Mathematics Education in the Age of Artificial Intelligence

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 techniquesand « 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.

• Didactics of Mathematics
• Artificial Intelligence and Mathematics
• Teaching and Learning of Geometry
• Teacher Training in Mathematics
• Computer-assisted Reasoning, Instrumental Proof and Discovery
• Instrumented learning of Mathematics
• Intelligent Tutorial Systems
• Automated Reasoning in Education
• AI-supported Learning of Mathematics
• Instrumented Mathematics
• Adapting Artificial Intelligence for Education
• AI-aided Educational Working Spaces

• Département de didactique, Université de Montréal, Montréal, Canada

  Philippe R. Richard

• Departamento de Ingeniería Industrial, Universidad Antonio de Nebrija, Madrid, Spain

  M. Pilar Vélez

• Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

  Steven Van Vaerenbergh

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).

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