حل مسائل ریاضی

This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in'higher-order thinking skills'in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics,'rules of thumb'for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students'(often counterproductive) mathematical behavior. Mathematical Problem Solving provides information pertinent to the nature of mathematical thinking at any level. This book provides a framework for the analysis of complex problem-solving behavior. Organized into two parts encompassing 10 chapters, this book begins with an overview of the four qualitatively different aspects of complex intellectual activity, namely, cognitive resources, heuristics, control, and belief systems. This text then presents a series of empirical investigations that flesh out the analytical framework. Other chapters consider the ways that competent problem solvers make the most of the knowledge at their disposal. This book discusses as well the kind s of learning that can result from carefully designed instruction. The final chapter deals with observations made in typical high school classrooms, which serve to indicate some of the sources of students' mathematical behavior. This book is a valuable resource for mathematicians and mathematics teachers. Readers who are interested in higher-order thinking skills in any domain will also find this book useful. Alan H. Schoenfeld. Includes Indexes. Bibliography: P. 388-397.