Towards an Intelligent Tutor for Mathematical Proofs

Computer-supported learning is an increasingly important form of study since it allows for independent learning and individualized instruction. In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs. We characterize the particularities of the domain and discuss common ITS design models. Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment. We show how an intelligent tutor for textbook-style mathematical proofs can be built on top of an adapted assertion-level proof assistant by reusing representations and proof search strategies originally developed for automated and interactive theorem proving. The resulting prototype was successfully evaluated on a corpus of tutorial dialogs and yields good results.Comment: In Proceedings THedu'11, arXiv:1202.453

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Improving QED-Tutrix by Automating the Generation of Proofs

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects. QED-Tutrix is an intelligent tutor for geometry offering an interface to help high school students in the resolution of demonstration problems. It focuses on specific goals: 1) to allow the student to freely explore the problem and its figure, 2) to accept proofs elements in any order, 3) to handle a variety of proofs, which can be customized by the teacher, and 4) to be able to help the student at any step of the resolution of the problem, if the need arises. The software is also independent from the intervention of the teacher. QED-Tutrix offers an interesting approach to geometry education, but is currently crippled by the lengthiness of the process of implementing new problems, a task that must still be done manually. Therefore, one of the main focuses of the QED-Tutrix' research team is to ease the implementation of new problems, by automating the tedious step of finding all possible proofs for a given problem. This automation must follow fundamental constraints in order to create problems compatible with QED-Tutrix: 1) readability of the proofs, 2) accessibility at a high school level, and 3) possibility for the teacher to modify the parameters defining the "acceptability" of a proof. We present in this paper the result of our preliminary exploration of possible avenues for this task. Automated theorem proving in geometry is a widely studied subject, and various provers exist. However, our constraints are quite specific and some adaptation would be required to use an existing prover. We have therefore implemented a prototype of automated prover to suit our needs. The future goal is to compare performances and usability in our specific use-case between the existing provers and our implementation.Comment: In Proceedings ThEdu'17, arXiv:1803.0072

Notes for a study of the didactic transposition of mathematical proof

It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case either because following an old pedagogical tradition of rote learning proof was reduced to the formalism of a text and deprived from its meaning or, despiteits acknowledged presence anywhere in mathematics, proof did not get the status of something to learn for what it is. On the long way from its absence as such in the past to its contemporary presence as a content to be taught at all grades, proof has had to go through a process of didactical transposition to satisfy a number of different constraints either of an epistemic, didactical, logical ormathematical nature. I will follow a chronological order to outline the main features of this process with the objective to better understand the didactical problem that our current research is facing.Comment: ISSN 1465-2978 (online). Philosophy of Mathematics Education Journal, In pres

How to give effective explanations: Guidelines for business education, discussion of their scope and their application to teaching operations research

Giving effective instructional explanations is one of the most important teacher competences. Recent di dactic literature provides, however, little insight on teacher explanations. In our previous work we devel- oped guidelines for designing comprehensible explanations in the field of business (teacher) education, which are along general lines transferable to other subject areas and target audiences. In this article, we first compare our guidelines to the state of research in general and mathematics didactics. We then in vestigate their applicability to teaching operations research at university level, based on interviews with professors of the international operations research community

Through the Eyes of Our Neighbors: A collaborative model for cultural, educational, and community organizations to meaningfully address homelessness in San Francisco

Abstract The following paper proposes a collaborative model in which an arts institution, a community organization, and a university come together to present a dual photography and architecture/ design exhibition, along with a series of public programs and education initiatives, to raise awareness regarding the issue of homelessness, empower members of the homeless community, and encourage museum-goers to take action. Furthermore, the project aims to partner with the City of San Francisco to implement design solutions to homelessness. The project, while large in scope, was inspired by a rather simple idea: that the museum should respond more effectively to its immediate community and exist as a place for people to engage in dialogue about how contemporary art can effect social change. Research in the museum studies field indicates that it is rare for cultural institutions to address homelessness through programming; and even less common to directly engage homeless persons or provide access to educational resources. However, by expanding the confines of traditional museum programming, it is possible to address matters of inequality and social justice more clearly and with greater impact. Keywords: access; architecture; art; community; contemporary art; cultural institution; education; exhibition; design; inequality; photography; museum studies; homeless; public program; social change; social justic