Learning How Children Process Mathematical Problems

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This book is the result of three years of qualitative research observation conducted in a classroom. Grade five students were observed during their extended mathematics problem-solving class. Data was audio-taped, video-recorded, and analyzed to isolate the language of problem solving. The children work with multi-step mathematical problems that are well-designed. Insights gleaned from the analysis showed the different ways that children interpret what they understand in mathematics. It also shows how they explain their problem-solving strategies to each other. The study shows teachers and teacher-educators positive ways of assisting the problem-solving process. Through multiple examples of hands-on instruction, manipulatives-based learning environments, and well-designed classroom settings, teachers and teacher-educators can help build positive mathematical experiences for young children. The data also shows that students work in a space that requires high concentration and abstraction, and it brings out the fat that youngsters need to communicate about what they’re learning.


“This book draws upon the works of Halliday and Vygotsky to illuminate the domain-specific and culturally embedded nature of the language of problem solving among young children….Dr. Klein addresses this sophisticated topic in an accessible, even playful, manner as she explores the evolving language of grade five problem solvers and provides the reader with an insider’s view of their individual strategies and discourse patterns….While this work is sophisticated in content and contributes to the research base in problem solving discourse, Klein’s vivid descriptions of classroom interactions and experiences make this book accessible to classroom teachers. This project is a beautiful example of the recursive process of theory informing practice, which in turn informs theory. From the perspective of one committed to practitioner-based reform in mathematics education through innovations that require us to think outside the box, Klein’s book is a valuable resource and a step in the right direction.” – Dr. Cynthia Marie Smith, Associate Director, School of Education, SUNY Fredonia

Table of Contents

Table of Contents:
Preface; Introduction
1. Prologue
2. Strands of Learning in the Classroom
3. A Conceptual Framework and Review of the Literature
4. Research Site and Problem Solving Program
5. Classroom Episodes
6. Analysis and Interpretation
7. Conclusion
Epilogue: A Confirmation
Bibliography; Index