This book highlights the contribution of artificial intelligence for mathematics education. It provides concrete ideas supported by mathematical work obtained through dynamic international collaboration, and discusses the flourishing of new mathematics in the contemporary world from a sustainable development perspective.
Over the past thirty years, artificial intelligence has gradually infiltrated all facets of society. When it is deployed in interaction with the human designer or user, AI certainly raises new ethical questions. But as soon as it aims to augment intelligence in a kind of human-machine partnership, it goes to the heart of knowledge development and the very performance of work. The proposed themes and the sections of the book address original issues relating to the creation of AI milieus to work on mathematics, to the AI-supported learning of mathematics and to the coordination of « usual » paper/pencil techniques and « new » AI-aided educational working spaces. The authors of the book and the coordinators of each section are all established specialists in mathematics didactics, mathematics and computer science. In summary, this book is a must-read for everyone interested in the teaching and learning of mathematics, and it concerns the interaction between the human and the machine in both directions. It contains ideas, questions and inspiration that invite to take up the challenge of Artificial Intelligence contributing to Mathematical Human Learning.
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Creation of AI Milieus to Work on Mathematics |
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Evolution of Automated Deduction and Dynamic Constructions in Geometry |
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3 | (20) |
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Automated Reasoning Tools with GeoGebra: What Are They?What Are They Good For? |
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23 | (22) |
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Intelligence in QED-Tutrix: Balancing the Interactions Between the Natural Intelligence of the User and the Artificial Intelligence of the Tutor Software |
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45 | (32) |
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A Decision Making Tool for Mathematics Curricula Formal Verification |
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77 | (12) |
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Angelica Martfnez-Zarzuelo |
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A Classification of Artificial Intelligence Systems for Mathematics Education |
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89 | (18) |
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AI and Mathematics Interaction for a New Learning Paradigm on Monumental Heritage |
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107 | (34) |
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Al-Supported Learning of Mathematics |
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Using Didactic Models to Design Adaptive Pathways to Meet Students' Learning Needs in an Online Learning Environment |
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141 | (26) |
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Francoise Chenevotot-Quentin |
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Combining Pencil/Paper Proofs and Formal Proofs, A Challenge for Artificial Intelligence and Mathematics Education |
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167 | (26) |
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Interaction Between Subject and DGE by Solving Geometric Problems |
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193 | (20) |
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Creative Use of Dynamic Mathematical Environment in Mathematics Teacher Training |
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213 | (18) |
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Experimental Study of Isoptics of a Plane Curve Using Dynamical Coloring |
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231 | (20) |
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Teaching Programming for Mathematical Scientists |
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251 | (32) |
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The present and future of AI in ME: Insight from empirical research CAS Use in University Mathematics Teaching and Assessment: Applying Oates' Taxonomy for Integrated Technology |
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283 | (36) |
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Modeling Practices to Design Computer Simulators for Trainees' and Mentors' Education |
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319 | (24) |
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Exploring Dynamic Geometry Through Immersive Virtual Reality and Distance Teaching |
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343 | (22) |
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Historical and Didactical Roots of Visual and Dynamic Mathematical Models: The Case of "Rearrangement Method" for Calculation of the Area of a Circle |
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365 | (34) |
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Implementing STEM Projects Through the EDP to Learn Mathematics: The Importance of Teachers' Specialization |
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399 | (18) |
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Jose-Manuel Diego-Mantecon |
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Digital Technology and Its Various Uses from the Instrumental Perspective: The Case of Dynamic Geometry |
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417 | (14) |
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| Conclusions |
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431 | (6) |
| Epilogue |
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437 | (4) |
| Appendix: Photographs of the Book Project and Some of the Authors |
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441 | (6) |
| Index |
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Philippe R. Richard is professeur titulaire (full professor) in the Département de didactique at the Université de Montréal. He is a specialist in didactics of mathematics and computer science. He has participated in and has led several major programs concerning didactics, mathematics and computer science. His current research activity extends the recent technological achievements of his research team in artificial intelligence. He is regularly invited to chair thematic groups (CERME, ICME) and to preside over symposia on mathematical work (ETM). He also gives research seminars and participates in the writing of synthesis texts and as editors for books. He has been a visiting professor at the Universitat Autònoma de Barcelona, the Université de Paris and the École Polytechnique de Montréal, and he is currently editor-in-chief of the journal Annales de didactique et de sciences cognitives (IREM, Université de Strasbourg).
M. Pilar Vélez is professor of applied mathematics at the Universidad Antonio de Nebrija (Madrid, Spain). She is member of the research group PID2020-113192GB-I00 (Mathematical Visualization: Foundations, Algorithms and Applications) from the Spanish MICINN. She has been Rector of Universidad Antonio de Nebrija from 2010 to 2014. She authorship several scientific papers in different indexed journals and many scientific communications and conferences on topics as Real Algebraic Geometry, Computer Algebra, Automatic Reasoning in Dynamic Geometry and Mathematics Education. Now her research interest is focused in automatic reasoning in geometry, as well as algorithms, implementation and its applications to other fields as math education, linkages visualization and augmented reality. She has been organizer of international workshops, special sessions and conferences, as well as program committe (ACA, CAGDME, ATCM, Maple Conference, Bienal RSME, RAAG). She has been a guest researcher at Università di Pisa, Louisiana State University, Johannes Kepler University and at the University of Montreal. She has been invited to deliver lectures at the IHP of Paris, the University of Trento, the Eindhoven University of Technology, the Louisiana State University or the University of Pisa.
Steven Van Vaerenbergh is assistant professor in the Department of Mathematics, Statistics and Computing at Universidad de Cantabria (Spain). He has conducted research in artificial intelligence, co-authoring scientific publications on machine learning theory and multivariate statistics. Drawing upon this experience, his current research activity focuses on the applications of artificial intelligence in mathematics education, in particular on novel technological learning environments and automated systems to provide individualized learning experiences. He has co-authored several scientific papers on these topics, as well as publications on related subjects such as dynamic geometry systems. He hasparticipated in the organizing committees of international conferences and, in particular, he recently co-organized the Symposium on Artificial Intelligence for Mathematics Education (AI4ME).
