This proceedings contains 75 research reports, 8 discussion groups, 32 oral reports, and 28 poster presentation entries from the 1996 Annual Meeting of the American Chapter of the International Group for the Psychology of Mathematics Education. A one-page synopsis is included for discussion groups, oral reports, and poster presentations. Topic…

This resource book for algebra contains games, tricks, and quick activities for the classroom. Categories of activities include puzzlers, patterns, manipulatives, measurement, graphing, and a section that contains reproducible statement and value cards. Twenty one puzzle problems, four pattern activities, and 11 quick activities that engage…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…

This study, involving 65 undergraduates at the Georgia Institute of Technology (Atlanta); explores a scheme for representing problem-solving knowledge and predicting transfer as a function of problem-solving subgoals acquired from examples. A subgoal is an unknown entity (numerical or conceptual) that needs to be found in order to achieve a higher…

The high percentage of high school pre-algebra students having difficulty learning the abstract concept of graphing ordered pairs on the Cartesian rectangular coordinate system was addressed by the creation and implementation of a computer-managed instructional program. Modules consisted of a pretest, instruction, two practice sessions, and a…

This is the final test for students in the twelfth grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in 1988, it is available in both English and French. It contains 52 multiple-choice questions and 3 written-response problems, with 2.5 hours allowed for completion. Approved calculators may be used.…

This paper analyzes the quantitative and situational structure of algebra story problems, uses these materials to propose an interpretive framework for written problem soving protocols, and then presents an exploratory study of the episodic structure of algebra story problem solving in a sizable group of mathematically competent subjects. Analyses…

Mathematics 30 is a 12th-grade mathematics course for students in Alberta, Canada. This document is the final test for the course. Intended for administration during January 1989, it contains 45 multiple-choice questions, seven open-ended scannable questions, and three written-response questions. Two and one-half hours are allowed for completing…

These materials are intended to provide meaningful mathematical experiences for pre-algebra students. These experiences emphasize the development of computational skills, mathematical concepts, and problem-solving techniques. This bulletin may be used as the basis for the first term of a one-year course. The complete course is divided into 12…

This booklet is a catalog of error patterns found in basic arithmetic and algebra courses. It is intended to be used as a resource by instructors and tutors teaching these concepts. The material is divided into major concept headings with subheadings. The error patterns are named and given a brief general description followed by a specific example…

Previous studies were conducted with 14- to 15-year-old students on the nature of the processes they used to solve tasks given the incorrect/buggy/mal-rules. The computer-based Leeds Modelling System (LMS) was implemented and a database of examples, correct and incorrect, or mal-rules had been established which was sufficient to diagnose the…

This document consists of two major sections. The first of these is actually three units that look at applications of arithmetic to business. Basic pre-algebra mathematics is an assumed prerequisite. These units are titled: 367-The Real Numbers; 368-Fractions and Their Uses: Ratio and Proportion; and 369-Exponents: Powers and Roots. Each module…

The various difficulties and cognitive obstacles that students face when they are introduced to algebra are well documented and described in the relevant bibliography. If it is possible, in order to avoid these difficulties, we have adopted the functional approach widening the meaning of algebraic thinking. In this paper, which is part of wider…

In this paper we report on some patterns of reasoning, which emerged during an activity of proving a mathematical statement performed by nine grade and university mathematics students. The statement in question involves drawing figures, working in arithmetic and in algebra. As for secondary students we detected fluency, flexibility and ability of…

The proceedings of the 24th annual meeting of the Psychology of Mathematics Education North American Chapter (PME-NA) contains research reports, plenaries, and poster presentations. Papers include: (1) "What Do We Believe about Teacher Learning and How Can We Learn With and From Our Beliefs?" (Deborah Loewenberg Ball); (2) "Toward Evidence for…