E-Book, Englisch, 184 Seiten
Janssens / Verschaffel The Illusion of Linearity
1. Auflage 2007
ISBN: 978-0-387-71164-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
From Analysis to Improvement
E-Book, Englisch, 184 Seiten
ISBN: 978-0-387-71164-5
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.
Autoren/Hrsg.
Weitere Infos & Material
1;Contents;6
2;Contributing Authors;7
3;Foreword;8
4;Acknowledgments;12
5;Chapter 1 A WIDESPREAD PHENOMENON;14
5.1;1. INTRODUCTION;14
5.2;2. PROPERTIES AND REPRESENTATIONS OF LINEARITY: A CONCEPTUAL ANALYSIS;16
5.3;3. MANIFESTATIONS OF OVER-RELIANCE ON LINEARITY;18
5.3.1;3.1 Improper applications of linearity while solving arithmetic word problems;19
5.3.2;3.2 Over-reliance on linearity in graphical environments;23
5.3.3;3.3 Improper application of linearity in probabilistic situations;24
5.3.4;3.4 Number patterns, algebra, and calculus;27
5.3.5;3.5 The overuse of linearity in numerical estimation;29
5.4;4. THE CASE OF GEOMETRY;29
5.4.1;4.1 The effect of a linear enlargement (reduction) on area and volume;31
5.4.2;4.2 Introduction to the research program;34
6;Chapter 2 IN SEARCH OF EMPIRICAL EVIDENCE;36
6.1;1. INTRODUCTION;36
6.2;2. STUDY 1;37
6.3;3. STUDY;44
6.4;4. DISCUSSION;50
7;Chapter 3 SEARCHING FOR EXPLANATIONS: A SERIES OF FOLLOW- UP STUDIES;52
7.1;1. INTRODUCTION;52
7.2;2. FOLLOW-UP STUDY 1: EFFECTS OF METACOGNITIVE AND VISUAL SCAFFOLDS;53
7.3;3. FOLLOW-UP STUDY 2: EFFECTS OF PROBLEM FORMULATION ;63
7.4;4. FOLLOW-UP STUDY 3: EFFECTS OF AUTHENTIC CONTEXTS AND DRAWING ACTIVITY;68
7.5;5. FOLLOW-UP STUDY 4: FROM INDIRECT TO DIRECT MEASURES ;85
7.6;6. GENERAL SUMMARY AND DISCUSSION;96
8;Chapter 4 AN IN- DEPTH INVESTIGATION;99
8.1;1. INTRODUCTION;99
8.2;2. METHOD;100
8.3;3. RESULTS;105
8.3.1;3.1 Two sample interviews;106
8.3.2;3.2 Overview of students’ reactions;111
8.3.3;3.3 Phase 1: Solving the word problem;111
8.3.4;3.4 Phase 2: Reactions to the weak form of cognitive conflict;113
8.3.5;3.5 Phase 3: Reactions to the argumentation of a fictitious peer;114
8.3.6;3.6 Phase 4: Reactions to the solution process of a fictitious peer;115
8.3.7;3.7 Phase 5: Reactions to the explicit link with area measurement;117
8.4;4. DISCUSSION;117
9;Chapter 5 A TEACHING EXPERIMENT;121
9.1;1. INTRODUCTION;121
9.2;2. DESIGNING A LEARNING ENVIRONMENT;122
9.2.1;2.1 Overview of the lesson series;122
9.2.2;2.2 General design principles;129
9.3;3. RESEARCH METHOD;131
9.4;4. RESEARCH QUESTIONS AND HYPOTHESES;132
9.5;5. RESULTS;132
9.6;6. CONCLUSIONS AND DISCUSSION;136
10;Chapter 6 STEPPING OUTSIDE THE CLASSROOM;138
10.1;1. INTRODUCTION;138
10.2;2. THEORETICAL BACKGROUND;139
10.3;3. METHODOLOGY;142
10.4;4. RESULTS ;146
10.5;5. CONCLUSIONS AND DISCUSSION;150
11;Chapter 7 PSYCHOLOGICAL AND EDUCATIONAL ANALYSIS;153
11.1;1. INTRODUCTION;153
11.2;2. SEARCHING FOR THE ROOTS OF THE OVERUSE OF LINEARITY;154
11.2.1;2.1 Linearity, intuitiveness and everyday life situations;154
11.2.2;2.2 The effects of schooling;158
11.2.3;2.3 Content-specific effects;160
11.2.4;2.4 Perspectives for further research;161
11.3;3. RECOMMENDATIONS FOR THE IMPROVEMENT OF EDUCATIONAL PRACTICE;163
11.3.1;3.1 Concrete suggestions for educational practice;164
11.3.2;3.2 A more comprehensive instructional approach;169
12;References;175
13;Index;189
