Acknowledgements |
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vii | |
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xiii | |
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xv | |
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xvii | |
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1 The Theory of Formal Discipline |
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1 | (26) |
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5 | (8) |
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1.2 Transfer and the Educational Psychologists |
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13 | (12) |
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25 | (2) |
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2 Investigating the Theory of Formal Discipline |
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27 | (26) |
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27 | (13) |
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2.1.1 Syllogisms and belief bias |
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29 | (3) |
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2.1.2 Conditional inference |
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32 | (6) |
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2.1.3 Wason's selection task |
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38 | (2) |
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2.2 Incorrect Norms? And Criticisms of Transfer Research |
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40 | (6) |
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2.3 A Strategy for Testing the Theory of Formal Discipline |
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46 | (5) |
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2.4 Plan for the Remainder of the Book |
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51 | (2) |
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3 Cross-Sectional Differences in Reasoning Behaviour |
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53 | (16) |
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3.1 Conditional Inference and Syllogistic Reasoning |
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54 | (7) |
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3.2 The Wason Selection Task |
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61 | (8) |
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4 Longitudinal Development in Conditional Reasoning |
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69 | (20) |
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4.1 Does Studying A Level Mathematics Develop Conditional Reasoning? |
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70 | (7) |
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4.2 Do Mathematics Students Respond Defectively to the Truth Table Task? |
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77 | (3) |
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4.3 Post-compulsory Mathematical Study and Reasoning Development in Cyprus |
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80 | (6) |
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86 | (3) |
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5 The Modus Tollens Inference and Mathematics |
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89 | (10) |
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5.1 Modus Tollens and Advanced Mathematics |
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89 | (6) |
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5.2 Modus Tollens Development During Advanced Mathematical Study |
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95 | (2) |
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97 | (2) |
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6 Conditional Inference Across the Mathematical Lifespan |
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99 | (6) |
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7 Why Would Studying Advanced Mathematics Develop Conditional Reasoning? |
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105 | (12) |
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7.1 `Only If' in Mathematical English |
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107 | (2) |
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7.2 Reasoning with `If... Then' and `Only If' |
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109 | (8) |
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8 Summary and Conclusions |
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117 | (14) |
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8.1 Evidence Presented in the Book |
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117 | (5) |
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8.2 Does Studying Mathematics Actually Improve Logical Thinking? |
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122 | (2) |
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8.3 The `Real World' Objection |
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124 | (5) |
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129 | (2) |
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Appendix A Reasoning Tasks |
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131 | (14) |
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Appendix B Abstract Conditional Inference Task |
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145 | (6) |
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Appendix C Thematic Conditional Inference Task |
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151 | (4) |
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Appendix D Abstract Syllogism Task |
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155 | (2) |
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Appendix E Thematic Syllogism Task |
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157 | (2) |
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Appendix F Abstract Truth Table Task |
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159 | (6) |
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Appendix G The Cypriot Curriculum |
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165 | (4) |
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G.1 Low-Intensity Curriculum: Year 1 |
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165 | (1) |
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G.2 Low-Intensity Curriculum: Year 2 |
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165 | (1) |
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G.3 High-Intensity Curriculum: Year 1 |
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166 | (1) |
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G.4 High-Intensity Curriculum: Year 2 |
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167 | (2) |
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Appendix H Proof Comprehension |
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169 | (4) |
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169 | (1) |
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H.2 Proof Comprehension Items |
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169 | (4) |
Bibliography |
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173 | (10) |
Index |
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183 | |