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Understanding the Generality of Mathematical Statements
Milena Damrau
其他書名
An Experimental Study at the Transition from School to University
出版Springer Nature, 2023
ISBN36584376349783658437633
URLhttp://books.google.com.hk/books?id=B2L8EAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋Intro -- Foreword -- Acknowledgements -- Abstract -- Contents -- List of Figures -- List of Tables -- 1 Introduction -- 2 Theoretical Background of Mathematical Statements and Proof -- 2.1 Mathematical Statements -- 2.2 Generality in Mathematics -- 2.3 What is Proof? -- 2.3.1 Brief Historical Background -- 2.3.2 Different Views and Usages of the Term Proof -- 2.3.3 Characteristics and Acceptance Criteria for Proof -- 2.4 Reasoning, Argumentation, and Proving in Mathematics Education -- 2.4.1 Definition of and Relation between Reasoning, Argumentation, and Proving -- 2.4.2 Types of Arguments -- 3 State of Research -- 3.1 Understanding Generality and the Role of (Counter-)Examples -- 3.2 Activities Related to Proof -- 3.2.1 Comprehension of Statements -- 3.2.2 Estimation of Truth of Statements -- 3.2.3 Proof Evaluation -- 3.2.4 Proof Comprehension -- 3.2.5 Justification -- 3.2.6 Relation Between Activities -- 3.3 Resources -- 4 Derivation of Research Questions -- 5 Methodology -- 5.1 Research Design -- 5.1.1 Justification of the Research Approach -- 5.1.2 Overview of the Research Process -- 5.2 Data Collection -- 5.2.1 Setting -- 5.2.2 Participants -- 5.2.3 Structure of the Experiment -- 5.3 Instruments -- 5.3.1 Selection of Statements and Arguments -- 5.3.2 Conviction of the Truth of Statements -- 5.3.3 Comprehension of Arguments -- 5.3.4 Justification: Students' Proof Schemes -- 5.3.5 Understanding the Generality of Statements -- 5.3.6 Cognitive Reflection Test -- 5.3.7 Demographics -- 5.4 Data Analysis -- 5.4.1 Statistical Analysis -- 5.4.2 Content Analysis -- 5.4.3 Conviction of the Truth of Statements -- 5.4.4 Comprehension of Arguments -- 5.4.5 Justification: Students' Proof Schemes -- 5.4.6 Understanding the Generality of Statements -- 6 Results -- 6.1 Preliminary Analysis -- 6.2 Conviction of the Truth of Statements.