Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

Discusses a problem that appeared in the September, 1999 issue of this journal and presents solutions from students in grades 2-6. The question involved using colored cubes rearranged to make different stacked towers. (KHR)

This analysis of 44 research studies concerned with word problems contains: (1) a brief overview; (2) 44 major findings and conclusions; (3) 64 suggestions and questions for further research; and (4) a reference list. The author suggests that the experimental research of the 1980s seemed to focus on the children, the instruction, and the word…

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)

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…

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)

Describes four methods to structure estimation activities that enable students to make connections between their understanding of numbers and extensions of those concepts to estimating. Presents activities that connect estimation with other curricular areas, other mathematical topics, and real-world applications. (MDH)

Describes the method to solve problems called T-E-M-T-T: trial, error, and modified trial through technology. The method integrates students' skills of estimation, mental computation, and appropriate choice of calculator use. Includes 2 activities for each of grades K-4 and 5-8 that illustrate the method. (MDH)

The problem-of-the-week (POW) and problem-solving class openers are exemplified as methods for the integration of course-relevant problem solving into a first-year algebra classroom without sacrificing time spent on developing skills and learning concepts. Illustrated examples, as well as problem sources, are included. (JJK)

Examined the effects of intervention in the instruction of 12 male seventh-grade students for the purpose of developing number sense. Results indicate that after instruction students were more likely to use strategies to solve number magnitude, mental computation, and computational estimation problems that reflected number sense. (Contains 50…