Automatic Generation of Analogous Problems to Help Resolving Misconceptions in an Intelligent Tutor System for Written Subtraction

In domains involving procedural skills such as mathematics or programming, students often are prone to misconceptions which result in erroneous solutions. We present the ASG algorithm for generation of analogous problems of written subtraction as an extension of an intelligent tutor system (ITS) proposed by Zinn (2014). The student module of this ITS does not rely on an error library but uses algorithmic de-bugging where an erroneous solution is recognized by identifying which expert rules fail when trying to reproduce the student solution. Since the ITS allows students to create their own subtraction problems, feedback generation must be online and automatic. ASG is a constraint-based algorithm for constructing problems which are structurally isomorphic to the current, erroneously solved student problem

Un modèle pour la génération d'indices par une plateforme de tuteurs par traçage de modèle

La présente thèse décrit des travaux de recherche effectués dans le domaine des systèmes tutoriels intelligents (STI). Plus particulièrement, elle s'intéresse aux tuteurs par traçage de modèle (MTT). Les MTTs ont montré leur efficacité pour le tutorat de la résolution de tâches bien définies. Par contre, les interventions pédagogiques qu'ils produisent doivent être incluses, par l'auteur du tuteur, dans le modèle de la tâche enseignée. La recherche effectuée répond à cette limite en proposant des méthodes et algorithmes permettant la génération automatique d'interventions pédagogiques. Une méthode a été développée afin de permettre à la plateforme Astus de générer des indices par rapport à la prochaine étape en examinant le contenu du modèle de la tâche enseignée. De plus, un algorithme a été conçu afin de diagnostiquer les erreurs des apprenants en fonction des actions hors trace qu'ils commettent. Ce diagnostic permet à Astus d'offrir une rétroaction par rapport aux erreurs sans que l'auteur du tuteur ait à explicitement modéliser les erreurs. Cinq expérimentations ont été effectuées lors de cours enseignés au département d'informatique de l'Université de Sherbrooke afin de valider de façon empirique les interventions générées par Astus. Le résultat de ces expérimentations montre que 1) il est possible de générer des indices par rapport à la prochaine étape qui sont aussi efficaces et aussi appréciés que ceux conçus par un enseignant et que 2) la plateforme Astus est en mesure de diagnostiquer un grand nombre d'actions hors trace des apprenants afin de fournir une rétroaction par rapport aux erreurs

An application of formal semantics to student modelling : an investigation in the domain of teaching Prolog

This thesis reports on research undertaken in an exploration of the use of formal semantics for student modelling in intelligent tutoring systems. The domain chosen was that of tutoring programming languages and within that domain Prolog was selected to be the target language for this exploration. The problem considered is one of how to analyse students' errors at a level which allows diagnosis to be more flexible and meaningful than is possible with the 'mal-rules' and 'bugcatalogue' approach of existing systems. The ideas put forward by Robin Milner [1980] in his Calculus of Communicating Systems (CCS) form the basis of the formalism which is proposed as a solution to this problem. Based on the findings of an empirical investigation, novices' misconceptions of control flow in Prolog was defined as a suitable area in which to explore the application of this solution. A selection of Prolog programs used in that investigation was formally described in terms of CCS. These formal descriptions were used by a production rule system to generate a number of the incomplete or faulty models of Prolog execution which were identified in the first empirical study. In a second empirical study, a machine-analysis tool, designed to be part of a diagnostic tutoring module, used these models to diagnose students' misconceptions of Prolog control flow. This initial application of CCS to student modelling showed that the models of Prolog execution generated by the system could be used successfully to detect students' misunderstandings. Results from the research reported here indicate that the use of formal semantics to model programming languages has a useful contribution to make to the task of student modelling

Applying science of learning in education: Infusing psychological science into the curriculum

The field of specialization known as the science of learning is not, in fact, one field. Science of learning is a term that serves as an umbrella for many lines of research, theory, and application. A term with an even wider reach is Learning Sciences (Sawyer, 2006). The present book represents a sliver, albeit a substantial one, of the scholarship on the science of learning and its application in educational settings (Science of Instruction, Mayer 2011). Although much, but not all, of what is presented in this book is focused on learning in college and university settings, teachers of all academic levels may find the recommendations made by chapter authors of service. The overarching theme of this book is on the interplay between the science of learning, the science of instruction, and the science of assessment (Mayer, 2011). The science of learning is a systematic and empirical approach to understanding how people learn. More formally, Mayer (2011) defined the science of learning as the “scientific study of how people learn” (p. 3). The science of instruction (Mayer 2011), informed in part by the science of learning, is also on display throughout the book. Mayer defined the science of instruction as the “scientific study of how to help people learn” (p. 3). Finally, the assessment of student learning (e.g., learning, remembering, transferring knowledge) during and after instruction helps us determine the effectiveness of our instructional methods. Mayer defined the science of assessment as the “scientific study of how to determine what people know” (p.3). Most of the research and applications presented in this book are completed within a science of learning framework. Researchers first conducted research to understand how people learn in certain controlled contexts (i.e., in the laboratory) and then they, or others, began to consider how these understandings could be applied in educational settings. Work on the cognitive load theory of learning, which is discussed in depth in several chapters of this book (e.g., Chew; Lee and Kalyuga; Mayer; Renkl), provides an excellent example that documents how science of learning has led to valuable work on the science of instruction. Most of the work described in this book is based on theory and research in cognitive psychology. We might have selected other topics (and, thus, other authors) that have their research base in behavior analysis, computational modeling and computer science, neuroscience, etc. We made the selections we did because the work of our authors ties together nicely and seemed to us to have direct applicability in academic settings

Design considerations of an intelligent tutoring system for programming languages

The overall goal of the thesis is to attempt to highlight the major topics which must be considered in the design of any Intelligent Tutoring System and to illustrate their application within the particular domain of LISP programming. There are two major sections to the thesis. The first considers the background to the educational application of computers. It examines possible roles for the computer, explores the relationship between education theory and computer-based teaching, and identifies some important links among existing Tutoring Systems. The section concludes with a summary of the design goals which an Intelligent Tutoring System should attempt to fulfill. The second section applies the design goals to the production of an Intelligent Tutoring System for programming languages. It devises a formal semantic description for programming languages and illustrates its application to tutoring. A method for modelling the learning process is introduced. Some techniques for maintaining a structured tutoring interaction are described. The work is set within the methodology of Artificial Intelligence research. Although a fully implemented tutoring system is not described, all features discussed are implemented as short programs intended to demonstrate the feasibility of the approach taken

Widening the Knowledge Acquisition Bottleneck for Intelligent Tutoring Systems

Empirical studies have shown that Intelligent Tutoring Systems (ITS) are effective tools for education. However, developing an ITS is a labour-intensive and time-consuming process. A major share of the development effort is devoted to acquiring the domain knowledge that accounts for the intelligence of the system. The goal of this research is to reduce the knowledge acquisition bottleneck and enable domain experts to build the domain model required for an ITS. In pursuit of this goal an authoring system capable of producing a domain model with the assistance of a domain expert was developed. Unlike previous authoring systems, this system (named CAS) has the ability to acquire knowledge for non-procedural as well as procedural tasks. CAS was developed to generate the knowledge required for constraint-based tutoring systems, reducing the effort as well as the amount of expertise in knowledge engineering and programming required. Constraint-based modelling is a student modelling technique that assists in somewhat easing the knowledge acquisition bottleneck due to the abstract representation. CAS expects the domain expert to provide an ontology of the domain, example problems and their solutions. It uses machine learning techniques to reason with the information provided by the domain expert for generating a domain model. A series of evaluation studies of this research produced promising results. The initial evaluation revealed that the task of composing an ontology of the domain assisted with the manual composition of a domain model. The second study showed that CAS was effective in generating constraints for the three vastly different domains of database modelling, data normalisation and fraction addition. The final study demonstrated that CAS was also effective in generating constraints when assisted by novice ITS authors, producing constraint sets that were over 90% complete

Information enforcement in learning with graphics : improving syllogistic reasoning skills

This thesis is an investigation into the factors that contribute to good choices among graphical systems used in teaching, and the feasibility of implementing teaching software that uses this knowledge.The thesis describes a mathematical metric derived from a cognitive theory of human diagram processing. The theory characterises differences among representations by their ability to express information. The theory provides the factors and relationships needed to build the metric. It says that good representations are easily processed because they are more vivid, more tractable and less expressive, than poor representations.The metric is applied to abstract systems for teaching and learning syllogistic reasoning, TARSKI'S WORLD, EULER CIRCLES, VENN DIAGRAMS and CARROLL'S GAME OF LOGIC. A rank ordering reflects the value of each system predicted by the theory and the metric. The theory, the metric and the systems are then tested in empirical studies. Five studies involving sixty-eight learners, examined the benefit of software based on these abstract systems.Studies showed the theory correctly predicted learners' success with the circle systems and poorer performance with TARSKI'S WORLD. The metric showed small but clear differences in expressivity between the circle systems. Differences between results of the learners using the circle systems contradicted the predictions of the metric.Learners with mathematical training were better equipped and more successful at learning syllogistic reasoning with the systems. Performance of learners without mathematical training declined after using the software systems. Diagrams drawn by learners together with video footage collected during problem solving, led to a catalogue of errors, misconceptions and some helpful strategies for learning from graphical systems.A cognitive style test investigated the poor performance of non-mathematically trained learners. Learners with mathematics training showed serialist and versatile learning styles while learners without this training showed a holist learning style. This is consistent with the hypothesis that non-mathematically trained learners emphasise the use of semantic cues during learning and problem solving.A card-sorting task investigated learners' preferences for parts of the graphical lexicon used in the diagram systems. Preferences for the EULER lexicon increased difficulty in explaining the system's poor results in earlier studies. Video footage of learners using the systems in the final study illustrated useful learning strategies and improved performance with EULER while individual instruction was available.Further work describes a preliminary design for an adaptive syllogism tutor and other related work

Rethinking teaching strategies : a framework and demonstration through augmenting Maple

In this work, an interdisciplinary approach has been adopted for the study of • teaching strategies of an Intelligent Tutoring System, in the paradigm of multiple teaching strategies, and • the use of Computer Algebra Systems (CAS) in teaching problem solving in university mathematics. As a result, the SIMTA (Styles Implemented by Methods Tactics Actions) theoretical framework has been developed to support and sustain teaching strategies in the paradigm of multiple teaching strategies. TeLoDe (TEaching Linear Ordinary Differential Equations), is a prototype Intelligent Tutoring System, teaching the ,solution of linear second order differential equations with constant coefficients in a novel way. This novel way, which has been empirically tested, has been achieved by augmenting Maple and represents an alternative use of CASs where the human lecturer and Maple are interlocked in a symbiotic and interdependent manner. In SIMTA, the contemporary concept of teaching strategy is rethought and proposed to be viewed at two fundamental levels: • the organisational level • and the operational level. The organisational level deals with the structure of the teaching strategy whereas the operational level deals with the manifestation of that structure. In SIMTA the organisational level is represented by a triple generic structure, method, tactic(s), action(s). A method is a mechanism for structuring the subject matter (e.g. analogy, examples, generalisation, specialisation). Likewise, a tactic is a mechanism for facilitating the interaction (e.g. explicit interaction, implicit interaction). An action is a low level activity such as display this message, ask this question. In SIMTA, the exact manifestation of the above generic structures (analogies, examples, implicit interaction, explicit interaction) depends on the concept of style: different styles result in different manifestations of the same generic structures. Thus, in SIMTA the concept of multiple teaching strategies is seen as merely a collection of teaching strategies manifested under the same style. These strategies operate with the aim of offering alternative representations of the same task at hand and ensuring that the lea~er is active by activating, directing and maintaining exploration. To help demonstrate the feasibility of SIMTA, two styles, the expository style and the , guided discovery style have been formed. The expository style draws on Ausubel's theory of meaningful learning, whereas, the guided discovery style draws on Bruner's work. These styles have been implemented in TeLoDe. TeLoDe, incorporates a teaching strategy module, based on a style, and declarative knowledge. Its purpose is threefold: (i) to serve as a research tool for the SIMTA framework, (ii) to serve as a prototype, demonstrating clearly how a 'second generation' CAS which undertakes the procedural aspect of mathematics allowing the human tutor to concentrate on its conceptual aspect, could be developed, (iii) to demonstrate how Maple and human lecturers are given clear roles which are, nevertheless, interdependent in carrying out the teaching of university mathematics. Two small-scale empirical studies were carried out in order to test SIMTA and TeLoDe respectively. The first study involved lecturers whereas the second study was carried out in a classroom environment. The results found from these studies demonstrate that TeLoDe has a potential as a teaching tool for problem solving in university mathematics in a novel way