Understanding the Generality of Mathematical Statements An Experimental Study at the Transition from School to University
| Autor principal: | |
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| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Wiesbaden :
Springer Vieweg. in Springer Fachmedien Wiesbaden GmbH
2024.
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| Edición: | 1st ed |
| Colección: | Bielefelder Schriften Zur Didaktik der Mathematik Series
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| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009799919506719 |
Tabla de Contenidos:
- 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.
