External performance assessments for teachers of mathematics have traditionally been accomplished through reviews of student comments as well as through formal evaluations by superiors. Additionally, evaluating lecture-based teaching (as opposed to more active learning environments) focuses primarily on classroom performance, curriculum planning,…

This book is designed to give mathematics teachers a host of interesting and useful ideas thereby raising their consciousness level and enabling an enrichment of the mathematics instruction program. The chapters in this book capture a broad spectrum of ideas in the area of mathematics problem solving. Chapters are: (1) "Strategies for Problem…

These materials have been designed for use with the upper elementary through high school levels especially, but not exclusively, with the Lunar Sample Disk. This book contains: information on the Lunar Sample Disk, a curriculum content matrix, a teacher's guide, Moon ABCs fact sheet, rock ABCs fact sheet, Progress in Lunar Science chart, 17…

This book provides a collection of 191 mathematical problems aimed at the advanced high school student level and above. Problems cover general mathematical areas including plane geometry, three-dimensional geometry, number theory, algebra, combinatorics and graph theory, and a number of miscellaneous questions that combine mathematical…

The composition classroom has traditionally been seen as one of the most important places to develop critical thinking and problem-solving skills. Composition theory based on developing students' rhetorical skills in argument seeks, in particular, to address development of these skills. Rhetoric is audience-based and culminates in an argument that…

This paper reports a study that sought to explain student understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of data analysis, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examined the differences in the problem-solving activities of solvers who…

This study sought to provide an explanation of (n=13) university students' understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of the analysis of the data, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examines the differences in the…

Strategic communication scholars agree that planning is critical to human action. An investigation tested plan modification aspects of cognitive planning theory. Two experiments tested whether success and failure of a plan served as predictors of plan modification and whether individuals can accurately predict whether and how they will modify a…

This book focuses on curricular issues involved in preparing students for taking the SAT I--Reasoning Test using a problem-solving focus. There is a particular philosophy with which this book is presented. First, the illustrations have been selected to demonstrate in dramatic form the power of the procedure presented. Second, the problems both in…

This book is designed to prepare students for taking the SAT I--Reasoning Test using a problem-solving focus. It clarifies the purpose, structure, and use of the SAT I and provides meaningful instructional material and explanations which illuminate the necessary skills. The book begins with a review of essential fundamentals, including useful…

The books in this series provide an essential ingredient in the transition from concrete mathematical experience to the symbolic reasoning used in algebra. They aim to guide the student in building and extending manipulative patterns, collecting numerical data, and analyzing the results. The main objective of the activities in this book is for the…

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this…

This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…

Recent research has demonstrated that knowledge about specific instances may be of more relevance to reasoning than has previously been assumed. Students can rely on principles they have learned, or they can recall something similar previously experienced, and base the new prediction on it in an instance-based approach. Instance-based (or…

This book describes the friend-to-friend process, a non-professional approach for helping a friend through a problem. The first chapter presents a transcript of a high school senior working through a problem. The use of three questions which address three levels of the human personality (thoughts, feelings, and actions) is described. Guidelines…