Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer-adaptive practice

We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person-by-item data matrix and reproduces the sufficient statistics of the complete data matrix. Hence, longitudinal comparisons can be easily made based on simple summaries, such as proportion correct, sum score, etc. As an illustration of the method, an example is provided using data from a computer-adaptive practice mathematical environment

Feedback services for stepwise exercises

Advanced learning environments such as intelligent tutoring systems for algebra, logic, programming, physics, etc. let a student practice with stepwise exercises, and support a student solving such exercises by providing feedback. These environments usually provide various types of feedback, for example about the correctness of a step, common errors, hints about how to proceed, or complete worked-out solutions. Calculating feedback is generally delegated to a dedicated expert knowledge module, also known as a domain reasoner. Existing architectural descriptions of learning environments do not precisely specify the interaction between this module and the rest of the learning system. We propose a design based on the stateless client-server architecture that clearly decouples the expert knowledge module from the learning environment. We describe a set of feedback services that support the inner (interactions within an exercise) and outer (over a collection of exercises) loops of a learning system, and that provide meta-information about a class of exercises, such as solving quadratic equations, or performing Gaussian elimination. The feedback services do not depend on a particular domain and are based on the various feedback types described in the literature. The paper analyzes which domain-specic knowledge about an exercise class is needed for implementing the feedback services. Based on this analysis, we developed a framework for implementing domain reasoners that oers generic functionality such as rewriting, simplifying, and comparing terms. We have implemented several domain reasoners in this framework, both for external learning environments and for simple prototypes. The proposed design is evaluated with these implementations, and we re ect on our experience with developing domain reasoners

Knowledge models from PDF textbooks

Textbooks are educational documents created, structured and formatted by domain experts with the primary purpose to explain the knowledge in the domain to a novice. Authors use their understanding of the domain when structuring and formatting the content of a textbook to facilitate this explanation. As a result, the formatting and structural elements of textbooks carry the elements of domain knowledge implicitly encoded by their authors. Our paper presents an extensible approach towards automated extraction of knowledge models from textbooks and enrichment of their content with additional links (both internal and external). The textbooks themselves essentially become hypertext documents where individual pages are annotated with important concepts in the domain. The evaluation experiments examine several aspects and stages of the approach, including the accuracy of model extraction, the pragmatic quality of extracted models using one of their possible applications— semantic linking of textbooks in the same domain, the accuracy of linking models to external knowledge sources and the effect of integration of multiple textbooks from the same domain. The results indicate high accuracy of model extraction on symbolic, syntactic and structural levels across textbooks and domains, and demonstrate the added value of the extracted models on the semantic level

Knowledge models from PDF textbooks

Textbooks are educational documents created, structured and formatted by domain experts with the primary purpose to explain the knowledge in the domain to a novice. Authors use their understanding of the domain when structuring and formatting the content of a textbook to facilitate this explanation. As a result, the formatting and structural elements of textbooks carry the elements of domain knowledge implicitly encoded by their authors. Our paper presents an extensible approach towards automated extraction of knowledge models from textbooks and enrichment of their content with additional links (both internal and external). The textbooks themselves essentially become hypertext documents where individual pages are annotated with important concepts in the domain. The evaluation experiments examine several aspects and stages of the approach, including the accuracy of model extraction, the pragmatic quality of extracted models using one of their possible applications— semantic linking of textbooks in the same domain, the accuracy of linking models to external knowledge sources and the effect of integration of multiple textbooks from the same domain. The results indicate high accuracy of model extraction on symbolic, syntactic and structural levels across textbooks and domains, and demonstrate the added value of the extracted models on the semantic level

Order out of Chaos: Construction of Knowledge Models from PDF Textbooks

Textbooks are educational documents created, structured and formatted by domain experts with the main purpose to explain the knowledge in the domain to a novice. Authors use their understanding of the domain when structuring and formatting the content of a textbook to facilitate this explanation. As a result, the formatting and structural elements of textbooks carry the elements of domain knowledge implicitly encoded by their authors. Our paper presents an extendable approach towards automated extraction of this knowledge from textbooks taking into account their formatting rules and internal structure. We focus on PDF as the most common textbook representation format; however, the overall method is applicable to other formats as well. The evaluation experiments examine the accuracy of the approach, as well as the pragmatic quality of the obtained knowledge models using one of their possible applications - semantic linking of textbooks in the same domain. The results indicate high accuracy of model construction on symbolic, syntactic and structural levels across textbooks and domains, and demonstrate the added value of the extracted models on the semantic level

Interlingua: Linking textbooks across different languages

Increasing numbers of students enrol in formal and informal courses taught in a foreign language. Studying a course from an unfamiliar university/program is difficult enough, but the difficulties multiply when the transition to new course requirements is exacerbated by the necessity to learn course material in a foreign language. This paper describes Interlingua a platform where students can study textbooks in a foreign language supported by on-demand access to relevant reading material in their mother tongue. Interlingua automatically recognises important terminology within textbooks content, extracts structural models of textbooks and links sections and subsections across textbooks in different languages covering the same academic subject. The interface and architecture of Interlingua as well as the technologies underlying the platform are described

A domain reasoner for propositional logic

An important topic in courses in propositional logic is rewriting propositional formulae with standard equivalences. This paper analyses what kind of feedback is offered by the various learning environments for rewriting propositional logic formulae, and discusses how we can provide these kinds of feedback in a learning environment. To give feedback and feed forward, we define solution strategies for several classes of exercises. We offer an extensive description of the knowledge necessary to support solving this kind of propositional logic exercises in a learning environment

Building a Generic Feedback System for Rule-Based Problems

We present a generic framework that provides hints on how to achieve a goal to users of software supporting rule-based problem solving from different domains. Our approach consists of two parts. First, we present a DSL that relates and unifies different rule-based problems. Second, we use generic search algorithms to solve various kinds of problems. This solution can then be used to calculate a hint for the user. We present three rule-based problem frameworks to illustrate our approach: the Ideas framework, PuzzleScript and iTasks. By taking real world examples from these three example frameworks and instantiating feedback systems for them, we validate our approach

Type-changing rewriting and semantics-preserving transformation

We have identified a class of whole-program transformations that are regular in structure and require changing the types of terms throughout a program while simultaneously preserving the initial semantics after transformation. This class of transformations cannot be safely performed with typical term rewriting techniques, which do not allow for changing the types of terms. In this paper, we present a formalization of type-and-transform systems, an automated approach to the whole-program transformation of terms of one type to terms of a different, isomorphic type using type-changing rewrite rules. A type-and-transform system defines typing and semantics relations between all corresponding source and target subprograms such that a complete transformation guarantees that the whole programs have equivalent types and semantics. We describe the type-and-transform system for the lambda calculus with let-polymorphism and general recursion, including several examples from the literature and properties of the system. (C) 2015 Elsevier B.V. All rights reserved

Type-changing rewriting and semantics-preserving transformation

We have identified a class of whole-program transformations that are regular in structure and require changing the types of terms throughout a program while simultaneously preserving the initial semantics after transformation. This class of transformations cannot be safely performed with typical term rewriting techniques, which do not allow for changing the types of terms. In this paper, we present a formalization of type-and-transform systems, an automated approach to the whole-program transformation of terms of one type to terms of a different, isomorphic type using type-changing rewrite rules. A type-and-transform system defines typing and semantics relations between all corresponding source and target subprograms such that a complete transformation guarantees that the whole programs have equivalent types and semantics. We describe the type-and-transform system for the lambda calculus with let-polymorphism and general recursion, including several examples from the literature and properties of the system