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

Designing intelligent computer‐based simulations: A pragmatic approach

This paper examines the design of intelligent multimedia simulations. A case study is presented which uses an approach based in part on intelligent tutoring system design to integrate formative assessment into the learning of clinical decision‐making skills for nursing students. The approach advocated uses a modular design with an integrated intelligent agent within a multimedia simulation. The application was created using an object‐orientated programming language for the multimedia interface (Delphi) and a logic‐based interpreted language (Prolog) to create an expert assessment system. Domain knowledge is also encoded in a Windows help file reducing some of the complexity of the expert system. This approach offers a method for simplifying the production of an intelligent simulation system. The problems developing intelligent tutoring systems are examined and an argument is made for a practical approach to developing intelligent multimedia simulation systems

Requirements for an Adaptive Multimedia Presentation System with Contextual Supplemental Support Media

Investigations into the requirements for a practical adaptive multimedia presentation system have led the writers to propose the use of a video segmentation process that provides contextual supplementary updates produced by users. Supplements consisting of tailored segments are dynamically inserted into previously stored material in response to questions from users. A proposal for the use of this technique is presented in the context of personalisation within a Virtual Learning Environment. During the investigation, a brief survey of advanced adaptive approaches revealed that adaptation may be enhanced by use of manually generated metadata, automated or semi-automated use of metadata by stored context dependent ontology hierarchies that describe the semantics of the learning domain. The use of neural networks or fuzzy logic filtering is a technique for future investigation. A prototype demonstrator is under construction

The importance of epistemic cognition in student-centred learning

To infer the sophistication of epistemic thinking in a sample of undergraduate students, 25 participants completed a free-response task in which they were asked to give reasons for their agreement or disagreement with a small number of beliefs about the role of tutorials and of tutors in gaining knowledge. Responses were analysed according to King & Kitchener's (1994) stages of reasoning, revealing that the justifications offered were either at the stages of pre-reflective or quasi-reflective thinking with none exhibiting reflective thinking. The findings have two main pedagogical implications: first that good teaching be understood not as a set of performance skills which may only be opportunistically related to students' extant conceptualisations but as the locus through which students confront their own epistemic beliefs. A second implication is that to extend students' reasoning, teaching practices must focus explicitly on the difficult issue of what counts as evidenc

An evaluation of pedagogically informed parameterised questions for self assessment

Self-assessment is a crucial component of learning. Learners can learn by asking themselves questions and attempting to answer them. However, creating effective questions is time-consuming because it may require considerable resources and the skill of critical thinking. Questions need careful construction to accurately represent the intended learning outcome and the subject matter involved. There are very few systems currently available which generate questions automatically, and these are confined to specific domains. This paper presents a system for automatically generating questions from a competency framework, based on a sound pedagogical and technological approach. This makes it possible to guide learners in developing questions for themselves, and to provide authoring templates which speed the creation of new questions for self-assessment. This novel design and implementation involves an ontological database that represents the intended learning outcome to be assessed across a number of dimensions, including level of cognitive ability and subject matter. The system generates a list of all the questions that are possible from a given learning outcome, which may then be used to test for understanding, and so could determine the degree to which learners actually acquire the desired knowledge. The way in which the system has been designed and evaluated is discussed, along with its educational benefits