A strong and fluent competency in mathematics is a necessary condition for scientific, technological and economic progress. However, it is widely recognized that problem solving, reasoning, and thinking processes are critical areas in which students' performance lags far behind what should be expected and desired. Mathematics is indeed an important subject, but is also important to be able to use it in extra-mathematical contexts. Thinking strictly in terms of mathematics or thinking in terms of its relations with the real world involve quite different processes and issues. This book includes the revised papers presented at the NATO ARW "Information Technology and Mathematical Problem Solving Research", held in April 1991, in Viana do Castelo, Portugal, which focused on the implications of computerized learning environments and cognitive psychology research for these mathematical activities. In recent years, several committees, professional associations, and distinguished individuals throughout the world have put forward proposals to renew mathematics curricula, all emphasizing the importance of problem solving. In order to be successful, these reforming intentions require a theory-driven research base. But mathematics problem solving may be considered a "chaotic field" in which progress has been quite slow.

Inhalt

A Framework for Research on Problem-Solving Instruction.- Researching Problem Solving from the Inside.- Some Issues in the Assessment of Mathematical Problem Solving.- Assessment of Mathematical Modelling and Applications.- A Cognitive Perspective on Mathematics: Issues of Perception, Instruction, and Assessment.- The Crucial Role of Semantic Fields in the Development of Problem Solving Skills in the School Environment.- Cognitive Models in Geometry Learning.- Examinations of Situation-Based Reasoning and Sense-Making in Students' Interpretations of Solutions to a Mathematics Story Problem.- Aspects of Hypothetical Reasoning in Problem Solving.- Problem Solving, Mathematical Activity and Learning: The Place of Reflection and Cognitive Conflict.- Pre-Algebraic Problem Solving.- Can We Solve the Problem Solving Problem Without Posing the Problem Posing Problem?.- Problem Solving in Geometry: From Microworlds to Intelligent Computer Environments.- Task Variables in Statistical Problem Solving Using Computers.- The Computer as a Problem Solving Tool; It Gets a Job Done, but Is It Always Appropriate?.- Insights into Pupils' and Teachers' Activities in Pupil-Controlled Problem-Solving Situations: A Longitudinally Developing Use for Programming by All in a Primary School.- Cognitive Processes and Social Interactions in Mathematical Investigations.- Aspects of Computerized Learning Environments Which Support Problem Solving.- A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments.- Problem Solving: Its Assimilation to the Teacher's Perspective.- Computer Spreadsheet and Investigative Activities: A Case Study of an Innovative Experience.- Examining Effects of Heuristic Processes on the Problem-Solving Education of Preservice Mathematics Teachers.- Mathematics Problem Solving: Some Issues Related to Teacher Education, School Curriculum, and Instruction.