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.

Reasoning by Mathematical Induction in Children's Arithmetic (Advances in Learning and Instruction Series)

Business & Money

Smith, Leslie

SMITH, L.

Education & Reference

Emerald Publishing Limited

Modern British Farce: A Selective Study of the British Farce from Pinero to the Present Day

Literature & Fiction

PALGRAVE~MACMILLAN

Contents: The Nature of Farce; A.W. Pinero and the Court Farces; Ben Travers and the Aldwych Farces; Brian Rix and the Whitehall Farces; Post-Whitehall Farces; Joe Orton; Farce and Contemporary Drama: I; Farce and Contemporary Drama: II; Conclusion; ^R Appendix: a Chronological List of Plays; Notes;  Bibliography; Index

Modern British Farce: A Selective Study of British Farce from Pinero to the Present Day

Dramas & Plays

Rowman & Littlefield Publishers

Originally published in 1954, the purpose of this book was to provide a set of practical exercises for young engineers wishing to apply mathematical principles to problems confronting them in the workshop. The text was designed primarily for use in the Technical Secondary School, the County College, and the Works Training School. It will be of value to anyone with an interest in the development of engineering and educational practice.

Exercises in Workshop Mathematics for Young Engineers

Engineering & Transportation

Engineering

Cambridge University Press

This monograph addresses a central problem in Piaget's work, which is the temporal construction of necessary knowledge. The main argument is that both normative and empirical issues are relevant to a minimally adequate account of the development of modal understanding. This central argument embodies three main claims. One claim is philosophical. Although the concepts of knowledge and necessity are problematic, there is sufficient agreement about their core elements due to the fundamental difference between truth-value and modality. Any account of human rationality has to respect this distinction. The second claim is that this normative distinction is not always respected in psychological research on the origins of knowledge where emphasis is placed on the procedures and methods used to gain good empirical evidence. An account of the initial acquisition of knowledge is not thereby an account of its legitimation in the human mind. The third claim relates to epistemology. Intellectual development is a process in which available knowledge is used in the construction of better knowledge. The monograph identifies features of a modal model of intellectual construction, whereby some form of necessary knowledge is always used. Intellectual development occurs as the reduction of modal errors through the differentiation and coordination of available forms of modal understanding. Piaget's work continues to provide distinctive and intelligible answers to a substantive and outstanding problem.

Necessary Knowledge: Piagetian Perspectives on Constructivism (Essays in Developmental Psychology)

Health, Fitness & Dieting

Mental Health

Psychology Press

Originally published in 1993, this monograph addresses a central problem in Piaget’s work, which is the temporal construction of necessary knowledge. The main argument is that both normative and empirical issues are relevant to a minimally adequate account of the development of modal understanding. This central argument embodies three main claims. One claim is philosophical. Although the concepts of knowledge and necessity are problematic, there is sufficient agreement about their core elements due to the fundamental difference between truth-value and modality. Any account of human rationality has to respect this distinction. The second claim is that this normative distinction is not always respected in psychological research on the origins of knowledge where emphasis is placed on the procedures and methods used to gain good empirical evidence. An account of the initial acquisition of knowledge is not thereby an account of its legitimation in the human mind. The third claim relates to epistemology. Intellectual development is a process in which available knowledge is used in the construction of better knowledge. The monograph identifies features of a modal model of intellectual construction, whereby some form of necessary knowledge is always used. Intellectual development occurs as the reduction of modal errors through the differentiation and coordination of available forms of modal understanding. Piaget’s work continues to provide distinctive and intelligible answers to a substantive and outstanding problem.

Necessary Knowledge: Piagetian Perspectives on Constructivism (Psychology Library Editions: Child Development)

Psychology & Counseling

Routledge

The Cambridge Companion to Piaget

Müller, Ulrich

Carpendale, Jeremy I. M.

History & Criticism

Lucy Lemon - The night of the comet

Children's Books

Action & Adventure

Papierfresserchens MTM-Verlag

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