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

Human-machine communication for educational systems design

This book contains the papers presented at the NATO Advanced Study Institute (ASI) on the Basics of man-machine communication for the design of educational systems, held August 16-26, 1993, in Eindhoven, The Netherland

Recognising the design decisions in Prolog programs as a prelude to critiquing

This thesis presents an approach by which an automated teaching system can analyse the design of novices' Prolog programs for tutorial critiquing. Existing methodologies for tutorial analysis of programs focus on the kind of small pro¬ gramming examples that are used only in the early stages of teaching. If an automated teaching system is to be widely useful, it must cover a substantial amount of the teaching syllabus, and a critiquing system must be able to analyse and critique programs written during the later stages of the syllabus.The work is motivated by a study of students' Prolog programs which were written as assessed exercises towards the end of their course. These programs all work (in some sense), yet they reveal a wide range of design (laws (bodges) for which some form of tutoring would be useful. They present problems for any automated analysis in terms of the size of the programs, the number of individual decisions that must be made to create each program and the range of correct and incorrect decisions that may be made in each case.This study identifies two areas in the analysis of students' program in which further work is needed. Existing work has focussed only on the design and implementation decisions that relate closely to the programming language. That is not sufficient for these slightly more advanced programs, for which decisions in the problem domain must also be recognised. Existing work has focussed on the different ways to implement code, but in these programs the students also make decisions about which data structures are to be used. These decisions must also be part of an analysis.The thesis provides an approach which represents both decisions in the domain of the problem being solved and decisions about how to implement them in Prolog. Decisions in the problem domain are represented by tasks (for code) and by domain objects (for data structures). Decisions that are specific to the Prolog implementation are represented by prototypes which encapsulate standard programming techniques (for code) and by a polymorphic data type language (for data structures). Issues in devising these representations are discussed.An analysis-by synthesis approach is used for code recognition. This is aug¬ mented by a procedure called "clausal split" which isolates novel or poorly de¬ signed parts of an implementation. Following an incomplete analysis of the program by synthesis, the results of this analysis provide the basis for making inferences about the parts of the program that have not been understood. For analysing data structures, a type inference mechanism is combined with inference about the parts of domain objects. Inferred data type information is also used to limit search, both for synthesis and analysis.An architecture using this approach has been implemented. The success of the architecture is assessed on student's programs. From this assessment it is clear that much further work remains to be done, but the results are hopeful

Leonora Duarte (1610–1678): Converso Composer in Antwerp

Leonora Duarte (1610–1678), a converso of Jewish descent living in Antwerp, is the author of seven five-part Sinfonias for viol consort — the only known seventeenth-century viol music written by a woman. This music is testament to a formidable talent for composition, yet very little is known about the life and times in which Duarte produced her work. Her family were merchants and art collectors of Jewish descent who immigrated from Portugal in the early sixteenth century to escape the Inquisition; in exile in Antwerp, they achieved enormous success and provided the means with which to educate their children and integrate them into certain aspects of their business world. Duarte’s musical education reveals knowledge of many instruments as well as lessons in composition and it is manifested in the prominence her music played in her internationally-known family. Examining Duarte’s life presents a remarkable opportunity to consider performance within the early modern domestic sphere — this is a project that intersects with embodiment and display, as well as issues of gender and race. This dissertation considers Duarte and her music as products of diverse influences within the landscape of post-Inquisition Antwerp, as evidence of complex and symbiotic relationships with contemporaries, and as vital testimony to the cultural accomplishments of women conversos in early modern Europe, about which almost nothing is known. It draws upon musical analysis, critical theory, art history, Jewish studies, and my own performances and recording of her music. What emerges is a narrative in which the experience of domestic musical performance allowed Duarte to navigate the waters of social diplomacy within the broader context of cultural exchange in Antwerp