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E-raamat: Does Mathematical Study Develop Logical Thinking?: Testing The Theory Of Formal Discipline

(Univ Of Bath, Uk), (Loughborough Univ, Uk)
  • Formaat: 204 pages
  • Ilmumisaeg: 06-Sep-2016
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786340702
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  • Formaat: 204 pages
  • Ilmumisaeg: 06-Sep-2016
  • Kirjastus: World Scientific Europe Ltd
  • Keel: eng
  • ISBN-13: 9781786340702

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For centuries, educational policymakers have believed that studying mathematics is important, in part because it develops general thinking skills that are useful throughout life. This 'Theory of Formal Discipline' (TFD) has been used as a justification for mathematics education globally. Despite this, few empirical studies have directly investigated the issue, and those which have showed mixed results.Does Mathematical Study Develop Logical Thinking? describes a rigorous investigation of the TFD. It reviews the theory's history and prior research on the topic, followed by reports on a series of recent empirical studies. It argues that, contrary to the position held by sceptics, advanced mathematical study does develop certain general thinking skills, however these are much more restricted than those typically claimed by TFD proponents.Perfect for students, researchers and policymakers in education, further education and mathematics, this book provides much needed insight into the theory and practice of the foundations of modern educational policy.
Acknowledgements vii
List of Figures
xiii
List of Tables
xv
List of Abbreviations
xvii
1 The Theory of Formal Discipline
1(26)
1.1 The TFD Today
5(8)
1.2 Transfer and the Educational Psychologists
13(12)
1.3 Summary and Plan
25(2)
2 Investigating the Theory of Formal Discipline
27(26)
2.1 Measuring Reasoning
27(13)
2.1.1 Syllogisms and belief bias
29(3)
2.1.2 Conditional inference
32(6)
2.1.3 Wason's selection task
38(2)
2.2 Incorrect Norms? And Criticisms of Transfer Research
40(6)
2.3 A Strategy for Testing the Theory of Formal Discipline
46(5)
2.4 Plan for the Remainder of the Book
51(2)
3 Cross-Sectional Differences in Reasoning Behaviour
53(16)
3.1 Conditional Inference and Syllogistic Reasoning
54(7)
3.2 The Wason Selection Task
61(8)
4 Longitudinal Development in Conditional Reasoning
69(20)
4.1 Does Studying A Level Mathematics Develop Conditional Reasoning?
70(7)
4.2 Do Mathematics Students Respond Defectively to the Truth Table Task?
77(3)
4.3 Post-compulsory Mathematical Study and Reasoning Development in Cyprus
80(6)
4.4 Summary
86(3)
5 The Modus Tollens Inference and Mathematics
89(10)
5.1 Modus Tollens and Advanced Mathematics
89(6)
5.2 Modus Tollens Development During Advanced Mathematical Study
95(2)
5.3 Summary
97(2)
6 Conditional Inference Across the Mathematical Lifespan
99(6)
7 Why Would Studying Advanced Mathematics Develop Conditional Reasoning?
105(12)
7.1 `Only If' in Mathematical English
107(2)
7.2 Reasoning with `If... Then' and `Only If'
109(8)
8 Summary and Conclusions
117(14)
8.1 Evidence Presented in the Book
117(5)
8.2 Does Studying Mathematics Actually Improve Logical Thinking?
122(2)
8.3 The `Real World' Objection
124(5)
8.4 Concluding Remarks
129(2)
Appendix A Reasoning Tasks
131(14)
Appendix B Abstract Conditional Inference Task
145(6)
Appendix C Thematic Conditional Inference Task
151(4)
Appendix D Abstract Syllogism Task
155(2)
Appendix E Thematic Syllogism Task
157(2)
Appendix F Abstract Truth Table Task
159(6)
Appendix G The Cypriot Curriculum
165(4)
G.1 Low-Intensity Curriculum: Year 1
165(1)
G.2 Low-Intensity Curriculum: Year 2
165(1)
G.3 High-Intensity Curriculum: Year 1
166(1)
G.4 High-Intensity Curriculum: Year 2
167(2)
Appendix H Proof Comprehension
169(4)
H.1 The Proof
169(1)
H.2 Proof Comprehension Items
169(4)
Bibliography 173(10)
Index 183