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Table of Contents
Intro
Foreword
Preface
Abstract
Zusammenfassung
Contents
1 Introduction
1.1 Motivation
1.2 Research on the Topic of Epistemological Beliefs
1.2.1 Epistemological Beliefs-a Clarification of Terms
1.2.2 History of Research on Epistemological Beliefs
1.2.3 Relevance of This Topic
1.3 The Research Project LeScEd
1.3.1 Overview of All Publications from Sub-Project #3 of LeScEd
2 Interviews Regarding Epistemological Beliefs
2.1 Interview Study-Certainty of Mathematical Knowledge
2.1.1 Introduction
2.1.2 The Structure of Epistemological Beliefs
2.1.3 Certainty of Knowledge
2.1.4 Methodology
2.1.5 Results
2.1.6 Discussion and Outlook
2.2 "Is Mathematical Knowledge Certain?-Are You Sure?"
2.2.1 Introduction
2.2.2 The Classroom Discussion
2.2.3 Conclusion
3 Measuring Mathematical Critical Thinking
3.1 Mathematical Critical Thinking: Construction and Validation of a Test
3.1.1 Motivation
3.1.2 Measuring Critical Thinking
3.1.3 Rationale
3.1.4 Theoretical Background
3.1.5 Constructing a Test for Mathematical Critical Thinking
3.1.6 Validating the Test for Mathematical Critical Thinking
3.1.7 Conclusion and Discussion
3.1.8 Additional Remarks and Future Prospects
3.2 Mathematical Critical Thinking: A Question of Dimensionality
3.2.1 Motivation and Additional Theoretical Background
3.2.2 Matching the CT Test to the Two Models of CT
3.2.3 Methodology
3.3 Results
3.3.1 Discussion
3.4 Mathematical Critical Thinking: Correlations with Other Constructs
3.4.1 Correlations Between Critical Thinking and Problem Solving
3.4.2 Correlations Between Critical Thinking and Mathematical Reasoning, Argumentation, and Proof
3.4.3 Correlations Between Critical Thinking and Metacognition
3.4.4 Discussion of the Three Correlation Studies
References
4 Critical Thinking and Epistemological Beliefs of Pre-service Teachers
4.1 Background
4.1.1 Structure of the Belief Dimension
4.1.2 Structure of the Knowledge Dimension
4.2 The Study
4.2.1 Methodology
4.2.2 Results
4.2.3 Discussion
4.3 Appendix: Sample Items of the Mathematical Critical Thinking Test
References
5 Epistemological Beliefs and Critical Thinking in Pre-Service Teacher Education
5.1 Background
5.1.1 Theoretical Background
5.2 The Study
5.2.1 Goals and Research Questions
5.2.2 Methodology
5.2.3 Instruments
5.2.4 Results
5.2.5 Discussion
References
6 Inductive and Deductive Justification of Knowledge
6.1 Background
6.1.1 Introduction
6.1.2 Theoretical Background
6.1.3 Justification of Knowledge
6.2 Study 1
6.2.1 Results of the Interview Study
6.2.2 Interpretation with Respect to the Category of Epistemological Judgments
6.3 Study 2
6.3.1 Results of the Extended Questionnaire Study
6.4 Discussion
6.4.1 Discussion of Study 1
6.4.2 Discussion of Study 2.
Foreword
Preface
Abstract
Zusammenfassung
Contents
1 Introduction
1.1 Motivation
1.2 Research on the Topic of Epistemological Beliefs
1.2.1 Epistemological Beliefs-a Clarification of Terms
1.2.2 History of Research on Epistemological Beliefs
1.2.3 Relevance of This Topic
1.3 The Research Project LeScEd
1.3.1 Overview of All Publications from Sub-Project #3 of LeScEd
2 Interviews Regarding Epistemological Beliefs
2.1 Interview Study-Certainty of Mathematical Knowledge
2.1.1 Introduction
2.1.2 The Structure of Epistemological Beliefs
2.1.3 Certainty of Knowledge
2.1.4 Methodology
2.1.5 Results
2.1.6 Discussion and Outlook
2.2 "Is Mathematical Knowledge Certain?-Are You Sure?"
2.2.1 Introduction
2.2.2 The Classroom Discussion
2.2.3 Conclusion
3 Measuring Mathematical Critical Thinking
3.1 Mathematical Critical Thinking: Construction and Validation of a Test
3.1.1 Motivation
3.1.2 Measuring Critical Thinking
3.1.3 Rationale
3.1.4 Theoretical Background
3.1.5 Constructing a Test for Mathematical Critical Thinking
3.1.6 Validating the Test for Mathematical Critical Thinking
3.1.7 Conclusion and Discussion
3.1.8 Additional Remarks and Future Prospects
3.2 Mathematical Critical Thinking: A Question of Dimensionality
3.2.1 Motivation and Additional Theoretical Background
3.2.2 Matching the CT Test to the Two Models of CT
3.2.3 Methodology
3.3 Results
3.3.1 Discussion
3.4 Mathematical Critical Thinking: Correlations with Other Constructs
3.4.1 Correlations Between Critical Thinking and Problem Solving
3.4.2 Correlations Between Critical Thinking and Mathematical Reasoning, Argumentation, and Proof
3.4.3 Correlations Between Critical Thinking and Metacognition
3.4.4 Discussion of the Three Correlation Studies
References
4 Critical Thinking and Epistemological Beliefs of Pre-service Teachers
4.1 Background
4.1.1 Structure of the Belief Dimension
4.1.2 Structure of the Knowledge Dimension
4.2 The Study
4.2.1 Methodology
4.2.2 Results
4.2.3 Discussion
4.3 Appendix: Sample Items of the Mathematical Critical Thinking Test
References
5 Epistemological Beliefs and Critical Thinking in Pre-Service Teacher Education
5.1 Background
5.1.1 Theoretical Background
5.2 The Study
5.2.1 Goals and Research Questions
5.2.2 Methodology
5.2.3 Instruments
5.2.4 Results
5.2.5 Discussion
References
6 Inductive and Deductive Justification of Knowledge
6.1 Background
6.1.1 Introduction
6.1.2 Theoretical Background
6.1.3 Justification of Knowledge
6.2 Study 1
6.2.1 Results of the Interview Study
6.2.2 Interpretation with Respect to the Category of Epistemological Judgments
6.3 Study 2
6.3.1 Results of the Extended Questionnaire Study
6.4 Discussion
6.4.1 Discussion of Study 1
6.4.2 Discussion of Study 2.