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Brno : Masaryk University, 2021

1 online resource (373 pages)

ISBN 9788021099838 (electronic bk.)

ISBN 9788021099821

Print version: Jaworski, Barbara Inquiry in University Mathematics Teaching and Learning Brno : Masaryk University, c2021 ISBN 9788021099821

Intro -- Authors -- Foreword -- Chapter 1. Introduction -- References -- Part 1. Inquiry Communities in Mathematics Teaching and Learning -- Chapter 2. Conceptual Foundations of the PLATINUM Project -- 2.1. The PLATINUM Project -- 2.2. A Need to Redefine Teaching -- 2.3. IBME: A Brief History in the PLATINUM Countries and Beyond -- 2.4. IBME in Mathematics Education -- 2.5. IBME in the PLATINUM Project -- 2.6. Discussion and Conclusions -- References -- Chapter 3. Spidercharts: A Tool for Describing and Reflecting IBME Activities -- 3.1. Introduction -- 3.2. Developing the Spidercharts -- 3.3. The Three Spidercharts and How to Work With Them -- 3.4. The Spidercharts of the PLATINUM Cases -- 3.5. Discussion -- References -- Chapter 4. Students With Identified Needs and IBME -- 4.1. Introduction -- 4.2. Diversity of Students’ Characteristics and Needs -- 4.3. PLATINUM Partners’ Perspectives -- 4.4. Typology of Students With Identified Needs -- 4.5. Inquiry-Based Instruction and Students With Identified Needs -- 4.6. Universal Design of Inquiry-Based Mathematical Education -- 4.7. Conclusion and Discussion -- References -- Part 2. PLATINUM: The Project -- Chapter 5. Origins and Implementation of the Project -- 5.1. Introduction -- 5.2. Formation of the Consortium -- 5.3. Choosing the Project’s Format and Focus -- 5.4. PLATINUM Intellectual Outputs and Project Management -- 5.5. PLATINUM Community Meetings and Lessons Learned -- 5.6. Reflection About Collaboration Between Mathematicians and Mathematics Educators -- References -- Chapter 6. Creating Teaching Units for Student Inquiry -- 6.1. Introduction -- 6.2. Frameworks Used in PLATINUM for Designing Student Inquiry -- 6.3. Documentation of Inquiry Tasks in PLATINUM -- 6.4. Examples of Inquiry Tasks Developed and Used in PLATINUM -- 6.5. Use of ICT in Student Inquiry.

6.6. Guiding Design Principles Identified in PLATINUM -- 6.7. Accessibility of Teaching Units for Students With Identified Needs -- 6.8. Concluding Remarks -- References -- Chapter 7. Methods and Materials for Professional Development of Lecturers -- 7.1. Introduction -- 7.2. Professional Development in IBME -- 7.3. IBME Workshops -- 7.4. Summary and Looking Ahead -- 7.5. Conclusions -- References -- Chapter 8. Mathematical Modelling and Inquiry-Based Mathematics Education -- 8.1. Introduction -- 8.2. Mathematical Modelling and Inquiry-Based Mathematics Education in Our Teaching -- 8.3. Active Knowledge: Connecting IBME and MM -- 8.4. Examples From Three PLATINUM Partners -- 8.5. Conclusions -- References -- Chapter 9. Evaluation of Inquiry-Based Mathematics Education -- 9.1. Introduction -- 9.2. Research Methodology -- 9.3. Presentation of the Cases -- 9.4. Contribution of the Cross-Cases Study: Challenges and Issues -- 9.5. Conclusions -- References -- Part 3. Learning About Teaching: Case Studies -- Chapter 10. Introduction to the Case Studies in PLATINUM -- 10.1. Inquiry-Based Mathematics Education-Basis for Our Case Studies -- 10.2. Elements of Our Inquiry Activity in the Case Study Chapters Which Follow -- 10.3. Introduction to Each of the Case Studies -- 10.4. Concluding Thoughts -- References -- Chapter 11. Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience -- 11.1. Mathematics Education at the University of Agder -- 11.2. The MatRIC-PLATINUM Community at the University of Agder -- 11.3. Promoting Conceptual Understanding in a Differential Equations Course for Engineers -- 11.4. Innovation Versus Students’ Inertia and Institutional Constraints -- 11.5. Lessons Learned -- Acknowledgements -- References.

Chapter 12. Design and Implementation of an Inquiry-Based Mathematics Module for First-Year Students in Biomedical Sciences -- 12.1. Setting the Scene -- 12.2. Background Information -- 12.3. Work of the CoI on the First Version of the Module -- 12.4. Work of the CoI on the Redesign of the Module -- 12.5. Concluding Remarks -- Acknowledgements -- References -- Chapter 13. The First Experience With IBME at Masaryk University, Brno -- 13.1. Introduction -- 13.2. The Historical and Institutional Background -- 13.3. The Community of Inquiry at Masaryk University -- 13.4. Statistics 1: The Experience of Tamara and Patricia -- 13.5. Mathematical Analysis 1: The Experience of Lenny and Luke -- 13.6. Mathematics 2: The Experience of Marge -- 13.7. Summary -- References -- Chapter 14. In Critical Alignment With IBME -- 14.1. Introduction -- 14.2. Context of the Teaching Project of the LUH-group: The Course, the Concern for Reflective Agency, and the Sample Task -- 14.3. Phenomena and Contradictions of the Inquiry Teaching Project: Reflections Against the Background of Concepts Underlying Reflective Agency -- 14.4. Reflecting on Issues Regarding IBME, the Three-Layer Model and CoIs, and How They Underlie PLATINUM -- 14.5. Concluding Remark -- References -- Chapter 15. Two Decades of Inquiry-Based Developmental Activity in University Mathematics -- 15.1. Introduction -- 15.2. Chapter Structure -- 15.3. History -- 15.4. The Teaching Group: A Community of Inquiry -- 15.5. Inquiry-based Tasks in a Foundation Mathematics Course -- 15.6. Teaching Engineering Students -- 15.7. Discussion -- References -- Chapter 16. Teaching Inquiry-Oriented Mathematics: Establishing Support for Novice Lecturers -- 16.1. Introduction -- 16.2. Complutense University of Madrid -- 16.3. Community of Inquiry (CoI) at UCM -- 16.4. Designing Materials for Professional Development.

16.5. The Matrix Factorisation Inquiry Project -- 16.6. Implementation Results With Novice Lecturers -- 16.7. Concluding Remarks and Ongoing Work -- References -- Chapter 17. Development of a Community of Inquiry Based on Reflective Teaching -- 17.1. Introduction -- 17.2. Background, History, and the Team of the BUT CoI -- 17.3. Contribution of IBME to Reflective Teaching -- 17.4. Challenges, Achievements, and Experiences of the CoI -- 17.5. Conclusion and Future Development of the CoI -- References -- Chapter 18. Experience in Implementing IBME at the Borys Grinchenko Kyiv University -- 18.1. Development of an IBME Community at BGKU -- 18.2. IBME for the Formation of Conceptual Knowledge During Teaching of Mathematical Analysis -- 18.3. Evaluating Effectiveness of IBME to Achieve Educational Goals -- 18.4. Discussion of the Case in the Community of Inquiry -- References -- Part 4. Lessons Learned -- Chapter 19. Epilogue -- 19.1. Conceptualisation of Inquiry at University Level -- 19.2. Pathways in the Design of Materials in University Mathematics -- 19.3. Methods and Materials for Professional Development of Lecturers -- 19.4. And to Conclude -- Prazdna stranka.

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Intro // Authors // Foreword // Chapter 1. Introduction // References // Part 1. Inquiry Communities in Mathematics Teaching and Learning // Chapter 2. Conceptual Foundations of the PLATINUM Project // 2.1. The PLATINUM Project // 2.2. A Need to Redefine Teaching // 2.3. IBME: A Brief History in the PLATINUM Countries and Beyond // 2.4. IBME in Mathematics Education // 2.5. IBME in the PLATINUM Project // 2.6. Discussion and Conclusions // References // Chapter 3. Spidercharts: A Tool for Describing and Reflecting IBME Activities // 3.1. Introduction // 3.2. Developing the Spidercharts // 3.3. The Three Spidercharts and How to Work With Them // 3.4. The Spidercharts of the PLATINUM Cases // 3.5. Discussion // References // Chapter 4. Students With Identified Needs and IBME // 4.1. Introduction // 4.2. Diversity of Students’ Characteristics and Needs // 4.3. PLATINUM Partners’ Perspectives // 4.4. Typology of Students With Identified Needs // 4.5. Inquiry-Based Instruction and Students With Identified Needs // 4.6. Universal Design of Inquiry-Based Mathematical Education // 4.7. Conclusion and Discussion // References // Part 2. PLATINUM: The Project // Chapter 5. Origins and Implementation of the Project // 5.1. Introduction // 5.2. Formation of the Consortium // 5.3. Choosing the Project’s Format and Focus // 5.4. PLATINUM Intellectual Outputs and Project Management // 5.5. PLATINUM Community Meetings and Lessons Learned // 5.6. Reflection About Collaboration Between Mathematicians and Mathematics Educators // References // Chapter 6. Creating Teaching Units for Student Inquiry // 6.1. Introduction // 6.2. Frameworks Used in PLATINUM for Designing Student Inquiry // 6.3. Documentation of Inquiry Tasks in PLATINUM // 6.4. Examples of Inquiry Tasks Developed and Used in PLATINUM // 6.5. Use of ICT in Student Inquiry //

6.6. Guiding Design Principles Identified in PLATINUM // 6.7. Accessibility of Teaching Units for Students With Identified Needs // 6.8. Concluding Remarks // References // Chapter 7. Methods and Materials for Professional Development of Lecturers // 7.1. Introduction // 7.2. Professional Development in IBME // 7.3. IBME Workshops // 7.4. Summary and Looking Ahead // 7.5. Conclusions // References // Chapter 8. Mathematical Modelling and Inquiry-Based Mathematics Education // 8.1. Introduction // 8.2. Mathematical Modelling and Inquiry-Based Mathematics Education in Our Teaching // 8.3. Active Knowledge: Connecting IBME and MM // 8.4. Examples From Three PLATINUM Partners // 8.5. Conclusions // References // Chapter 9. Evaluation of Inquiry-Based Mathematics Education // 9.1. Introduction // 9.2. Research Methodology // 9.3. Presentation of the Cases // 9.4. Contribution of the Cross-Cases Study: Challenges and Issues // 9.5. Conclusions // References // Part 3. Learning About Teaching: Case Studies // Chapter 10. Introduction to the Case Studies in PLATINUM // 10.1. Inquiry-Based Mathematics Education-Basis for Our Case Studies // 10.2. Elements of Our Inquiry Activity in the Case Study Chapters Which Follow // 10.3. Introduction to Each of the Case Studies // 10.4. Concluding Thoughts // References // Chapter 11. Teaching Students to Think Mathematically Through Inquiry: The Norwegian Experience // 11.1. Mathematics Education at the University of Agder // 11.2. The MatRIC-PLATINUM Community at the University of Agder // 11.3. Promoting Conceptual Understanding in a Differential Equations Course for Engineers // 11.4. Innovation Versus Students’ Inertia and Institutional Constraints // 11.5. Lessons Learned // Acknowledgements // References //

Chapter 12. Design and Implementation of an Inquiry-Based Mathematics Module for First-Year Students in Biomedical Sciences // 12.1. Setting the Scene // 12.2. Background Information // 12.3. Work of the CoI on the First Version of the Module // 12.4. Work of the CoI on the Redesign of the Module // 12.5. Concluding Remarks // Acknowledgements // References // Chapter 13. The First Experience With IBME at Masaryk University, Brno // 13.1. Introduction // 13.2. The Historical and Institutional Background // 13.3. The Community of Inquiry at Masaryk University // 13.4. Statistics 1: The Experience of Tamara and Patricia // 13.5. Mathematical Analysis 1: The Experience of Lenny and Luke // 13.6. Mathematics 2: The Experience of Marge // 13.7. Summary // References // Chapter 14. In Critical Alignment With IBME // 14.1. Introduction // 14.2. Context of the Teaching Project of the LUH-group: The Course, the Concern for Reflective Agency, and the Sample Task // 14.3. Phenomena and Contradictions of the Inquiry Teaching Project: Reflections Against the Background of Concepts Underlying Reflective Agency // 14.4. Reflecting on Issues Regarding IBME, the Three-Layer Model and CoIs, and How They Underlie PLATINUM // 14.5. Concluding Remark // References // Chapter 15. Two Decades of Inquiry-Based Developmental Activity in University Mathematics // 15.1. Introduction // 15.2. Chapter Structure // 15.3. History // 15.4. The Teaching Group: A Community of Inquiry // 15.5. Inquiry-based Tasks in a Foundation Mathematics Course // 15.6. Teaching Engineering Students // 15.7. Discussion // References // Chapter 16. Teaching Inquiry-Oriented Mathematics: Establishing Support for Novice Lecturers // 16.1. Introduction // 16.2. Complutense University of Madrid // 16.3. Community of Inquiry (CoI) at UCM // 16.4. Designing Materials for Professional Development //

16.5. The Matrix Factorisation Inquiry Project // 16.6. Implementation Results With Novice Lecturers // 16.7. Concluding Remarks and Ongoing Work // References // Chapter 17. Development of a Community of Inquiry Based on Reflective Teaching // 17.1. Introduction // 17.2. Background, History, and the Team of the BUT CoI // 17.3. Contribution of IBME to Reflective Teaching // 17.4. Challenges, Achievements, and Experiences of the CoI // 17.5. Conclusion and Future Development of the CoI // References // Chapter 18. Experience in Implementing IBME at the Borys Grinchenko Kyiv University // 18.1. Development of an IBME Community at BGKU // 18.2. IBME for the Formation of Conceptual Knowledge During Teaching of Mathematical Analysis // 18.3. Evaluating Effectiveness of IBME to Achieve Educational Goals // 18.4. Discussion of the Case in the Community of Inquiry // References // Part 4. Lessons Learned // Chapter 19. Epilogue // 19.1. Conceptualisation of Inquiry at University Level // 19.2. Pathways in the Design of Materials in University Mathematics // 19.3. Methods and Materials for Professional Development of Lecturers // 19.4. And to Conclude

(Au-PeEL)EBL6913633

(MiAaPQ)EBC6913633

(OCoLC)1305846703