Connecting Mathematics and Mathematics Education : (Record no. 306693)
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| 000 -LEADER | |
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| fixed length control field | 08567nam a22004213i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6422808 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240122001308.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 231124s2020 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783030615703 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9783030615697 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6422808 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6422808 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1231606432 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA10.92-20 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Wittmann, Erich Christian. |
| 245 10 - TITLE STATEMENT | |
| Title | Connecting Mathematics and Mathematics Education : |
| Remainder of title | Collected Papers on Mathematics Education As a Design Science. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Cham : |
| Name of producer, publisher, distributor, manufacturer | Springer International Publishing AG, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2020. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | �2021. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (332 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Foreword -- Preface -- Contents -- About the Author -- 1 Unfolding the Educational and Practical Resources Inherent in Mathematics for Teaching Mathematics -- 1 From ``Instruction and Receptivity'' to ``Organization and Activity'' in Teaching -- 2 The Learning Environment ``Calculating with Remainders'' -- 3 Mathematics for Specialists and Mathematics for Teachers -- 4 From ``Instruction and Receptivity'' to ``Organization and Activity'' in Teacher Education -- References -- 2 Teaching Units as the Integrating Core of Mathematics Education -- 1 Discussion of the Status and Role of Mathematics Education -- 2 Problems of Integration -- 3 Some Views on Mathematics Teaching -- 4 Teaching Units as the Integrating Core of Mathematics Education -- 4.1 Some Teaching Units -- 4.2 Teaching Units in Teacher Training -- 4.3 Teaching Units in Didactical Research -- 5 Conclusion -- References -- 3 Clinical Interviews Embedded in the ``Philosophy of Teaching Units''-A Means of Developing Teachers' Attitudes and Skills -- 1 Cooperation Between Theory and Practice Through ``Intermediate Practice'' -- 2 Clinical Interviews as a Special Kind of Intermediate Practice -- 3 Concluding Remarks -- References -- 4 The Mathematical Training of Teachers from the Point of View of Education -- 1 The Problem of Integrating Mathematical and Educational aspects in Mathematics Education and Teacher Training -- 2 The Educational Substance of Subject Matter -- 3 Elementary Mathematics in Teacher Training -- 4 The Elementary Mathematics Research Program of Mathematics Education -- References -- 5 When Is a Proof a Proof? -- 1 Proofs and ``Proofs'' -- 2 Formalism as a Fiction: The Indispensability of Intuition ... -- 3 The Elementary-Mathematics-Research-Program of Mathematics Education -- References -- 6 Mathematics Education as a `Design Science'. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1 The `Core' and the `Related Areas' of Mathematics Education -- 2 A Basic Problem in the Present Development of Mathematics Education: The Neglect of the Core -- 3 Mathematics Education as a Systemic-Evolutionary `Design Science' -- 4 The Design of Teaching Units and Empirical Research -- 5 And the Future of Mathematics Education? -- References -- 7 Designing Teaching: The Pythagorean Theorem -- 1 Introduction -- 2 Thinking About the Pythagorean Theorem within the School Context -- 3 Understanding the Structure of the Pythagorean Theorem -- 3.1 Different Proofs of the Pythagorean Theorem -- 3.2 Heuristic Approaches to the Pythagorean Theorem -- 3.3 Exploring Students' Understanding of Area and Similarity -- 4 Designing Teaching Units on the Pythagorean Theorem -- 4.1 Approaching the Pythagorean Theorem via the Diagonal of a Rectangle -- 4.2 Japanese Approach to the Pythagorean Theorem -- 5 Reflecting on the Units: Some Key Generalizable Concepts -- 5.1 Informal Proofs -- 5.2 ``Specializing''-A Fundamental Heuristic Strategy -- 5.3 The Operative Principle -- 6 Appendix: Solutions to the Problems in Exploration 3 -- References -- 8 Standard Number Representations in the Teaching of Arithmetic -- 1 Principles of Learning and Teaching -- 2 The Epistemological Nature of Number Representations -- 2.1 Notes on the History of Number Representations: From Tools of Teaching to Tools of Learning -- 2.2 Representations in Mathematics -- 3 Selection of Standard Number Representations -- 3.1 Criteria for Selecting and Designing Standard Representations -- 3.2 Fundamental Ideas of Arithmetic -- 3.3 Standard Number Representations -- 4 Some Teaching Units -- 4.1 The Twenty Frame and the Addition Table (Grade 1) -- 4.2 Multiplication Chart (Grade 2) -- 4.3 An Introduction into the Thousand Book (Grade 3) -- 4.4 ``Always 22'' (Grade 3). |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.5 Place Value Chart (Grade 4) -- 5 Conclusion -- References -- 9 Developing Mathematics Education in a Systemic Process -- 1 Bridging the Gap Between Theory and Practice: … -- 2 (Burst) Dreams -- 2.1 Descartes' Dream -- 2.2 Hilbert's Dream -- 2.3 Comenius' Dream -- 2.4 The `Systemic-Evolutionary'' Versus the ``Mechanistic-Technomorph'' Approach to the Management of Complexity -- 3 Consequences for Mathematics Education -- 4 Substantial Learning Environments for Practising Skills -- 5 Substantial Learning Environments in Teacher Education -- 5.1 Didactics Courses -- 5.2 Mathematics Courses -- 6 Conclusion -- References -- 10 The Alpha and Omega of Teacher Education: Organizing Mathematical Activities -- 1 Introduction -- 2 Mathematics in Contexts -- 3 The Context of Teacher Education -- 4 The O-Script/A-Script Method -- 5 Operative Proofs -- 6 Experiences with the Course -- References -- 11 Operative Proofs in School Mathematics and Elementary Mathematics -- 1 Some Learning Environments with Embedded Operative Proofs -- 1.1 Even and Odd Numbers -- 1.2 Multiplicative Arrow Strings -- 1.3 Egyptian Fractions -- 1.4 Fitting Polygons -- 2 The Concept of Operative Proof -- 3 The Theoretical Background of Operative Proofs -- 3.1 Mathematics as the Science of Patterns -- 3.2 The Quasi-empirical Nature of Mathematics -- 3.3 The Operative Principle -- 3.4 Practicing Skills in a Productive Way -- 4 Concluding Remarks -- References -- 12 Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education -- 1 Mathematics Education as a ``Systemic-Evolutionary'' Design Science -- 2 Taking Systemic Complexity Systematically into Account: Lessons … -- 3 Empowering Teachers to Cope with Systemic Complexity as Reflective Practitioners. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4 Collective Teaching Experiments: A Joint Venture of Reflective Teachers … -- 5 Closing Remarks: The Role of Mathematics in Mathematics Education -- References -- 13 Structure-Genetic Didactical Analyses-Empirical Research ``of the First Kind'' -- 1 Introduction of the Multiplication Table in Grade 2 -- 2 Designing a Substantial Learning Environment for Practicing Long Addition -- 3 Nets of a Cube -- 4 Structure-Genetic Didactical Analyses -- 5 Conclusion -- References -- 14 Understanding and Organizing Mathematics Education as a Design Science-Origins and New Developments -- 1 Origins -- 1.1 The Rise of the Sciences of the Artificial -- 1.2 Developments in Management Theory -- 1.3 Prototypes of Design in Mathematics Education -- 1.4 The Map of Mathematics Education as a Design Science -- 2 Conceptual Developments -- 2.1 The Natural Theory of Teaching: ``Well-Understood Mathematics'' -- 2.2 Structure-Genetic Didactical Analyses -- 2.3 A Differentiated Conception of Practicing Skills -- 2.4 Awareness of Systemic Constraints -- 3 Practical Consequences -- 3.1 Integrating ``Well-Understood Mathematics'' -- 3.2 Designing a Consistent and Coherent Curriculum -- 3.3 Including Operative Proofs -- 3.4 Addressing Teachers as ``Reflective Practitioners'' -- 4 Final Remarks -- References -- Appendix Excerpts from The Book of Numbers (BN). |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2023. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Wittmann, Erich Christian |
| Title | Connecting Mathematics and Mathematics Education |
| Place, publisher, and date of publication | Cham : Springer International Publishing AG,c2020 |
| International Standard Book Number | 9783030615697 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/bacm-ebooks/detail.action?docID=6422808">https://ebookcentral.proquest.com/lib/bacm-ebooks/detail.action?docID=6422808</a> |
| Public note | Click to View |
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