Mathematics Books

Book Synopsis Kapitel 1. Grundbegriffe der Differentialgleichungen - Kapitel 2. Differentialgleichungen erster Ordnung - Kapitel 3. Differentialgleichungen zweiter Ordnung - Kapitel 4. Laplace-Transformationen.- Kapitel 5. System von linearen Differentialgleichungen.- Kapitel 6. Potenzreihenlösungen.- Kapitel 7. Numerische Methoden für Anfangswertprobleme.- Kapitel 8. Schießverfahren für lineare Randbedingungen.- Anhang A. Potenzreihen.- Anhang B. Einige elementare Integrationsformeln.- Anhang C. Tabelle der Laplace-Transformationen.          ?

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Book SynopsisThis collective volume in the history of early-modern science and medicine investigates the transfer of knowledge between Germany and Scotland focusing on the Scottish mathematician and physician Duncan Liddel of Aberdeen. It offers a contextualized study of his life and work in the cultural and institutional frame of the northern European Renaissance, as well as a reconstruction of his scholarly networks and of the scientific debates in the time of post-Copernican astronomy, Melanchthonian humanism and Paracelsian controversies. Contributors are: Sabine Bertram, Duncan Cockburn, Laura Di Giammatteo, Mordechai Feingold, Karin Friedrich, Elizabeth Harding, John Henry, Richard Kirwan, Jane Pirie, Jonathan Regier.Trade Review“This is a rich and very valuable book. It is also an exemplary volume that throws light not only on a rather unknown figure in the history of science but also on sixteenth-century scholarly life in general.” Rienk Vermij, University of Oklahoma. In: Journal for the History of Astronomy, Vol. 48, No. 4 (2017), pp. 482-483.Table of ContentsPART 1 Liddel’s World 1 Science and Medicine in the Humanistic Networks of the Northern European Renaissance Pietro Daniel Omodeo 2 Confabulatory Life Mordechai Feingold 3 The European Career of a Scottish Mathematician and Physician Pietro Daniel Omodeo PART 2 Mathematics, Medicine and Epistemology 4 A Pragmatic Aspect of Polymathy: The Alliance of Mathematics and Medicine in Liddel’s Time John Henry 5 Logic, Mathematics and Natural Light: Liddel on the Foundations of Knowledge Jonathan Regier 6 Liddel’s Ars Medica (1607): The Effective Method as Foundation of Medical Knowledge and of Ethics Laura Di Giammatteo PART 3 Academic Life and Higher Education 7 It’s Who You Know: Scholarly Networks in Liddel’s Helmstedt Richard Kirwan 8 Home-Styling Matters: Symbolic Dimensions of the Professorial Household at Liddel’s Helmstedt Elizabeth Harding 9 Liddel and the University of Aberdeen Duncan Cockburn PART 4 New Sources 10 Liddel on the Geo-Heliocentric Controversy: His Letter to Brahe from 1600 Pietro Daniel Omodeo and Jonathan Regier 11 Liddel’s Oratio de praestantia mathematicarum Pietro Daniel Omodeo PART 5 Bibliographical Reconstructions 12 Reconstructing Liddel’s Library at Aberdeen Jane Pirie 13 Liddel’s Published and Unpublished Works Sabine Bertram

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Book SynopsisThe relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.Table of ContentsAcknowledgements Figures and Tables Notes on Contributors Introduction  Dianne Siemon, Tasos Barkatsas and Rebecca Seah 1 Knowing and Building on What Students Know: The Case of Multiplicative Thinking  Dianne Siemon 2 Learning Trajectories in Early Mathematics Education  Julie Sarama and Douglas H. Clements 3 HLT: A Lens on Conceptual Transition between Mathematical “Markers”  Ron Tzur 4 Using Digital Diagnostic Classroom Assessments Based on Learning Trajectories to Drive Instruction  Jere Confrey, William McGowan, Meetal Shah, Michael Belcher, Margaret Hennessey and Alan Maloney 5 Researching Mathematical Reasoning: Building Evidence-Based Resources to Support Targeted Teaching in the Middle Years  Dianne Siemon and Rosemary Callingham 6 Reframing Mathematical Futures II: Developing Students’ Algebraic Reasoning in the Middle Years  Marj Horne, Max Stephens and Lorraine Day 7 A Learning Progression for Geometric Reasoning  Rebecca Seah and Marj Horne 8 Statistics and Probability: From Research to the Classroom  Rosemary Callingham, Jane Watson and Greg Oates 9 Investigating Mathematics Students’ Motivations and Perceptions  Tasos Barkatsas and Claudia Orellana 10 Secondary Students’ Mathematics Education Goal Orientations  Tasos Barkatsas and Claudia Orellana Epilogue  Mike Askew

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Book SynopsisThe relationship between research and practice has long been an area of interest for researchers, policy makers, and practitioners alike. One obvious arena where mathematics education research can contribute to practice is the design and implementation of school mathematics curricula. This observation holds whether we are talking about curriculum as a set of broad, measurable competencies (i.e., standards) or as a comprehensive set of resources for teaching and learning mathematics. Impacting practice in this way requires fine-grained research that is focused on individual student learning trajectories and intimate analyses of classroom pedagogical practices as well as large-scale research that explores how student populations typically engage with the big ideas of mathematics over time. Both types of research provide an empirical basis for identifying what aspects of mathematics are important and how they develop over time. This book has its origins in independent but parallel work in Australia and the United States over the last 10 to 15 years. It was prompted by a research seminar at the 2017 PME Conference in Singapore that brought the contributors to this volume together to consider the development and use of evidence-based learning progressions/trajectories in mathematics education, their basis in theory, their focus and scale, and the methods used to identify and validate them. In this volume they elaborate on their work to consider what is meant by learning progressions/trajectories and explore a range of issues associated with their development, implementation, evaluation, and on-going review. Implications for curriculum design and future research in this field are also considered. Contributors are: Michael Askew, Tasos Barkatsas, Michael Belcher, Rosemary Callingham, Doug Clements, Jere Confrey, Lorraine Day, Margaret Hennessey, Marj Horne, Alan Maloney, William McGowan, Greg Oates, Claudia Orellana, Julie Sarama, Rebecca Seah, Meetal Shah, Dianne Siemon, Max Stephens, Ron Tzur, and Jane Watson.Table of ContentsAcknowledgements Figures and Tables Notes on Contributors Introduction  Dianne Siemon, Tasos Barkatsas and Rebecca Seah 1 Knowing and Building on What Students Know: The Case of Multiplicative Thinking  Dianne Siemon 2 Learning Trajectories in Early Mathematics Education  Julie Sarama and Douglas H. Clements 3 HLT: A Lens on Conceptual Transition between Mathematical “Markers”  Ron Tzur 4 Using Digital Diagnostic Classroom Assessments Based on Learning Trajectories to Drive Instruction  Jere Confrey, William McGowan, Meetal Shah, Michael Belcher, Margaret Hennessey and Alan Maloney 5 Researching Mathematical Reasoning: Building Evidence-Based Resources to Support Targeted Teaching in the Middle Years  Dianne Siemon and Rosemary Callingham 6 Reframing Mathematical Futures II: Developing Students’ Algebraic Reasoning in the Middle Years  Marj Horne, Max Stephens and Lorraine Day 7 A Learning Progression for Geometric Reasoning  Rebecca Seah and Marj Horne 8 Statistics and Probability: From Research to the Classroom  Rosemary Callingham, Jane Watson and Greg Oates 9 Investigating Mathematics Students’ Motivations and Perceptions  Tasos Barkatsas and Claudia Orellana 10 Secondary Students’ Mathematics Education Goal Orientations  Tasos Barkatsas and Claudia Orellana Epilogue  Mike Askew

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Book SynopsisIn Between Tradition and Innovation, Ad Meskens traces the profound influence of a group of Flemish Jesuits on the course of mathematics in the seventeenth century. Using manuscript evidence, this book argues that one of the Flemish mathematics school’s professors, Gregorio a San Vicente (1584–1667), had developed a logically sound integration method more than a decade before the Italian mathematician Bonaventura Cavalieri. Although San Vincente’s superiors refused to grant him permission to publish his results, his methods went on to influence numerous other mathematicians through his students, many of whom became famous mathematicians in their own right. By carefully tracing their careers and outlining their biographies, Meskens convincingly shows that they made a number of ground-breaking contributions to fields ranging from mathematics and mechanics to optics and architecture.Table of ContentsPreface Abbreviations Introduction: The Low Countries, Spain, and Europe  1 The Jesuits in the Netherlands 1 The College and Its School of Mathematics  1 Schools in Antwerp  2 Jesuit Educational Policy  3 Mathematics in the Jesuit Curriculum  4 The Academy of Mathematics at the Collegio Romano  5 The College of Leuven  6 The Antwerp College in the Sixteenth Century  7 The Antwerp College in the Seventeenth Century  8 The School of Mathematics  9 Michiel Coignet and the Jesuits 2 The Seventeenth Century: The Dawn of a New Era  1 Conic Sections  2 Squaring the Circle the Archimedean Way  3 The Humble Beginnings of Infinitesimal Calculus  4 Infinitesimals: The Keplerian Revolution  5 Cavalieri’s Indivisibles  6 The Jesuits and Indivisibles 3 Francisco de Aguilón and Mathematical Optics  1 Opticorum libri sex  2 Aguilón’s Catoptrica Manuscript 4 Gregorio a San Vicente: An Ignored Genius  1 A Tragic Life  2 Mathematical Oeuvre  3 The Mechanics Theses 5 The Creative Antwerp–Leuven Period  1 Trisection of an Angle  2 Mean Proportionals  3 Properties of Conic Sections 6 Exhaustion: The Road to Infinitesimals  1 Sequences and Series  2 The Exhaustion Method  3 San Vicente’s Use of Infinitesimals  4 The Cavalieri Dispute 7 Infinitesimal Calculus at Work  1 The Hyperbola  2 Calculation of the Volume of Ductus Figures  3 Lateral Area of the Ungula cylindrica and Relations between Ductus Figures 8 Rome and Prague, the Final Discoveries  1 The Missives to Rome  2 The Chartae Romanae  3 San Vicente’s Legacy  4 Conclusion 9 The Erroneous Circle Quadrature 10 Joannes della Faille and the Beginning of Projective Geometry  1 An Itinerant Life  2 Conic Sections  3 De centro gravitatis 11 The Antwerp Students  1 Philip Nuyts  2 Ignatius Derkennis  3 Other Students 12 The Leuven Students  1 Theodorus Moretus  2 Jan Ciermans  3 Willem Boelmans  4 Willem Hesius  5 Other Students 13 The Later Disciples  1 Andreas Tacquet  2 Gilles-François de Gottignies  3 Alphonse Antonius de Sarasa 14 The Jesuit Architects  1 Ad maiorem Dei gloria  2 Descensus ad inferos 15 The Influence of the School of Mathematics Appendix 1: Chronology of San Vicente’s Manuscripts Appendix 2: Students of the School of Mathematics after 1625 Bibliography Index

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Book SynopsisThis second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors looked back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and looked forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 1, Knowledge, Beliefs, and Identity in Mathematics Teaching and Teaching Development, edited by Despina Potari and Olive Chapman, examines teacher knowledge, beliefs, identity, practice and relationships among them. These important aspects of mathematics teacher education continue to be the focus of extensive research and policy debate globally. Thus, as the first volume in the series, it appropriately addresses central topics/issues that provide an excellent beginning to engage in the field of mathematics education through the handbook. Contributors are: Jill Adler, Mike Askew, Maria Bartolini Bussi, Anne Bennison, Kim Beswick, Olive Chapman, Charalambos Charalambus, Helen Chick, Marta Civil, Sandra Crespo, Sean Delaney, Silvia Funghi, Merrilyn Goos, Roberta Hunter, Barbara Jaworski, Kim Koh, Esther S. Levenson, Yeping Li, Niamh O’ Meara, JoengSuk Pang, Randolph Phillipp, Despina Potari, Craig Pournara, Stephen Quirke, Alessandro Ramploud, Tim Rowland, John (Zig) Siegfried, Naiqing Song, Konstantinos Stouraitis, Eva Thanheiser, Collen Vale, Hamsa Venkat, and Huirong Zhang.Trade Review"Unlike most second editions, this text is much more than an update and correction of the previous edition (2008). Though the five organizing subthemes are maintained, the current text provides a reexamination and extension of each subtheme based on recent research, state-of-the-art ideas and trends, and new outlooks on future research directions. [...] Each chapter includes supporting references and is complemented by a helpful introductory overview of the chapter content and an index. Summing up: recommended." - J. Johnson, in: CHOICE, 58 (7), March 2021Table of ContentsPreface List of Figures and Tables Mathematics Teaching and Its Development: Looking into Teacher Knowledge, Beliefs and Identity: An Introduction  Despina Potari Part 1: Mathematics Teacher Knowledge and Its Relation to Teaching 1. Mathematical Subject Knowledge for Teaching Primary School Mathematics: Evidence and Models for Professional Development  Mike Askew and Hamsa Venkat 2. Building Teachers’ Capacity in Mathematics Authentic Assessment  Kim Koh and Olive Chapman 3. Mathematics Conceptual Knowledge for Teaching: Helping Prospective Teachers Know Mathematics Well Enough for Teaching  Yeping Li, JeongSuk Pang, Huirong Zhang and Naiqing Song 4. Researching Mathematical Knowledge in Teaching  Tim Rowland Part 2: Mathematics Teacher Beliefs about Mathematics and Its Teaching 5. Mathematics Teachers’ Cultural Beliefs: The Case of Lesson Study  Maria G. Bartolini Bussi, Silvia Funghi and Alessandro Ramploud 6. Mathematical Creativity in the Classroom: Teachers’ Conceptions and Professional Development  Esther S. Levenson Part 3: The Interplay of Mathematics Teacher Identity, Beliefs and Knowledge 7. Beliefs and Pedagogical Content Knowledge for Teachers of Mathematics  Kim Beswick and Helen Chick 8. Developing Professional Knowledge and Identities of Non-Specialist Teachers of Mathematics  Merrilyn Goos, Anne Bennison, Stephen Quirke, Niamh O’Meara and Colleen Vale Part 4: Mathematics Teaching and Its Development 9. Mathematics Teachers Committed to Equity: A Review of Teaching Practices  Marta Civil, Roberta Hunter and Sandra Crespo 10. Inquiry-Based Practice in University Mathematics Teaching Development  Barbara Jaworski 11. Teacher Decision Making: Developments in Research and Theory  Despina Potari and Konstantinos Stouraitis Part 5: From Mathematics Teaching Practices to Teacher Education 12. Exemplifying with Variation and Its Development in Mathematics Teacher Education  Jill Adler and Craig Pournara 13. Mathematics Teaching Practices and Practice-Based Pedagogies: A Critical Review of the Literature Since 2000  Charalambos Y. Charalambous and Seán Delaney 14. Seeing Mathematics through the Lens of Children’s Mathematical Thinking: Perspective on the Development of Mathematical Knowledge for Teaching  Randolph A. Philipp, John (Zig) Siegfried and Eva Thanheiser Index

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Book SynopsisThis second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors looked back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and looked forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 1, Knowledge, Beliefs, and Identity in Mathematics Teaching and Teaching Development, edited by Despina Potari and Olive Chapman, examines teacher knowledge, beliefs, identity, practice and relationships among them. These important aspects of mathematics teacher education continue to be the focus of extensive research and policy debate globally. Thus, as the first volume in the series, it appropriately addresses central topics/issues that provide an excellent beginning to engage in the field of mathematics education through the handbook. Contributors are: Jill Adler, Mike Askew, Maria Bartolini Bussi, Anne Bennison, Kim Beswick, Olive Chapman, Charalambos Charalambus, Helen Chick, Marta Civil, Sandra Crespo, Sean Delaney, Silvia Funghi, Merrilyn Goos, Roberta Hunter, Barbara Jaworski, Kim Koh, Esther S. Levenson, Yeping Li, Niamh O’ Meara, JoengSuk Pang, Randolph Phillipp, Despina Potari, Craig Pournara, Stephen Quirke, Alessandro Ramploud, Tim Rowland, John (Zig) Siegfried, Naiqing Song, Konstantinos Stouraitis, Eva Thanheiser, Collen Vale, Hamsa Venkat, and Huirong Zhang.Trade Review"Unlike most second editions, this text is much more than an update and correction of the previous edition (2008). Though the five organizing subthemes are maintained, the current text provides a reexamination and extension of each subtheme based on recent research, state-of-the-art ideas and trends, and new outlooks on future research directions. [...] Each chapter includes supporting references and is complemented by a helpful introductory overview of the chapter content and an index. Summing up: recommended." - J. Johnson, in: CHOICE, 58 (7), March 2021Table of ContentsPreface List of Figures and Tables Mathematics Teaching and Its Development: Looking into Teacher Knowledge, Beliefs and Identity: An Introduction  Despina Potari Part 1: Mathematics Teacher Knowledge and Its Relation to Teaching 1. Mathematical Subject Knowledge for Teaching Primary School Mathematics: Evidence and Models for Professional Development  Mike Askew and Hamsa Venkat 2. Building Teachers’ Capacity in Mathematics Authentic Assessment  Kim Koh and Olive Chapman 3. Mathematics Conceptual Knowledge for Teaching: Helping Prospective Teachers Know Mathematics Well Enough for Teaching  Yeping Li, JeongSuk Pang, Huirong Zhang and Naiqing Song 4. Researching Mathematical Knowledge in Teaching  Tim Rowland Part 2: Mathematics Teacher Beliefs about Mathematics and Its Teaching 5. Mathematics Teachers’ Cultural Beliefs: The Case of Lesson Study  Maria G. Bartolini Bussi, Silvia Funghi and Alessandro Ramploud 6. Mathematical Creativity in the Classroom: Teachers’ Conceptions and Professional Development  Esther S. Levenson Part 3: The Interplay of Mathematics Teacher Identity, Beliefs and Knowledge 7. Beliefs and Pedagogical Content Knowledge for Teachers of Mathematics  Kim Beswick and Helen Chick 8. Developing Professional Knowledge and Identities of Non-Specialist Teachers of Mathematics  Merrilyn Goos, Anne Bennison, Stephen Quirke, Niamh O’Meara and Colleen Vale Part 4: Mathematics Teaching and Its Development 9. Mathematics Teachers Committed to Equity: A Review of Teaching Practices  Marta Civil, Roberta Hunter and Sandra Crespo 10. Inquiry-Based Practice in University Mathematics Teaching Development  Barbara Jaworski 11. Teacher Decision Making: Developments in Research and Theory  Despina Potari and Konstantinos Stouraitis Part 5: From Mathematics Teaching Practices to Teacher Education 12. Exemplifying with Variation and Its Development in Mathematics Teacher Education  Jill Adler and Craig Pournara 13. Mathematics Teaching Practices and Practice-Based Pedagogies: A Critical Review of the Literature Since 2000  Charalambos Y. Charalambous and Seán Delaney 14. Seeing Mathematics through the Lens of Children’s Mathematical Thinking: Perspective on the Development of Mathematical Knowledge for Teaching  Randolph A. Philipp, John (Zig) Siegfried and Eva Thanheiser Index

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Book SynopsisThis second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors look back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and look forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 2, Tools and Processes in Mathematics Teacher Education, describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating the mathematics teacher learning and development. It provides insights of how mathematics teacher educators think about and approach their work with teachers. Thus, as the second volume in the series, it broadens our understanding of the mathematics teacher and their learning and teaching.Table of ContentsPreface  Olive Chapman List of Figures and Tables Tools and Ways of Thinking in Mathematics Teacher Education: An Introduction  Salvador Llinares Part 1: Video, Tasks to Promote Reflective Skills and Lesson De-Brief Conversations as Tools in Mathematics Teacher Education 1. Leveraging the Power of Video for Teacher Learning: A Design Framework for Mathematics Teacher Educators  Elizabeth A. van Es, Miray Tekkumru-Kisa and Nanette Seago 2. Tasks Promoting Prospective Mathematics Teachers’ Reflective Skills: Focus on Individual Differences  Naïa Vondrová 3. Learning to Teach Mathematics: The Lesson De-Brief Conversation  Julian Brown, Laurinda Brown, Alf Coles and Tracy Helliwell Part 2: Technological Tools and Technological Mediation in Mathematics Teacher Education 4. Technology as a Curricular Instrument  Angel Ruiz 5. Digital Curriculum Resources in/for Mathematics Teacher Learning: A Documentational Approach Perspective  Ghislaine Gueudet and Birgit Pepin 6. Prospective and Practicing Teachers and the Use of Digital Technologies in Mathematical Problem-Solving Approaches  Manuel Santos-Trigo 7. Computational Modelling in Elementary Mathematics Teacher Education  George Gadanidis, Janette M. Hughes, Immaculate Namukasa and Ricardo Scucuglia 8. Technology Tools for Mathematics Teacher Learning: How Might They Support the Development of Capacity for Specific Teaching Assignments?  Patricio Herbst, Daniel Chazan and Amanda Milewski Part 3: Conceptual Instrumentation in Mathematics Teacher Education: Learning to Use Theories to Analyze Teaching 9. The Fractal Complexity of Using Theories in Mathematics Teacher Education: Issues and Debates, Opportunities and Limitations  Elisabeta Eriksen and Annette Hessen Bjerke 10. Controlled Implementations: Teaching Practice to Practicing Mathematics Teachers  Paola Sztajn, Lara Dick, Reema Alnizami, Dan Heck and Kristen Malzahn 11. Noticing as a Tool to Analyze Mathematics Instruction and Learning  Julie Amador 12. Theoretical Lenses to Develop Mathematics Teacher Noticing: Learning, Teaching, Psychological, and Social Perspectives  Ceneida Fernández and Ban Heng Choy 13. Transcending Contemporary Obsessions: The Development of a Model for Teacher Professional Development  Paulino Preciado-Babb, Martina Metz, Brent Davis and Soroush Sabbaghan Part 4: Crosscutting Issues on Tools and Processes in Mathematics Teacher Education 14. Using Professional Development Contexts to Structure Prospective Teacher Education  José Carrillo, Nuria Climent, Luis C. Contreras and Miguel Montes 15. From Tools to Resources in the Professional Development of Mathematics Teachers: General Perspectives and Crosscutting Issues  Abraham Arcavi Index

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Book SynopsisThis second edition of the International Handbook of Mathematics Teacher Education builds on and extends the topics/ideas in the first edition while maintaining the themes for each of the volumes. Collectively, the authors look back beyond and within the last 10 years to establish the state-of-the-art and continuing and new trends in mathematics teacher and mathematics teacher educator education, and look forward regarding possible avenues for teachers, teacher educators, researchers, and policy makers to consider to enhance and/or further investigate mathematics teacher and teacher educator learning and practice, in particular. The volume editors provide introductions to each volume that highlight the subthemes used to group related chapters, which offer meaningful lenses to see important connections within and across chapters. Readers can also use these subthemes to make connections across the four volumes, which, although presented separately, include topics that have relevance across them since they are all situated in the common focus regarding mathematics teachers. Volume 2, Tools and Processes in Mathematics Teacher Education, describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating the mathematics teacher learning and development. It provides insights of how mathematics teacher educators think about and approach their work with teachers. Thus, as the second volume in the series, it broadens our understanding of the mathematics teacher and their learning and teaching.Table of ContentsPreface  Olive Chapman List of Figures and Tables Tools and Ways of Thinking in Mathematics Teacher Education: An Introduction  Salvador Llinares Part 1: Video, Tasks to Promote Reflective Skills and Lesson De-Brief Conversations as Tools in Mathematics Teacher Education 1. Leveraging the Power of Video for Teacher Learning: A Design Framework for Mathematics Teacher Educators  Elizabeth A. van Es, Miray Tekkumru-Kisa and Nanette Seago 2. Tasks Promoting Prospective Mathematics Teachers’ Reflective Skills: Focus on Individual Differences  Naïa Vondrová 3. Learning to Teach Mathematics: The Lesson De-Brief Conversation  Julian Brown, Laurinda Brown, Alf Coles and Tracy Helliwell Part 2: Technological Tools and Technological Mediation in Mathematics Teacher Education 4. Technology as a Curricular Instrument  Angel Ruiz 5. Digital Curriculum Resources in/for Mathematics Teacher Learning: A Documentational Approach Perspective  Ghislaine Gueudet and Birgit Pepin 6. Prospective and Practicing Teachers and the Use of Digital Technologies in Mathematical Problem-Solving Approaches  Manuel Santos-Trigo 7. Computational Modelling in Elementary Mathematics Teacher Education  George Gadanidis, Janette M. Hughes, Immaculate Namukasa and Ricardo Scucuglia 8. Technology Tools for Mathematics Teacher Learning: How Might They Support the Development of Capacity for Specific Teaching Assignments?  Patricio Herbst, Daniel Chazan and Amanda Milewski Part 3: Conceptual Instrumentation in Mathematics Teacher Education: Learning to Use Theories to Analyze Teaching 9. The Fractal Complexity of Using Theories in Mathematics Teacher Education: Issues and Debates, Opportunities and Limitations  Elisabeta Eriksen and Annette Hessen Bjerke 10. Controlled Implementations: Teaching Practice to Practicing Mathematics Teachers  Paola Sztajn, Lara Dick, Reema Alnizami, Dan Heck and Kristen Malzahn 11. Noticing as a Tool to Analyze Mathematics Instruction and Learning  Julie Amador 12. Theoretical Lenses to Develop Mathematics Teacher Noticing: Learning, Teaching, Psychological, and Social Perspectives  Ceneida Fernández and Ban Heng Choy 13. Transcending Contemporary Obsessions: The Development of a Model for Teacher Professional Development  Paulino Preciado-Babb, Martina Metz, Brent Davis and Soroush Sabbaghan Part 4: Crosscutting Issues on Tools and Processes in Mathematics Teacher Education 14. Using Professional Development Contexts to Structure Prospective Teacher Education  José Carrillo, Nuria Climent, Luis C. Contreras and Miguel Montes 15. From Tools to Resources in the Professional Development of Mathematics Teachers: General Perspectives and Crosscutting Issues  Abraham Arcavi Index

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Book SynopsisThis third volume of the International Handbook of Mathematics Teacher Education focuses on teachers, teacher educators, researchers, and others who work to provide effective learning opportunities for teachers, with emphasis on describing and analysing their engagement in mathematics teacher education collaborations and contexts from various perspectives.Table of ContentsPreface  Olive Chapman List of Figures and Tables Collaborations and Contexts for Participation and Learning in Mathematics Teacher Education: An Introduction  Gwendolyn M. Lloyd Part 1: Mathematics Teachers in Collaboration 1. Frameworks for Analyzing Collaborative Teacher Activity  David Slavit 2. Collaborative Construction of Knowledge by Mathematics Teachers in Their Professional Development Communities: Perspectives from Israel and Singapore  Berinderjeet Kaur and Ronnie Karsenty 3. Creativity and Openness as Indicators of Professional Growth of Leaders in Communities of Practice of Teachers Who Teach the High-Level Track of High School Mathematics  Roza Leikin and Revital Aizik 4. Lesson Study as a Learning Context in Mathematics Education  João Pedro da Ponte Geoffrey Wake and Marisa Quaresma 5. Nothing Like Planning and Reflecting Together to Build Trust: Studies on Teams of Practicing Mathematics Teachers’ and Coaches’ Collaboration  Wanty Widjaja Colleen Vale and Brian Doig Part 2: Collaborations among Diverse Participants 6. Collaborations between Mathematics Educators and Mathematicians for Mathematics Teacher Education in the United States  Fran Arbaugh, Rebecca McGraw and Cody L. Patterson 7. Research-Practice Partnerships in Mathematics Teacher Education  Rossella Santagata, Jiwon Lee and Carlos Sandoval 8. Boundary Objects in Mathematics Education and Their Role across Communities of Teachers and Researchers in Interaction  Ornella Robutti, Gilles Aldon, Annalisa Cusi, Shai Olsher, Monica Panero, Jason Cooper, Paola Carante and Theodosia Prodromou 9. Building Multidirectional Learning Opportunities between Researcher, Teacher, and Teacher Educator Communities  Mellony Graven 10. School- and University-based Mathematics Teacher Educators’ Shared Expertise in a Third Space  Courtney Lynch Rice and Gwendolyn M. Lloyd Part 3: Participation and Development across Contexts and Perspectives 11. Prospective Teachers Learning to Connect to Multiple Mathematical Knowledge Bases across Multiple Contexts  Erin Turner, Tonya Gau Bartell, Corey Drake, Mary Foote, Amy Roth McDuffie and Julia Aguirre 12. Supporting the Development of Pedagogical Judgment: Connecting Instruction to Contexts through Classroom Video with Experienced Mathematics Teachers  Ilana Seidel Horn 13. Prospective Mathematics Teachers as Learners in University and School Contexts: From University-based Activities to Classroom Practice  Laurinda Brown, Ceneida Fernández, Tracy Helliwell and Salvador Llinares 14. Practising Mathematics Teachers and Teacher-Education Initiatives: Contexts and Possibilities for Identity Development  Leticia Losano and Dario Fiorentini 15. Organising Schools for Teacher and Leader Learning  Elham Kazemi and Alison Fox Resnick Index

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Book SynopsisThis third volume of the International Handbook of Mathematics Teacher Education focuses on teachers, teacher educators, researchers, and others who work to provide effective learning opportunities for teachers, with emphasis on describing and analysing their engagement in mathematics teacher education collaborations and contexts from various perspectives.Table of ContentsPreface  Olive Chapman List of Figures and Tables Collaborations and Contexts for Participation and Learning in Mathematics Teacher Education: An Introduction  Gwendolyn M. Lloyd Part 1: Mathematics Teachers in Collaboration 1. Frameworks for Analyzing Collaborative Teacher Activity  David Slavit 2. Collaborative Construction of Knowledge by Mathematics Teachers in Their Professional Development Communities: Perspectives from Israel and Singapore  Berinderjeet Kaur and Ronnie Karsenty 3. Creativity and Openness as Indicators of Professional Growth of Leaders in Communities of Practice of Teachers Who Teach the High-Level Track of High School Mathematics  Roza Leikin and Revital Aizik 4. Lesson Study as a Learning Context in Mathematics Education  João Pedro da Ponte Geoffrey Wake and Marisa Quaresma 5. Nothing Like Planning and Reflecting Together to Build Trust: Studies on Teams of Practicing Mathematics Teachers’ and Coaches’ Collaboration  Wanty Widjaja Colleen Vale and Brian Doig Part 2: Collaborations among Diverse Participants 6. Collaborations between Mathematics Educators and Mathematicians for Mathematics Teacher Education in the United States  Fran Arbaugh, Rebecca McGraw and Cody L. Patterson 7. Research-Practice Partnerships in Mathematics Teacher Education  Rossella Santagata, Jiwon Lee and Carlos Sandoval 8. Boundary Objects in Mathematics Education and Their Role across Communities of Teachers and Researchers in Interaction  Ornella Robutti, Gilles Aldon, Annalisa Cusi, Shai Olsher, Monica Panero, Jason Cooper, Paola Carante and Theodosia Prodromou 9. Building Multidirectional Learning Opportunities between Researcher, Teacher, and Teacher Educator Communities  Mellony Graven 10. School- and University-based Mathematics Teacher Educators’ Shared Expertise in a Third Space  Courtney Lynch Rice and Gwendolyn M. Lloyd Part 3: Participation and Development across Contexts and Perspectives 11. Prospective Teachers Learning to Connect to Multiple Mathematical Knowledge Bases across Multiple Contexts  Erin Turner, Tonya Gau Bartell, Corey Drake, Mary Foote, Amy Roth McDuffie and Julia Aguirre 12. Supporting the Development of Pedagogical Judgment: Connecting Instruction to Contexts through Classroom Video with Experienced Mathematics Teachers  Ilana Seidel Horn 13. Prospective Mathematics Teachers as Learners in University and School Contexts: From University-based Activities to Classroom Practice  Laurinda Brown, Ceneida Fernández, Tracy Helliwell and Salvador Llinares 14. Practising Mathematics Teachers and Teacher-Education Initiatives: Contexts and Possibilities for Identity Development  Leticia Losano and Dario Fiorentini 15. Organising Schools for Teacher and Leader Learning  Elham Kazemi and Alison Fox Resnick Index

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Book SynopsisIn Pi (π) in Nature, Art, and Culture Marcel Danesi revisits the importance of π as a pattern in the structure of reality, fitting in with the Pythagorean view of Order. Pi has cropped up in formulas that describe natural and physical structures which, on the surface, seem to have nothing to do with a circle, but might harbor the archetype of circularity as a principle. Through π, this book thus revisits the implicit ancient Greek view that geometry was a 'hermeneutic science,' a discipline aiming to investigate the connectivity among numbers, shapes, and natural phenomena. It also examines its manifestations in aesthetic, symbolic and cultural structures, which point to an abiding fascination with the circle as an unconscious archetype. Hermeneutic geometry is ultimately about the exploration of the meanings of geometric-mathematical notions to science and human life.Trade Review"Het voortreffelijke boek laat alle lezers op fascinerende wijze kennismaken met het wonder van π. Pi, of de verhouding van de omtrek van een cirkel tot de diameter, was een van de eerste irrationele getallen die werden ontdekt." [An exccellent book which introduces the author to the wonders of Pi.] -- Jan M. Broeders, Optische Fenomenen, newsletter 405, March 2021Table of ContentsPreface 1. Discovery of π and Its Manifestations Prologue Discovery, Calculation, Proof Geometric Archetypes Manifestations of Archetypal Structure Geometry as a Hermeneutic Science Epilogue 2. Pi in Mathematics and the Physical World Prologue Pythagoreanism Uniting Arithmetic and Geometry The Planetary Orbits Natural and Physical Phenomena Topology, Non-Euclidean Geometry, and Fractal Geometry Epilogue 3. Pi in Art and Architecture Prologue Pythagoreanism in Art The Circle in Art and Symbolism Pi in Art Epilogue 4. Pi in Popular Culture Prologue Mathematics in Popular Culture Pi in Popular Culture Pi-Mania Epilogue 5. Order and Chaos Prologue Cohen’s Dilemma Chaos Theory Order and Chaos Epilogue Final Remarks References Index

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Book SynopsisThis book highlights the emergence of a new mathematical rationality and the beginning of the mathematisation of physics in Classical Islam. Exchanges between mathematics, physics, linguistics, arts and music were a factor of creativity and progress in the mathematical, the physical and the social sciences. Goods and ideas travelled on a world-scale, mainly through the trade routes connecting East and Southern Asia with the Near East, allowing the transmission of Greek-Arabic medicine to Yuan Muslim China. The development of science, first centred in the Near East, would gradually move to the Western side of the Mediterranean, as a result of Europe’s appropriation of the Arab and Hellenistic heritage. Contributors are Paul Buell, Anas Ghrab, Hossein Masoumi Hamedani, Zeinab Karimian, Giovanna Lelli, Marouane ben Miled, Patricia Radelet-de Grave, and Roshdi Rashed.Table of ContentsList of Illustrations Notes on Contributors Introduction  Giovanna Lelli 1 Science in Islam and Classical Modernity  Roshdi Rashed 2 Physics and Mathematical Sciences in the Islamic Period: A Conceptual Survey  Hossein Masaoumi Hamedani 3 Ibn al-Haytham: between Mathematics and Physics  Roshdi Rashed 4 La musique parmi les sciences dans les textes arabes médiévaux  Anas Ghrab 5 Traditional and Modern Science in an Age of Transition: ʿAlī Muḥammad Iṣfahānī and the Logarithm of Numbers  Zeinab Karimian 6 Formalism and Language in the Beginnings of Arabic Algebra  Marouane ben Miled 7 Art and Mathematics, Two Different Paths to the Same Truth  Patricia Radelet-de Grave 8 The Pre-history of the Principle of Relativity  Patricia Radelet-de Grave 9 Intersections between Social and Scientific Thought: The Notion of muṭābaqa in the Muqaddima of Ibn Khaldūn  Giovanna Lelli 10 Arabic Medicine in China: Content and Context  Paul D. Buell Index

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Book SynopsisWhat is the most descriptively and explanatorily adequate format for syntactic structures and how are they constrained? Different theories of syntax have provided various answers: sets, feature structures, tree diagrams… Building on formal and empirical insights from a wide variety of approaches spanning more than 70 years (including Transformational Grammar, Relational Grammar, Lexical-Functional Grammar, and Tree Adjoining Grammar), this monograph develops a new, mathematically grounded, framework in which objects known as graphs, and the constraints that follow from them, are argued to provide the best characterisation of the system of expressions and relations that make up natural language grammars. This new approach is motivated and exemplified via detailed and formally explicit analyses of major syntactic phenomena in English and Spanish.Table of ContentsPreface Acknowledgments List of Figures Abbreviations 1 Introduction: Setting the Scene  1.1 Methodological and Historical Context  1.2 Transformations and the Preservation of Relations  1.3 Declarative vs. Procedural Syntax  1.4 On Graphs and Phrase Markers: First- and Second-Order Conditions on Structural Representations  1.5 Structural Uniformity (and Two Ways to Fix It)  1.6 You Only Have One Mother 2 Fundamentals of Graph-Theoretic Syntax  2.1 Defining (L-)Graphs  2.2 Syntactic Composition and Semantic Interpretation  2.3 Adjacency Matrices and Arcs: More on Allowed Relations 3 A Proof of Concept: Discontinuous Constituents 4 Some Inter-Theoretical Comparisons  4.1 Multiple-Gap Relative Constructions  4.2 Dependencies and Rootedness  4.3 Crossing Dependencies 5 Ordered Relations and Grammatical Functions  5.1 A Categorial Excursus on Unaccusatives and Expletives 6 Towards an Analysis of English Predicate Complement Constructions  6.1 Raising to Subject  6.2 Raising to Object  6.3 Object-Controlled Equi  6.4 Subject-Controlled Equi  6.5 A Note on Raising and Polarity: ‘Opacity’ Revisited 7 More on Cross-Arboreal Relations: Parentheticals and Clitic Climbing in Spanish  7.1 Discontinuity and Clitic Climbing in Spanish Auxiliary Chains 8 On Unexpected Binding Effects: a Graph-Theoretic Approach to Binding Theory  8.1 Grafts and Graphs 9 Complementation within the NP 10 Wh-Interrogatives: Aspects of Syntax and Semantics  10.1 Simple Wh-Questions 11 MIG s and Prizes 12 The Structural Heterogeneity of Coordinations 13 A Small Collection of Transformations  13.1 Passivisation  13.2 Dative Shift  13.3 Transformations vs. Alternations 14 Some Open Problems and Questions  14.1 A Note on Leftward and Rightward Extractions  14.2 Deletion without Deletion  14.3 Long Distance Dependencies and Resumptive Pronouns  14.4 Identity Issues in Local Reflexive Anaphora  14.5 Ghost in the Graph  14.6 A Derivational Alternative?  14.7 Future Prospects 15 Concluding Remarks Appendix: Some Notes on (Other) Graph-Based Approaches References Index

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Book SynopsisTranslating Technology in Africa brings together authors from different disciplines who engage with Science and Technology Studies (STS) to stimulate curiosity about the diversity of sociotechnical assemblages on the African continent. The contributions provide detailed praxeographic examinations of technologies at work in postcolonial contexts. The series of 5 volumes aims to catalyse the development of a field of research that is still in its infancy in Africa and promises to offer novel insights into past, present, and future challenges and opportunities facing the continent. The first volume, on "Metrics", explores practices of quantification and digitisation. The chapters examine how numbers are aggregated and how the resulting metrics shape new realities. Contributors include Kevin. P. Donovan, Véra Ehrenstein, Jonathan Klaaren, Emma Park, Helen Robertson, René Umlauf and Helen Verran

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Book SynopsisYou are invited to join a fascinating journey of discovery, as Marcia Birken and Anne C. Coon explore the intersecting patterns of mathematics and poetry — bringing the two fields together in a new way. Setting the tone with humor and illustrating each chapter with countless examples, Birken and Coon begin with patterns we can see, hear, and feel and then move to more complex patterns. Number systems and nursery rhymes lead to the Golden Mean and sestinas. Simple patterns of shape introduce tessellations and concrete poetry. Fractal geometry makes fractal poetry possible. Ultimately, patterns for the mind lead to questions: How do mathematicians and poets conceive of proof, paradox, and infinity? What role does analogy play in mathematical discovery and poetic expression? The book will be of special interest to readers who enjoy looking for connections across traditional disciplinary boundaries. Discovering Patterns in Mathematics and Poetry features centuries of creative work by mathematicians, poets, and artists, including Fibonacci, Albrecht Dürer, M. C. Escher, David Hilbert, Benoit Mandelbrot, William Shakespeare, Edna St. Vincent Millay, Langston Hughes, E.E. Cummings, and many contemporary experimental poets. Original illustrations include digital photographs, mathematical and poetic models, and fractal imagery.Table of ContentsPreface Introduction Chapter 1 — Counting Patterns Chapter 2 — Counting Patterns Take Form Chapter 3 — Patterns of Shape Chapter 4 — Fractal Patterns Chapter 5 — Patterns for the Mind Chapter 6 — Conclusion Permissions Acknowledgements Bibliography Index

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Book SynopsisThe book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.Table of ContentsJan Woleński: Foreword Philosophy of Mathematics Cantor’s Philosophy of Set Theory Leibniz’s and Kant’s Philosophical Ideas vs. Hilbert’s Program Truth vs. Provability. Philosophical and Historical Remarks Philosophy of Mathematics in the 20th Century. Main Trends and Doctrines On New Trends in the Philosophy of Mathematics Remarks on the Structuralistic Epistemology of Mathematics (with Izabela Bondecka-Krzykowska) From the History of the Concept of Number (with Thomas Bedürftig) Church’s Thesis and Its Epistemological Status Phenomenology and Philosophy of Mathematics History of Logic and Mathematics Hoene-Wroński – Genius or Madman? Grassmann’s Contribution to Mathematics Giuseppe Peano and Symbolic Logic E.L. Post and the Development of Logic John von Neumann and Hilbert’s School Contribution of Polish Logicians to Decidability Theory Contribution of Polish Logicians to Predicate Calculus The English Algebra of Logic in the 19th Century The Development of Symbolism in Logic and Its Philosophical Background (with Thomas Bedürftig) References Acknowledgments Name Index

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