relationship with numbers and numeration, design and pattern, architecture, and games of chance and skill. (MDH)

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…

Describes research which compared the processing loads of mathematical representations and strategies used by (n=3) teachers and (n=29) children aged 5-8 for interpreting subtraction operations represented in numerical form. Some representations and strategies appeared to impose an extra processing load which can interfere with conceptual…