A decision making tool for mathematics curricula formal verification

Abstract

The authors have been working on mathematics curricula organization for a long time. For instance, the first author is one of the advisors of the Ph.D. Thesis of the second author, that is closely related to this topic. We have recently developed a theoretical proposal of formalization and verification of mathematics curricula that is focused on allowing their verification using techniques borrowed from artificial intelligence. Mathematics curricula can be addressed due to the hierarchical nature of their contents. The underlying idea is that, if an “official curriculum” exists (provided, for instance, by the educational authorities), it is possible to automatically check the completeness and soundness of a given “development of the official curriculum” (for instance, a textbook or a project-based learning proposal). Now a computer tool, inspired by rule based expert system verification, that is, by well-known processes that check the logical consistency of the knowledge underlying the rules, is presented. Resumen del libro: 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.