The 13 leading mathematics educators who made up the task force that prepared this report were thoroughly acquainted with every major report on math education produced within the last decade. They were also thoroughly acquainted with the realities of instruction in the K-12 classrooms. Their aim, therefore, was to make appropriate compromises…

This collection of four papers deals with problem solving and the measurement of problem solving. "Climbing Up the Competence Ladder: Some Thoughts on Meaningful Assessment of Problem-Solving Tasks in the Classroom" by K. C. Cheung uses the metaphor of a competence ladder to represent the problem-solving continuum with progressive…

In this article, the authors seek to re-conceptualize the perspective regarding students' difficulties with algebra. While acknowledging that students "do" have difficulties when learning algebra, they also argue that the generally espoused criteria for algebra as the ability to work with the syntactical rules for solving equations is…

This report presents findings from a study of the cognitive processes and learning difficulties of ninth-grade students in Algebra I. A clinical interview approach was used with 14 students. A group of six Hispanic students and a group of five Anglo students were enrolled in the same algebra class; three Hispanic students were enrolled in an…

This document reports in detail an investigation of the cognitive processes and learning difficulties of ninth-grade students in Algebra I. A clinical interview approach was used with 14 students. A group of six Hispanic students and a group of five Anglo students were enrolled in the same algebra class; a group of three Hispanic students who had…

Since 1982, the National Council of Teachers of Mathematics has published a student periodical five times a year. Each four-page issue focuses on a single theme, developing it from a simple opening-page activity through more challenging extensions at a higher level of understanding. In this document each four-page issue published from September,…

This document is designed to assist administrators and teachers in planning, developing, and implementing grades K-9 mathematics programs and to provide some guidelines for grades 10-12 instruction. It is intended to provide a philosophical foundation and curricular framework from which educators may construct a comprehensive local program to meet…

The increasing availability of the computer in the classroom has created a need for informed and creative instructional software. Two areas of cognitive research in mathematics and science learning have implications to instruction and, consequently, to educational software design. These are research on misconceptions and on differences between…

This course, offered in the Option Y sequence of the high school mathematics program described in the Department of Education's Mathematics Program Guide, is designed to be less theoretical and more applications oriented than Algebra IA and IB. There are ten learner objectives for this course, which is designed along with Core Algebra to fulfill…

This document provides teaching guidelines and student material for a unit intended for use in 12th grade algebra classes. Time allotment is from four to six hours of classroom time. The objective of this capsule is to teach students how to solve compound interest problems using arithmetic, logorithms, and calculators. Prerequisites for the unit…

A two-part communication model for teaching elementary mathematics is proposed. Part I delineates symbols commonly used in teaching arithmetic. Parts of mathematical language (mathematical objects, relations, operations, expressions, and sentences) are compared to analogous parts of the English language. Part 2 is a conceptualization of strategies…

Methods of instruction and organization are discussed in the first chapter, including critiques of the Winnetka plan and the Dalton plan. The next author argues that algebra is a method of thinking and explains some mental processes involved. The following three chapters are concerned with the functional concept. Using function as a unifying…

Design techniques for generative computer-assisted-instructional (CAI) systems are described in this report. These are systems capable of generating problems for students and of deriving and monitoring solutions; problem difficulty, instructional pace, and depth of monitoring are all individually tailored and parts of the solution algorithms can…

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

Reports on the progress of a project designed to establish both a research agenda for mathematics education and a conceptual framework for such an undertaking. Describes four conferences which have been organized to consider teaching problem solving, effective teaching, teaching and learning algebra, and middle school number concepts. (TW)