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Intro; Foreword; Preface; Table of Contents; List of Figures; List of Tables; 1 Introduction; 2 Mathematical literacy in statistics; 2.1 The mathematizing and reflective sides of mathematical literacy; 2.2 Mathematical literacy in statistics; 2.2.1 Mathematizing as a statistical activity; 2.2.2 Mathematical literacy as an integrating framework for statistical literacy and reasoning; 2.3 Aims and goals of the mathematizing side of mathematical literacy; 2.3.1 Two mathematizing aims; 2.3.2 The mathematizing goal of mastering mathematizing activities
2.3.3 The mathematizing goal of developing mathematizing concepts2.4 Aims and goals of the reflective side of mathematical literacy; 2.4.1 Two reflective aims; 2.4.2 The reflective goal of mastering reflective activities; 2.4.3 The specification gap of reflection; 2.5 The concept of measure as the central learning content; 3 The mathematizing concept of measure; 3.1 A conceptualization of measure; 3.1.1 Measures and the mathematizing concept of average; 3.1.2 Conceptualizing measure; 3.2 Learners' intuitive situative measures; 3.3 Measures and Informal Statistical Inference
4 Developing concepts and mastering activities4.1 Learning-theoretical background; 4.1.1 The relationship between concepts and activities; 4.1.2 The importance of context; 4.1.3 Defining this thesis' central theoretical constructs; 4.2 The development of the mathematizing concept of measure; 4.2.1 A general learning trajectory towards the mathematizing goals; 4.2.2 The realization gap of reflection; 5 Summary and research questions; 6 Methodology; 6.1 Research framework; 6.1.1 Topic-specific Didactical Design Research; 6.1.2 Educational Reconstruction of reflective concepts
6.2 Methods of data collection6.3 Methods of data analysis; 7 Developing Typical; 7.1 Design of a teaching-learning arrangement for Cycle III; 7.1.1 Design principles for initiating mathematizing activity; 7.1.2 The Typical Antarctic Temperatures Problem; 7.1.3 The Arctic Sea Ice Problem; 7.2 Empirical reconstruction of students developing Typical; 7.2.1 Maria and Natalie: Developing with a focus on structuring; 7.2.2 Overarching effects for Maria and Natalie's learning processes; 7.2.3 Quanna and Rebecca: Developing with a focus on formalizing
7.2.4 Overarching effects for Quanna and Rebecca's learning processes7.3 Students' development of measures in Cycle III; 7.3.1 Connections to general measures; 7.3.2 The broadening of the contextual neighborhood; 7.3.3 Differences in richness of activity; 7.3.4 Unforeseen effects of design principles; 8 Students' reflective concepts; 8.1 Design of a teaching-learning arrangement for Cycle IV; 8.1.1 Refined design principles for initiating reflective activities; 8.1.2 The Antarctic Temperatures problem; 8.1.3 The Arctic Sea Ice Problem
2.3.3 The mathematizing goal of developing mathematizing concepts2.4 Aims and goals of the reflective side of mathematical literacy; 2.4.1 Two reflective aims; 2.4.2 The reflective goal of mastering reflective activities; 2.4.3 The specification gap of reflection; 2.5 The concept of measure as the central learning content; 3 The mathematizing concept of measure; 3.1 A conceptualization of measure; 3.1.1 Measures and the mathematizing concept of average; 3.1.2 Conceptualizing measure; 3.2 Learners' intuitive situative measures; 3.3 Measures and Informal Statistical Inference
4 Developing concepts and mastering activities4.1 Learning-theoretical background; 4.1.1 The relationship between concepts and activities; 4.1.2 The importance of context; 4.1.3 Defining this thesis' central theoretical constructs; 4.2 The development of the mathematizing concept of measure; 4.2.1 A general learning trajectory towards the mathematizing goals; 4.2.2 The realization gap of reflection; 5 Summary and research questions; 6 Methodology; 6.1 Research framework; 6.1.1 Topic-specific Didactical Design Research; 6.1.2 Educational Reconstruction of reflective concepts
6.2 Methods of data collection6.3 Methods of data analysis; 7 Developing Typical; 7.1 Design of a teaching-learning arrangement for Cycle III; 7.1.1 Design principles for initiating mathematizing activity; 7.1.2 The Typical Antarctic Temperatures Problem; 7.1.3 The Arctic Sea Ice Problem; 7.2 Empirical reconstruction of students developing Typical; 7.2.1 Maria and Natalie: Developing with a focus on structuring; 7.2.2 Overarching effects for Maria and Natalie's learning processes; 7.2.3 Quanna and Rebecca: Developing with a focus on formalizing
7.2.4 Overarching effects for Quanna and Rebecca's learning processes7.3 Students' development of measures in Cycle III; 7.3.1 Connections to general measures; 7.3.2 The broadening of the contextual neighborhood; 7.3.3 Differences in richness of activity; 7.3.4 Unforeseen effects of design principles; 8 Students' reflective concepts; 8.1 Design of a teaching-learning arrangement for Cycle IV; 8.1.1 Refined design principles for initiating reflective activities; 8.1.2 The Antarctic Temperatures problem; 8.1.3 The Arctic Sea Ice Problem