Argues that there is a sense of surprise and wonder that can result from looking back at problem solutions and there is a potential for then creating unexpected, even memorable, alternative solutions. Example problems with routine solutions and alternative approaches uncovered while "looking back" at the solution are given. (PK)

The purpose of this manual is to present a series of lessons on solving word problems, each focusing on a specific concept. The solving of story problems should be incorporated into the daily mathematics lesson so that children can maintain and increase their skills. The lessons are sequenced according to their complexity. Lessons one through…

This paper, part of a series of working papers published to provide documentation of research and development efforts associated with the Indigenous Mathematics Project of Papua New Guinea, discusses the role of problem solving in the mathematics curriculum and types and characteristics of good problems, with illustrations. Reasoning by analysis…

A one-semester course at the third-year level at York University is described. It tries to legitimize in students' eyes that it makes sense to talk about mathematics as well as do mathematics. Seven course themes are discussed, followed by nine problems used in the course. (MNS)

The article offers a curriculum of direct instruction to teach the process of solving arithmetic word problems to learning disabled students. Students are taught to use a plan, to test relevant hypotheses, and to evaluate their work. (Author/DB)

These materials were developed for use in workshops with teachers. The document suggests a four-stage framework which students can apply to problems: (1) get to know the problem; (2) choose what to do; (3) do it; and (4) look back. Suggestions are included for each of the four stages of the probem solving process. Other specific techniques for…

Describes a mathematical investigation of gold--how it is weighed, stored, used, and valued. For grades 3-4, children estimate the value of treasure chests filled with gold coins and explore the size and weight of gold bars. Children in grades 5-6 explore how gold is mined and used, and how the value of gold changes over time. (PVD)

The article includes a discussion of counting and counting strategies. In addition, there are eight problem sets appropriate for use with groups of different age and ability levels. Suggestions are given for finding variations of the problems. (PK)

A problem-solving component for the junior high school mathematics curriculum is described. A sample worksheet of routine problems is included, and suggestions for working with nonroutine problems are given. (MNS)

Presents three reproducible worksheets which contain verbal problem situations in which numerical quantities have been omitted and represented by geometric shapes. The objective of the material is to develop the students' ability to analyze the mathematical structure in verbal problem-solving situations. (PK)

The purpose of this booklet is to help teachers design and select appropriate mathematical problems for the early childhood years. Organizing the classroom for problem-solving sessions is its secondary focus. The material was gathered in early 1970s and first appeared in the National Council of Teachers of Mathematics' Thirty-Seventh Yearbook,…

This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)

These sample problems, exercises, questions, and projects were compiled to supplement the guide for the Manitoba course Mathematics 301 in order to assist teachers in implementing the program. Arranged according to the modules of the course guide, they are coded to the objectives of the program. Review exercises follow either the subtopics within…

Presents examples of word problems that can be used to illustrate the distributive property for preservice teachers. Includes examples involving extended sums, volume, area, prealgebra, place value, long multiplication, fractions, decimals, and algebra. (MDH)

Proposes methods to teach the more difficult concepts of linear algebra. Examines features of the Linear Algebra Curriculum Study Group Core Syllabus, and presents problems from the core syllabus that utilize the mathematical process skills of making conjectures, proving the results, and communicating the results to colleagues. Presents five…