The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…

Using data collected in 1977-78, the Evaluation System has computed fall and spring mathematics scores on the Prescriptive Mathematics Test (PMT) for classes of students in grades one through six. In addition, relationships of performance on the PMT to class size, attendance, percent of males in the class, number of different test levels used in a…

The uses of verbal rules in solving arithmetic problems are presented. Thirty-six problems were used in individual testing of five students who were enrolled in a remedial mathematics course at a community college. Two or three weeks prior to the individual exams, the students had been tested in their class on the material. The study indicated…

The National Assessment of Educational Progress (NAEP) administered the selected supplemental mathematics exercises to 13-year-old students during October and November 1975 and to 17-year-old students during March and April 1976. This assessment represents a specially modified supplement to 1972-73 full-scale mathematics assessment and was…

This report examines and summarizes the needs in mathematics of the Fresno City school system. The study is one in a series of needs assessment reports for PROJECT DESIGN, an ESEA Title III project administered by the Fresno City Unified School District. Theoretical concepts, rather than computational drill, would be emphasized in the proposed…

Describes the Approaching Algebra Numerically (AAN) Calculator as a computer-based simulation of a hand-held calculator designed with novice learners in mind. Includes a complete description of the calculator and suggests uses for the calculator, including exponentiation, order of operations, scientific notation, concept of variable, and problem…

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.…

This text explores teaching techniques and adaptations that have proven effective in teaching mathematics concepts and skills to students with learning disabilities. This fourth edition, consistent with the standards developed by the National Council of Teachers of Mathematics, 2000, continues to emphasize problem solving, number sense, student…

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…

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)

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)

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…