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Reasoning by Mathematical Induction in Children's Arithmetic (Advances in Learning and Instruction)
Reasoning by Mathematical Induction in Children's Arithmetic - Advances in Learning and Instruction Author:Leslie Smith . How do children understand reasoning by mathematical induction? Mathematical induction - Poincaré'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 lo... more »gical deduction and empirical induction, and yet is different from both. In a major study forty 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. The present study is an adaptation with a sample of one hundred children aged 5-7 years in school Years 1 and 2. There is convincing evidence that children can reason by mathematical induction on tasks based on iterative addition and that their inferences were« less