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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. , 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. , 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. , 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). , 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

Schlagwort(e): Electronic books. ; Aufsatzsammlung ; Konferenzschrift ; History ; Aufsatzsammlung ; Konferenzschrift

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URL: Volltext  (kostenfrei)

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Umfang: VIII, 278 p. 68 illus., 39 illus. in color. , online resource.

Ausgabe: 1st ed. 2019.

ISBN: 9783030110697

Serie: ICME-13 Monographs,

Inhalt: This open access book shares revealing insights into the development of mathematics education research in Germany from 1976 (ICME 3 in Karlsruhe) to 2016 (ICME 13 in Hamburg). How did mathematics education research evolve in the course of these four decades? Which ideas and people were most influential, and how did German research interact with the international community? These questions are answered by scholars from a range of fields and in ten thematic sections: (1) a short survey of the development of educational research on mathematics in German speaking countries (2) subject-matter didactics, (3) design science and design research, (4) modelling, (5) mathematics and Bildung 1810 to 1850, (6) Allgemeinbildung, Mathematical Literacy, and Competence Orientation (7) theory traditions, (8) classroom studies, (9) educational research and (10) large-scale studies. During the time span presented here, profound changes took place in German-speaking mathematics education research. Besides the traditional fields of activity like subject-matter didactics or design science, completely new areas also emerged, which are characterized by various empirical approaches and a closer connection to psychology, sociology, epistemology and general education research. Each chapter presents a respective area of mathematics education in Germany and analyzes its relevance for the development of the research community, not only with regard to research findings and methods but also in terms of interaction with the educational system. One of the central aspects in all chapters concerns the constant efforts to find common ground between mathematics and education. In addition, readers can benefit from this analysis by comparing the development shown here with the mathematical education research situation in their own country.

Anmerkung: Preface -- Chapter 1 - Educational Research on Mathematics - a Short Survey of its Development in German Speaking Countries -- Chapter 2 - Subject-matter Didactics -- Chapter 3 - Design Science and Design Research: the Significance of a Subject-specific Research Approach -- Chapter 4 - Mathematical Modelling -- Chapter 5 - Mathematics and Bildung 1810 to 1850 -- Chapter 6 - Allgemeinbildung, Mathematical Literacy, and Competence Orientation -- Chapter 7 - Theories of and in mathematics education -- Chapter 8 - Classroom Studies – Sociological Perspectives -- Chapter 9 - Educational Research on Learning and Teaching Mathematics -- Chapter 10 - Large-Scale Studies in Mathematics Education Research.

In: Springer eBooks

Weitere Ausg.: Printed edition: ISBN 9783030110680

Weitere Ausg.: Printed edition: ISBN 9783030110703

Sprache: Englisch

DOI: 10.1007/978-3-030-11069-7

URL: https://doi.org/10.1007/978-3-030-11069-7