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

Modelling human teaching tactics and strategies for tutoring systems

One of the promises of ITSs and ILEs is that they will teach and assist learning in an intelligent manner. Historically this has tended to mean concentrating on the interface, on the representation of the domain and on the representation of the student’s knowledge. So systems have attempted to provide students with reifications both of what is to be learned and of the learning process, as well as optimally sequencing and adjusting activities, problems and feedback to best help them learn that domain. We now have embodied (and disembodied) teaching agents and computer-based peers, and the field demonstrates a much greater interest in metacognition and in collaborative activities and tools to support that collaboration. Nevertheless the issue of the teaching competence of ITSs and ILEs is still important, as well as the more specific question as to whether systems can and should mimic human teachers. Indeed increasing interest in embodied agents has thrown the spotlight back on how such agents should behave with respect to learners. In the mid 1980s Ohlsson and others offered critiques of ITSs and ILEs in terms of the limited range and adaptability of their teaching actions as compared to the wealth of tactics and strategies employed by human expert teachers. So are we in any better position in modelling teaching than we were in the 80s? Are these criticisms still as valid today as they were then? This paper reviews progress in understanding certain aspects of human expert teaching and in developing tutoring systems that implement those human teaching strategies and tactics. It concentrates particularly on how systems have dealt with student answers and how they have dealt with motivational issues, referring particularly to work carried out at Sussex: for example, on responding effectively to the student’s motivational state, on contingent and Vygotskian inspired teaching strategies and on the plausibility problem. This latter is concerned with whether tactics that are effectively applied by human teachers can be as effective when embodied in machine teachers

Intelligent tutoring systems for systems engineering methodologies

The general goal is to provide the technology required to build systems that can provide intelligent tutoring in IDEF (Integrated Computer Aided Manufacturing Definition Method) modeling. The following subject areas are covered: intelligent tutoring systems for systems analysis methodologies; IDEF tutor architecture and components; developing cognitive skills for IDEF modeling; experimental software; and PC based prototype

OFMTutor: An operator function model intelligent tutoring system

The design, implementation, and evaluation of an Operator Function Model intelligent tutoring system (OFMTutor) is presented. OFMTutor is intended to provide intelligent tutoring in the context of complex dynamic systems for which an operator function model (OFM) can be constructed. The human operator's role in such complex, dynamic, and highly automated systems is that of a supervisory controller whose primary responsibilities are routine monitoring and fine-tuning of system parameters and occasional compensation for system abnormalities. The automated systems must support the human operator. One potentially useful form of support is the use of intelligent tutoring systems to teach the operator about the system and how to function within that system. Previous research on intelligent tutoring systems (ITS) is considered. The proposed design for OFMTutor is presented, and an experimental evaluation is described

Optimising ITS behaviour with Bayesian networks and decision theory

We propose and demonstrate a methodology for building tractable normative intelligent tutoring systems (ITSs). A normative ITS uses a Bayesian network for long-term student modelling and decision theory to select the next tutorial action. Because normative theories are a general framework for rational behaviour, they can be used to both define and apply learning theories in a rational, and therefore optimal, way. This contrasts to the more traditional approach of using an ad-hoc scheme to implement the learning theory. A key step of the methodology is the induction and the continual adaptation of the Bayesian network student model from student performance data, a step that is distinct from other recent Bayesian net approaches in which the network structure and probabilities are either chosen beforehand by an expert, or by efficiency considerations. The methodology is demonstrated by a description and evaluation of CAPIT, a normative constraint-based tutor for English capitalisation and punctuation. Our evaluation results show that a class using the full normative version of CAPIT learned the domain rules at a faster rate than the class that used a non-normative version of the same system

Intelligent computer-aided training and tutoring

Specific autonomous training systems based on artificial intelligence technology for use by NASA astronauts, flight controllers, and ground-based support personnel that demonstrate an alternative to current training systems are described. In addition to these specific systems, the evolution of a general architecture for autonomous intelligent training systems that integrates many of the features of traditional training programs with artificial intelligence techniques is presented. These Intelligent Computer-Aided Training (ICAT) systems would provide, for the trainee, much of the same experience that could be gained from the best on-the-job training. By integrating domain expertise with a knowledge of appropriate training methods, an ICAT session should duplicate, as closely as possible, the trainee undergoing on-the-job training in the task environment, benefitting from the full attention of a task expert who is also an expert trainer. Thus, the philosophy of the ICAT system is to emulate the behavior of an experienced individual devoting his full time and attention to the training of a novice - proposing challenging training scenarios, monitoring and evaluating the actions of the trainee, providing meaningful comments in response to trainee errors, responding to trainee requests for information, giving hints (if appropriate), and remembering the strengths and weaknesses displayed by the trainee so that appropriate future exercises can be designed

Natural‐language processing applied to an ITS interface

The aim of this paper is to show that with a subset of a natural language, simple systems running on PCs can be developed that can nevertheless be an effective tool for interfacing purposes in the building of an Intelligent Tutoring System (ITS). After presenting the special characteristics of the Smalltalk/V language, which provides an appropriate environment for the development of an interface, the overall architecture of the interface module is discussed. We then show how sentences are parsed by the interface, and how interaction takes place with the user. The knowledge‐acquisition phase is subsequently described. Finally, some excerpts from a tutoring session concerned with elementary geometry are discussed, and some of the problems and limitations of the approach are illustrated

Proceedings of QG2010: The Third Workshop on Question Generation

These are the peer-reviewed proceedings of "QG2010, The Third Workshop on Question Generation". The workshop included a special track for "QGSTEC2010: The First Question Generation Shared Task and Evaluation Challenge". QG2010 was held as part of The Tenth International Conference on Intelligent Tutoring Systems (ITS2010)