The Role of the History of Mathematics in the Teaching/Learning Process: A CIEAEM Sourcebook

Description

This volume presents multiple perspectives on the uses of the history of mathematics for teaching and learning, including the value of historical topics in challenging mathematics tasks, for provoking teachers’ reflection on the nature of mathematics, curriculum development questions that mirror earlier pedagogical choices in the history of mathematics education, and the history of technological innovations in the teaching and learning of mathematics. An ethnomathematical perspective on the history of mathematics challenges readers to appreciate the role of mathematics in perpetuating consequences of colonialism. Histories of the textbook and its uses offer interesting insights into how technology has changed the fundamental role of curriculum materials and classroom pedagogies. History is explored as a source for the training of teachers, for good puzzles and problems, and for a broad understanding of mathematics education policy. Third in a series of sourcebooks from the International Commission for the Study and Improvement of Mathematics Teaching, this collection of cutting-edge research, stories from the field, and policy implications is a contemporary and global perspective on current possibilities for the history of mathematics for mathematics education. This latest volume integrates discussions regarding history of mathematics, history of mathematics education and history of technology for education that have taken place at the Commission's recent annual conferences. Acknowledgements and Contributor Information The Role of the History of Mathematics in the Teaching/Learning Process What Is the Purpose of Teaching Mathematics from Its History? Origins Intellectual Horizon in the Incorporation of Elements of the History of Mathematics Proposal to Teach Mathematics with History References Contents Part I The Use of History in the Teaching of Mathematics Introduction References Chapter 1: The Exploration of Inaugural Understandings in the History of Mathematics and Its Potential for Didactic and Pedago... Introduction The Research Problem Inaugural Understandings in Mathematics An Example with the Work of Ptolemy A Source for Epistemological Reflections in Mathematics Education Conclusion References Chapter 2: The Value of Historical Knowledge Through Challenging Mathematical Tasks Introduction Learning Mathematics History of Mathematics to Learn Mathematics The Formative Experience Methodology Results Mathematical Activity of Students with Mathematical Tasks Involvement of Students in Carrying Out Mathematical Tasks Use of Mathematical Concepts and Representations in Solving Tasks Importance of HM-Based Maths Tasks to Student Learning Impact of HM on Learning Mathematical Content HM´s Role in Building a Holistic View of the Discipline Impact of HM for the Appreciation of Mathematics (Affective Domains) Conclusions References Chapter 3: An Historic Approach to Modelling: Enriching High School Student´s Capacities Introduction Use of the History of Mathematics in a Problematized and Modeled Teaching of Mathematics Reflection on Problem Solving as a Way to Mathematical Modelling Problematic that Can Be Posed: Study of Cases Problematic (MO): Conjectures, Proofs and Refutations ERACIS Project Experience with Secondary School Students in an ERACIS Center, in Time of the COVID 19 Pandemic Application Examples Note and Indication Problematic (C): In Reference to Content Conclusion References Chapter 4: The Introduction of the Algebraic Thought in Spain: The Resolution of the Second Degree Equation Introduction Methodology Results Sixteenth Century Books Seventeenth Century Books Eighteenth Century Book Discussion Conclusions References Part II History of Mathematics and Its Relation to Mathematical Education: Introduction References Chapter 5: Mathematics Education in Different Times and Cultures Introduction What Kind of Knowledge Is Necessary in a Mathematized Society? Some Historical Considerations of Mathematics in Relation to the New Social Visions of the World Combination of Education and Knowledge Needed to Prosper in Today´s Society Brief Reflection on Trends to Face Challenges in Mathematics Education Education as a Dynamic Process Current Trends in Mathematical Education New Challenges in the Teaching of Mathematics Multicultural and Intercultural Approaches in the Classroom As Heptalogue of IE Principles (Fig. 5.4) How to Apply an Intercultural Education in a Mathematics Classroom Multicultural Mathematics: Teaching Mathematics from a Global Perspective How to Work with Intercultural Education Cases in Developing Countries Case (a): The Use of Social and School Practices Within an Indigenous School Case (b): Afro-Colombian Studies and Basic Standards in Competencies Intercultural Dialogue Some Mathematical Competencies in the Project (CEA) Conclusion References Chapter 6: Integrating the History of Mathematics in Mathematics Education: Examples and Reflections from the Classroom Introduction Why and How Use History of Mathematics in Mathematics Education Categories of Historical Texts Examples and Reflections from the Classroom The Case of Quadratic Equation The Content of the Worksheets Evaluating the Worksheets The Case of Numbers Systems Reflections References Chapter 7: Re-constructing the Image of Mathematics Through the Diversity of the Historical Journeys of Famous Mathematicians Introduction History of Mathematics and Mathematics Education A Systemic, Interdisciplinary Approach to Teacher Training Though the History of Mathematics One Approach: Two Implementations Small-Scale Implementation: The Research Team Working Paradigm Large-Scale Implementation: Investigation-Presentations-Reflections-Written Report Concluding Remarks References Chapter 8: History of Ethnomathematics: Recent Developments Introduction: Looking for an Ethnomathematics Perspective Before EM-Connection of Culture and Mathematics Culture and Mathematics: Post-colonialism and the Emergence of Ethnomathematics Whither Ethnomathematics? Coda: History and Historiography References Part III The Role of History in the Process of Training the Mathematician Introduction References Chapter 9: Problems and Puzzles in History of Mathematics Introduction Problem Solving in Mathematics Teaching Curricula Problem Solving in Schools New Justifications for Problem Solving Different Perspectives on Mathematics Teaching First Book - Gaspar Nicolas Book - 1519 Second Book - Rui Mendes - 1541 Cultural Diversity and Intercultural Exchanges Final Considerations References Chapter 10: The Potential in Teaching the History of Mathematics to Pre-service Secondary School Teachers Introduction/Context The Process of Course Design Developing the Course Syllabus Course Readings Video Screenings Mini Lectures Activities List of Activities that Replicate Historical Ways of Doing Mathematics Major Course Assignments Did these Ideas Make a Difference for Future Teachers? Student Comments: General Remarks Other General Comments Student Comments on Objective 1: Understanding More About the Way that Mathematics Developed Historically, in All Cultures and... Student Comments on Objective 2: A Focus on Mathematics as Our Shared Human Heritage Student Comments on Objective 3: Incorporating an Appreciation of History and Culture in Their Future Teaching Student Comments on Objective 4: Communicating Mathematics in Diverse Modes to Stimulate Interest Why Does This Matter? Coda: Areas for Future Development References Chapter 11: The Role of History in Enriching Mathematics Teachers´ Training for Primary Education (6-12 Years Old Students) History of Mathematics and Elementary Teacher Knowledge History Can Help Increase Motivation: Money Systems and Number Systems Recognizing Students´ Difficulties: The Liu Hui Decompositions Example Developing Students´ Mathematical Thinking: Problem Posing Obstacles in the Development of Mathematics: The Case of Unit Measurement Humanistic Facets of Mathematical Knowledge: Isometries in Kosovo and Spain Empirical vs. Metaphorical Observations. The Case of Geometrical Reasoning Final Considerations References Chapter 12: Recent Trends of History of Mathematics Teacher Education: The Iberic American Tradition Introduction Theoretical and Historical Aspects Cognitive and Epistemic Aspects of MTE Preservice Teacher Development at Different Levels Knowledge and Practice of Mathematics Teacher Education Anthropological, Historicist, and Onto-Semiotic Approaches Identity of Teachers, Attitudes, and Beliefs Critical Issues and Ethnomathematics Studies The CIEAEM Contributions to Mathematics Teacher Education New Themes, New Perspectives References Part IV Technology in the Recent History of Mathematics Education Introduction References Chapter 13: Tools and Technologies in a Sociocultural Approach of Learning Mathematical Modelling Introduction Modern Mathematics in the 60s, Realistic Mathematics in the 70s, Modelling Process and the Emergence of Software to Support th... Use of Technology at the End of the Twentieth Century and the Beginning of the 21st Emergency of the Program on Science, Technology, Engineering and Mathematics (STEM) From a Constructivist Theoretical Framework to a Sociocultural Approach to Learning of Mathematics in a Technological Environm... Modelling Process in a Problem-Solving Approach Mathematical Modelling Mathematical Modelling, Realistic Mathematics and Use of Technology in the Mathematics Classroom Example of an Investigation in the Classroom Using ACODESA´s Method Example of Integrating a Cinematic Context, Technology and Mathematics Conclusions References Chapter 14: Technology in Primary and Secondary School to Teach and Learn Mathematics in the Last Decades Introduction Theoretical Frame and Literature Review Technology for Visualising, Representing and Manipulating Mathematical Objects Technology to Enrich and Gamify Mathematical Tasks Technology to Orchestrate and Instrument Mathematical Discussion Technology to Assess Mathematical Learning Technology for Distance Training Challenges to Be Faced Inquiring-Game Activities Within DGE to Discover Geometry Theorems Mathematical Internet Memes as Educational Resources Conclusion References Chapter 15: A Trajectory of Digital Technologies Integration in Mathematical Education in Brazil: Challenges and Opportunities Introduction Brief Historical Overview of DICT Integration in Mathematics Teaching Constructionism: A Theoretical Construct Computational Thinking and Mathematics The Common National Base Curriculum (BNCC) and the Teaching of Mathematics The Teacher Education and Professional Knowledge Final Considerations References Chapter 16: History, Technology and Dynamic Geometry: From Resources with Static Construction to DGE with Touchscreen Introduction Didactic Resources and the Search for Mathematical Innovation DGEs Transforming Mathematics and Curricular Contents Touchscreen Devices Entering the Learning Environment Teaching Parallel Lines Intersected by a Transversal Line with the GeoGebra App About Concurrent Lines with Angles (Task 1) About Parallel Lines Intersected by a Transversal Line (Task 2) Moving from Only Nominating to Understandings, Sharing, and Publicizing Ideas and Justifications Conclusion Appendix Task 1 Task 2 References Conclusion of the Book References Index