An investigation was conducted to determine the effectiveness of utilizing analogies to effect conceptual change in mathematics. Forty-one high school seniors participated in a knowledge reconstruction process regarding their beliefs about everyday probability situations such as sports events or lotteries. These mathematics students were given…

This document contains informal geometry explorations that provide students with opportunities to investigate the environment from a geometric perspective, construct connections between related mathematics and other content areas, and solve problems in a geometric context. The activities provide experiences that develop curiosity, understanding,…

This book is written to help teachers develop plans and ideas for implementing innovative approaches to assessment in their mathematics classes. Chapter titles are: (1) "Purposes and Goals of Assessment," (2) "Assessment and Mathematics Teaching," (3) "Procedural and Conceptual Knowledge," (4) "Problem Solving…

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

Suitable for secondary school students, the workbook provides flowcharting activities to help students understand the logical steps used in problem solving. Before applying the flowcharting procedures to mathematical problems, students are first introduced to familiar non-mathematical problems such as sharpening a pencil or eating peanuts. Section…

States that real problem solving must become an effective and integral part of education at all levels. Describes the relationship of real problem solving to the USMES class, interdisciplinary education, and the total school program. (GS)

A game similar to Nim is described. Students in grades three through six have played the game in conjunction with the study of modular arithmetic,and have been able to develop winning strategies. (SD)

The author observes that the predictor functions determined geometrically by Ranucci (EJ 090 184) can be algebraically derived, and that capable students might enjoy verifying them. Algebraic formulations and derivations are provided. (SD)

Back-of-the-envelope problems call for approximate calculations of quantities that can be related to information in a person's knowledge but are not solved precisely. These problems provide an opportunity for the study of processes and the role of general knowledge in ill-defined problem solving. Subjects with advanced and intermediate knowledge…

Preschool children's problem-solving strategies on structured and unstructured number tasks were compared in this study. Participants were 20 four-years-olds and 20 five-year-olds. Each child was administered a number conservation, addition and subtraction, and division task. The addition and subtraction task contained trials which were designed…