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

• Superior document: Bielefelder Schriften Zur Didaktik der Mathematik Series ; v.15
• Author: Damrau, Milena.
• Place / Publishing House: Wiesbaden : : Springer Vieweg. in Springer Fachmedien Wiesbaden GmbH,, 2024.; ©2023.
• Year of Publication: 2024
• Edition: 1st ed.
• Language: English
• Series: Bielefelder Schriften Zur Didaktik der Mathematik Series
• Physical Description: 1 online resource (222 pages)

Table of Contents

• 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.