Reasoning by Mathematical Induction in Children's Arithmetic

Erscheinungsjahr 2002
ISBN: 978-0-08-044128-3
Verlag: Pergamon Press

Buch, Englisch, 184 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 452 g

Reihe: Advances in Learning and Instruction

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.

Autoren/Hrsg.

Smith, Leslie

Smith, Liane

Fachgebiete

• Sozialwissenschaften Pädagogik Pädagogik Pädagogische Psychologie
• Interdisziplinäres Wissenschaften Wissenschaften Interdisziplinär Wirtschafts- und Sozialwissenschaften
• Sozialwissenschaften Psychologie Allgemeine Psychologie Entwicklungspsychologie Pädagogische Psychologie
• Sozialwissenschaften Psychologie Allgemeine Psychologie Entwicklungspsychologie Kinder- und Jugendpsychologie

Inhaltsverzeichnis

Acknowledgements. Summary. Introduction. Mathematical Induction. Mathematical induction, logical deduction, and empirical induction. Poincaré'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 Poincaré'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.