an icon showing a delivery van Shulph delivers to United Kingdom.
Book cover for Reasoning by Mathematical Induction in Children's Arithmetic, a book by Liane Smith Book cover for Reasoning by Mathematical Induction in Children's Arithmetic, a book by Liane Smith

Reasoning by Mathematical Induction in Children's Arithmetic

2002 ᛫


The central argument that Leslie Smith makes in this study is that reasoning by mathematical induction develops during childhood. The basis for this claim is a study conducted with children aged five to seven years in school years one and two.

Powered by RoundRead®
This book leverages Shulph’s RoundRead system - buy the book once and read it on both physical book and on up to 5 of your personal devices. With RoundRead, you’re 4 times more likely to read this book cover-to-cover and up to 3 times faster.
Buy Book + eBook £127.49
Add to Read List


Instant access to ebook. Print book delivers in 5 - 10 working days.

Summary


How do children understand reasoning by mathematical induction? Mathematical induction - Poincare's reasoning by recurrence - is a standard form of inference with two distinctive properties. One is its necessity. The other is its universality or inference from particular to general. This means that mathematical induction is similar to both logical deduction and empirical induction, and yet is different from both. In a major study 40 years ago, Inhelder and Piaget set out two conclusions about the development of this type of reasoning in advance of logical deduction during childhood. This developmental sequence has gone unremarked in research on cognitive development. This study is an adaptation with a sample of 100 hundred children aged five-seven years in school years one and two. It reveals evidence that children can reason by mathematical induction on tasks based on iterative addition and that their inferences were made by necessity. According to the study the main educational implication is clear: young children can carry out iterative actions on actual objects with a view to reasoning about abstract objects such as numbers.

Table of contents

  • Acknowledgements. Summary. Introduction. Mathematical Induction. Mathematical induction, logical deduction, and empirical induction. Poincare's analysis of mathematical induction. Frege's and Russell's analysis of mathematical induction. Critical review. Conclusion. Reasoning by Mathematical Induction: Piaget's Critique. Piaget on the analysis of Frege and Russell. Piaget on Poincare's analysis. Inhelder and Piaget's (1963) study. Conclusion. Research on the Development of Children's Reasoning. Reasoning. Deduction. Induction. Mathematical induction. Reasoning, Reasons and Responses. Critical method. Rationale for a critical method. Children's Reasoning by Mathematical Induction. Method. Results: statistical analysis of responses. Results: epistemological analysis of reasons for responses. Conservation task. Teams tasks. Recurrence task. Discussion. Hypotheses. Developmental mechanism. Educational Implications in a Constructivist Model of Education. Piaget's model of education. Educational implications in a constructivist pedagogy. Commentary by Damon Berridge. References. Boxes, figures, tables.