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Liane Smith Reasoning by Mathematical Induction in Children's Arithme (Hardback)
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eBay item number:314960730749
Item specifics
- Condition
- Book Title
- Reasoning by Mathematical Induction in Children's Arithmetic
- Publication Name
- Reasoning by Mathematical Induction in Children's Arithmetic
- Title
- Reasoning by Mathematical Induction in Children's Arithmetic
- Contributor
- Liane Smith (Edited by)
- Format
- Hardcover
- EAN
- 9780080441283
- ISBN
- 9780080441283
- Publisher
- Emerald Publishing The Limited
- Genre
- Society & Culture
- Topic
- Children's Learning & Education
- Release Year
- 2002
- Release Date
- 21/08/2002
- Language
- English
- Country/Region of Manufacture
- GB
- Item Height
- 234mm
- Item Length
- 9.4in
- Item Width
- 6.5in
- Item Weight
- 16.8 Oz
- Series
- Advances in Learning and Instruction Ser.
- Publication Year
- 2002
- Type
- Textbook
- Number of Pages
- 184 Pages
About this product
Product Information
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.
Product Identifiers
Publisher
Emerald Publishing The Limited
ISBN-10
0080441289
ISBN-13
9780080441283
eBay Product ID (ePID)
2345236
Product Key Features
Publication Name
Reasoning by Mathematical Induction in Children's Arithmetic
Format
Hardcover
Language
English
Publication Year
2002
Series
Advances in Learning and Instruction Ser.
Type
Textbook
Number of Pages
184 Pages
Dimensions
Item Length
9.4in
Item Width
6.5in
Item Weight
16.8 Oz
Additional Product Features
Lc Classification Number
Qa135.6.S6 2002
Table of Content
Acknowledgements. Summary. Introduction. Mathematical Induction. Mathematical induction, logical deduction, and empirical induction. Poincareacute;'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 Poincareacute;'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.
Copyright Date
2002
Target Audience
Scholarly & Professional
Topic
Education, General, Elementary, Logic, Teaching Methods & Materials / Mathematics
Lccn
2002-075400
Dewey Decimal
372.7/2
Dewey Edition
21
Illustrated
Yes
Genre
Education, Business & Economics, Mathematics, Philosophy
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