Understanding the Generality of Mathematical Statements : An Experimental Study at the Transition from School to University

• Autore: Damrau Milena
• Pubblicazione: Wiesbaden : , : Springer Vieweg. in Springer Fachmedien Wiesbaden GmbH, , 2024; ©2023
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (222 pages)
• Nota di contenuto: 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. ; 6.2.1 Estimation of Truth -- 6.2.2 Proof Evaluation Regarding Conviction -- 6.3 Comprehension of Arguments -- 6.4 Justification: Students' Proof Schemes -- 6.5 Understanding the Generality of Statements -- 6.6 Analysis of Missing Values -- 6.7 Summary of Main Results -- 6.7.1 Influence of the Type of Argument -- 6.7.2 Influence of the Type of Statement -- 6.7.3 Students' Understanding of Generality and the Relation to Proof -- 6.7.4 Predictive Power of Control Variables -- 7 Discussion -- 7.1 Interpretation -- 7.1.1 Estimation of Truth and Proof Evaluation Regarding Conviction -- 7.1.2 Comprehension of Arguments -- 7.1.3 Justification: Students' Proof Schemes -- 7.1.4 Understanding the Generality of Statements -- 7.2 Reflections and Limitations -- 7.2.1 The Adapted Framework on Proof-Related Activities -- 7.2.2 Overall Research Design -- 7.2.3 Conceptualization and Operationalization -- 7.2.4 Number, Selection, and Order of Statements -- 7.2.5 Open-Ended Questions and Content Analysis -- 7.2.6 Control Variables -- 7.2.7 Sample -- 7.3 Implications for the Learning and Teaching of Proof … -- 7.4 Directions for Future Research -- 7.4.1 Further Investigating Students' Understanding of the Generality of Statements -- 7.4.2 Self-Reported Data and Reality -- 7.4.3 Question Order Effects -- 8 Conclusions -- 1 References.
• Titolo autorizzato: Understanding the Generality of Mathematical Statements
• ISBN: 3-658-43763-4
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910829579403321
• Lo trovi qui: Univ. Federico II
• Serie: Bielefelder Schriften Zur Didaktik der Mathematik Series