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.
Author(s): Sixto Romero Sanchez, Ana Serradó Bayés, Peter Appelbaum Gilles Aldon
Series: Advances in Mathematics Education
Publisher: Springer-CIEAEM
Year: 2023
Language: English
Pages: 463
City: Torino
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
