Mathematical Problem Solving and New Information Technologies: Research in Contexts of Practice

ISBN-13: 9783540557357 / Angielski / Twarda / 1992 / 346 str.

Joao P. Ponte; Joao F. Matos; Jose M. Matos

Opis

This book discusses the implications of new informationtechnologies and cognitive psychology for mathematicalproblem solving research and practice.Based on a NATOAdvanced Research Workshop held in Portugal in 1991, itoffers both empirical research and theoretical papers.The book includes a thorough discussion on the nature andpurpose of problem solving as a mathematical activity, providing a view of the importance of complementaryactivities such as investigations, conjecturing and problemposing. It focuses on cognitive processes, instruction, classroom processes, and the teacher's role, and containsnew assessment and teacher education proposals.At a time of important reform movements, when emphasis isput on the role of new information technologies, the bookprovides an up-to-date view of the developmental work beingdone on computerized learning environments in the disciplineof mathematics, as well as on the efforts to introduce themin educational practice.

Spis treści

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.