Mathematical Problem Solving and New Information Technologies

1. Front Matter

   Pages i-xv

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2. A Framework for Research on Problem-Solving Instruction

   • Frank K. Lester Jr., Randall I. Charles

   Pages 1-15

3. Researching Problem Solving from the Inside

   • John Mason

   Pages 17-36

4. Some Issues in the Assessment of Mathematical Problem Solving

   • Jeremy Kilpatrick

   Pages 37-44

5. Assessment of Mathematical Modelling and Applications

   • Henk van der Kooij

   Pages 45-60

6. A Cognitive Perspective on Mathematics: Issues of Perception, Instruction, and Assessment

   • Patricia A. Alexander

   Pages 61-76

7. The Crucial Role of Semantic Fields in the Development of Problem Solving Skills in the School Environment

   • Paolo Boero

   Pages 77-91

8. Cognitive Models in Geometry Learning

   • José Manuel Matos

   Pages 93-112

9. Examinations of Situation-Based Reasoning and Sense-Making in Students’ Interpretations of Solutions to a Mathematics Story Problem

   • Edward A. Silver, Lora J. Shapiro

   Pages 113-123

10. Aspects of Hypothetical Reasoning in Problem Solving

    • Pier Luigi Ferrari

    Pages 125-136

11. Problem Solving, Mathematical Activity and Learning: The Place of Reflection and Cognitive Conflict

    • Alan Bell

    Pages 137-154

12. Pre-Algebraic Problem Solving

    • Ferdinando Arzarello

    Pages 155-166

13. Can We Solve the Problem Solving Problem Without Posing the Problem Posing Problem?

    • Judah L. Schwartz

    Pages 167-176

14. Problem Solving in Geometry: From Microworlds to Intelligent Computer Environments

    • Colette Laborde, Jean-Marie Laborde

    Pages 177-192

15. Task Variables in Statistical Problem Solving Using Computers

    • J. Díaz Godino, M.C. Batanero Bernabeu, A. Estepa Castro

    Pages 193-203

16. The Computer as a Problem-Solving Tool; It Gets a Job Done, but Is It Always Appropriate?

    • Joel Hillel

    Pages 205-218

17. Insights into Pupils’ and Teachers’ Activities in Pupil- Controlled Problem-Solving Situations: A Longitudinally Developing Use for Programming by All in a Primary School

    • Chronis Kynigos

    Pages 219-238

18. Cognitive Processes and Social Interactions in Mathematical Investigations

    • João Pedro Ponte, João Filipe Matos

    Pages 239-254

19. Aspects of Computerized Learning Environments Which Support Problem Solving

    • Tommy Dreyfus

    Pages 255-266

20. A General Model of Algebraic Problem Solving for the Design of Interactive Learning Environments

    • Jean-François Nicaud

    Pages 267-285

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.

• Algebra
• Computers in mathematics education
• Computerunterstütztes lernen
• Heuristics
• Heuristik
• Investigations
• Mathematikdidaktik
• Problem-solving
• Teacher education
• Variable
• cognitive psychology
• geometry
• learning
• mathematics
• programming

• Departamento de Educação, Faculdade de Ciências Universidade de Lisboa, Lisboa, Portugal

  João Pedro Ponte, João Filipe Matos

• Secção de Ciências da Educação, Faculdade de Ciências e Tecnologia Universidade Nova de Lisboa, Monte da Caparica, Portugal

  José Manuel Matos

• Instituto de Inovação Educacional, Lisboa, Portugal

  Domingos Fernandes

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