UID:
almahu_9949890505702882
Umfang:
1 online resource (283 pages)
Ausgabe:
1st ed.
ISBN:
9783030110697
Serie:
ICME-13 Monographs
Anmerkung:
Intro -- Preface -- Contents -- 1 Educational Research on Mathematics-A Short Survey of Its Development in German Speaking Countries -- 1.1 Early Developments -- 1.1.1 The Century of Humboldt -- 1.1.2 'Reformpädagogik' and Its Influence on the Teaching of Mathematics -- 1.1.3 New Ideas on the Teaching of Mathematics at Gymnasium -- 1.2 The Establishment of Didactics of Mathematics as an Academic Discipline -- 1.3 The New Math Reform and Its Consequences -- 1.4 Widening the Perspective -- 1.4.1 Theoretical Foundation of Didactics of Mathematics -- 1.4.2 Socio-Political Perspectives on Mathematics and Mathematics Education -- 1.4.3 The Teaching and Learning of Applications and Modelling -- 1.4.4 Construction of Meaning Within Classroom Interaction -- 1.5 Development of Empirical Research and Recent Stimuli -- 1.5.1 Educational Research on the Learning and Teaching of Mathematics -- 1.5.2 Large-Scale Research -- 1.5.3 Interdisciplinary Research Programs with Collaboration of Mathematics Education -- 1.6 Institutional Structure of Mathematics Education in German-Speaking Countries -- References -- 2 Subject-Matter Didactics -- 2.1 Introduction -- 2.2 Origins and Main Issues of Subject-Matter Didactics -- 2.2.1 The Origins -- 2.2.2 New Developments After 1945 -- 2.2.3 The Concept of Grundvorstellungen -- 2.2.4 Examples of Grundvorstellungen -- 2.2.5 Central Aspects of the Concept of Grundvorstellungen -- 2.3 Numbers, Fractions, Operations and Representations-Grundvorstellungen in Primary School -- 2.3.1 Grundvorstellungen and Levels of Representation -- 2.3.2 GV of Natural Numbers -- 2.3.3 Grundvorstellungen of Fractions -- 2.3.4 Grundvorstellungen of Operations: Subtraction -- 2.3.5 Representations: The Case of Multiplication -- 2.3.6 Summary -- 2.4 Clarity and Rigor in Teaching Calculus.
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2.4.1 Intended Understanding and Students' Concept Images-The Example of Tangents -- 2.4.2 Extreme Value Problems and the Monotonicity Theorem for Intervals -- 2.5 Conclusion -- References -- 3 Design Science and Design Research: The Significance of a Subject-Specific Research Approach -- 3.1 Introduction -- 3.2 Scope of Design Science: Learning Environments and Teaching Experiments -- 3.2.1 Roots of DESIGN SCIENCE -- 3.2.2 Characteristics of Substantial Learning Environments -- 3.2.3 Conducting Teaching Experiments for Improving the Design -- 3.3 Identifiying and Following Key Ideas as a Design Principle -- 3.3.1 Theoretical Reflections on Key Ideas of Mathematics -- 3.3.2 Two Examples of Using Key Ideas -- 3.3.3 Closing Remarks -- 3.4 Describing Number Patterns. an Example for Designing a Learning Environment -- 3.4.1 Stages of the Design Research Project -- 3.4.2 Stage 1: Clarifying the Starting Points -- 3.4.3 Stage 2: Interviews with Students -- 3.4.4 Stage 3: Teaching Experiment in Two Classrooms -- 3.4.5 Stage 4: Evaluation of the Materials in Seven Classrooms -- 3.5 From Design Science to Design Research: Trends and Developments in Germany -- 3.5.1 From DESIGN SCIENCE to DESIGN RESEARCH-Lines of Development in Dortmund -- 3.5.2 Topic-Specific Didactical DESIGN RESEARCH with a Focus on Learning Processes-A Model for DESIGN RESEARCH -- 3.5.3 Illustration of Research Outcomes for a Typical Project: Exploring Individual Schematization Pathways -- 3.5.4 Extensions of DESIGN RESEARCH to Other Subjects, Places, and to Teacher Education -- References -- 4 Mathematical Modelling -- 4.1 Introduction -- 4.2 Developments in Mathematics Modelling for Teaching in Germany -- 4.2.1 Background of the German Modelling Debate -- 4.2.2 Modelling as a Competency and German Educational Standards -- 4.2.3 Implementation of Modelling in Everyday Lessons.
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4.2.4 Implementation of Modelling via Modelling Projects -- 4.3 Modelling Cycles -- 4.3.1 Mathematical Models -- 4.3.2 Different Modelling Cycles -- 4.3.3 Modelling Cycle from Applied Mathematics -- 4.3.4 Didactical or Pedagogical Modeling Cycle -- 4.3.5 Diagnostic Modeling Cycle: Modeling Cycle from a Cognitive Perspective -- 4.3.6 Modelling and Digital Tools -- 4.4 Research on Modelling -- 4.4.1 The Development of Research on Mathematical Modelling in German-Speaking Countries -- 4.4.2 Research Questions in the Field of Mathematical Modelling -- 4.4.3 Multiple Solutions: An Example of Quantitative Research on Modelling -- 4.5 Conclusion and Summary -- References -- 5 Mathematics and Bildung 1810 to 1850 -- 5.1 Mathematics and Bildung at the Time of Humboldt -- 5.2 Bildung and Paideia and Their Presence in Some Undergraduate Programs (Reaction by Michael N. Fried) -- References -- 6 Allgemeinbildung, Mathematical Literacy, and Competence Orientation -- 6.1 Allgemeinbildung, Mathematical Literacy, and Competence Orientation in Mathematics Education in Germany (Rolf Biehler) -- 6.1.1 Introduction: Bildung and Allgemeinbildung in Germany -- 6.1.2 Looking Back into the Late 1960s and 1970s: New Math and Educational Reforms -- 6.1.3 Allgemeinbildung and Mathematics Education in the Mid-1990s-A Snapshot -- 6.1.4 Allgemeinbildung and Mathematical Literacy, Competence Orientation Since the Late 1990s Due to the TIMSS and PISA 'Shocks' -- 6.1.5 Mathematical Literacy, Allgemeinbildung and National Standards for Mathematics in Germany -- 6.1.6 Further Developments -- 6.2 Allgemeinbildung, Mathematical Competencies and Mathematical Literacy: Conflict or Compatibility? (Reaction by Mogens Niss) -- 6.2.1 The Concept of Allgemeinbildung -- 6.2.2 False or Genuine Dichotomies? -- 6.2.3 Conclusion -- References -- 7 Theories of and in Mathematics Education.
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7.1 Introduction -- 7.2 The Role of Theories in Relation to Mathematics Education as a Scientific Discipline: A Discussion in the 1980s -- 7.3 Theories of Mathematics Education (TME): A Program for Developing Mathematics Education as a Scientific Discipline -- 7.4 Post-TME Period -- 7.5 Two Theories, Their Origins and Their Purposes -- 7.5.1 Learning Activity -- 7.5.2 A Semiotic View on Mathematics: Sign Use and Semiotic Game -- 7.6 Reconsidering the TME Program by Networking the Two Theoretical Views -- 7.6.1 Networking Theories Approach -- 7.6.2 Try to Find a Fraction Representing sqrt2 -- 7.6.3 The Semiotic Game Analysis -- 7.6.4 The Learning Activity Analysis -- 7.6.5 Undertaking a Networking Analysis -- 7.7 Conclusions -- References -- 8 Classroom Studies-Sociological Perspectives -- 8.1 Introduction -- 8.2 Interpretative Classroom Research: Origins, Insights, Developments -- 8.2.1 Introduction -- 8.2.2 Theory -- 8.2.3 Practice Relevance -- 8.2.4 Summary-A Reflection on Research Practice -- 8.3 Classroom Research as Part of the Social-Political Agenda -- 8.3.1 Introduction -- 8.3.2 Research Issues -- 8.3.3 Conclusion -- References -- 9 Educational Research on Learning and Teaching Mathematics -- 9.1 Introduction -- 9.2 Interdisciplinary Research -- 9.2.1 Example 1: Problem Solving and Self-regulation -- 9.2.2 Example 2: Proof of Competence and Worked Examples -- 9.3 Mixed-Methods Research -- 9.3.1 Example 3: Understanding and Teaching Experimental Thinking in Mathematics -- 9.3.2 Understanding and Teaching Fractions -- 9.4 Conclusion -- References -- 10 Large-Scale Studies in Mathematics Education Research -- 10.1 Introduction -- 10.2 Large-Scale Assessment: Impact on Mathematics Educational Research and Practice in Germany -- 10.2.1 LSA of Mathematical Competence in Germany: How It Started (TIMSS 1995 and PISA 2000).
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10.2.2 Impact on (Mathematics) Educational Research in Germany -- 10.2.3 Impact on Mathematics Education as a Discipline -- 10.2.4 Impact on Schools and Mathematics Teachers -- 10.3 Consequences from Large-Scale Assessment: An Example of Research on Mathematical Competence in Germany -- 10.3.1 Understanding Mathematical Competence -- 10.3.2 Modeling Mathematical Competence -- 10.3.3 Summary -- 10.4 Consequences from Large-Scale Assessment: Competence Models and Evaluation of Classroom Practice in Austria -- 10.4.1 Development of Large-Scale Assessment in Austria -- 10.4.2 Mathematics Competence Models in Austria -- 10.4.3 Reporting of Assessment of National Education Standards -- 10.4.4 Informal Competence Measurement -- 10.4.5 Summary -- 10.5 Summary and Discussion -- 10.5.1 General Issues of Large-Scale Assessments from an International Perspective -- 10.5.2 Potential Risks for Research and Practice -- References.
Weitere Ausg.:
Print version: Jahnke, Hans Niels Traditions in German-Speaking Mathematics Education Research Cham : Springer International Publishing AG,c2019 ISBN 9783030110680
Sprache:
Englisch
Fachgebiete:
Mathematik
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