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Activemath: An intelligent tutoring system for mathematics
 In Seventh International Conference ‘Artificial Intelligence and Soft Computing’ (ICAISC), volume 3070 of LNAI
, 2004
"... Abstract. ActiveMath is a webbased intelligent tutoring system for mathematics. This article presents the technical and pedagogical goals of ActiveMath, its principles of design and architecture, its knowledge representation, and its adaptive behavior. In particular, we concentrate on those feature ..."
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Abstract. ActiveMath is a webbased intelligent tutoring system for mathematics. This article presents the technical and pedagogical goals of ActiveMath, its principles of design and architecture, its knowledge representation, and its adaptive behavior. In particular, we concentrate on those features that rely on AItechniques. 1
Strategy feedback in an elearning tool for mathematical exercises
 Utrecht University
, 2007
"... Abstract Exercises in mathematics are often solved using a standard procedure, such as for example solving a system of linear equations by subtracting equations from top to bottom, and then substituting variables from bottom to top. Students have to practice such procedural skills: they have to lear ..."
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Abstract Exercises in mathematics are often solved using a standard procedure, such as for example solving a system of linear equations by subtracting equations from top to bottom, and then substituting variables from bottom to top. Students have to practice such procedural skills: they have to learn how to apply a particular strategy to an exercise. Elearning systems offer excellent possibilities for practicing procedural skills. The first explanations and motivation for a procedure that solves a particular kind of problems are probably best taught in a class room, or studied in a book, but the subsequent practice can often be done behind a computer. There exist many elearning systems or intelligent tutoring systems that support practicing procedural skills. The tools vary widely in breadth, depth, userinterface, etc, but, unfortunately, almost all of them lack sophisticated techniques for providing immediate feedback. If feedback mechanisms are present, they are hard coded in the tools, often even with the exercises. This situation hampers the usage of elearning systems for practicing mathematical skills. This paper introduces a formalism for specifying strategies for solving exercises. It shows how a strategy can be viewed as a language in which sentences consist of transformation steps. Furthermore, it discusses how we can use advanced techniques from computer science, such as term rewriting, strategies, errorcorrecting parsers, and parser combinators to provide feedback at each intermediate step from the start towards the solution of an exercise. Our goal is to obtain elearning systems that give immediate and useful feedback. 1
eLearning Logic and Mathematics: What We Have and What We
"... Intelligent tutoring systems provide a promising application area for techniques from many subfields of Artificial Intelligence (AI), including knowledge representation, user modelling, rulebased systems, automated diagnosis, automated reasoning, adaptive hypermedia, natural language processing ..."
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Intelligent tutoring systems provide a promising application area for techniques from many subfields of Artificial Intelligence (AI), including knowledge representation, user modelling, rulebased systems, automated diagnosis, automated reasoning, adaptive hypermedia, natural language processing
Computer Supported Formal Work: Towards a Digital Mathematical Assistant
 STUDIES IN LOGIC, GRAMMAR AND RHETORIC
, 2007
"... The year 2004 marked the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number ” (with Martin Davis ’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated ..."
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The year 2004 marked the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number ” (with Martin Davis ’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Roughly at the same time in 1973, the Mizar project started as an attempt to reconstruct mathematics based on computers. Since 1989, the most important activity in the Mizar project has been the development of a database for mathematics. International cooperation resulted in creating a database which includes more than 7000 definitions of mathematical concepts and more than 42000 theorems. The work by
A Review of Mathematical Knowledge Management ⋆
"... Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to de ..."
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Abstract. Mathematical Knowledge Management (MKM), as a field, has seen tremendous growth in the last few years. This period was one where many research threads were started, and the field was defining itself. We believe that we are now in a position to use the MKM body of knowledge as a means to define what MKM is, what it worries about, etc. In this paper, we review the literature of MKM and gather various metadata from these papers. After offering some definitions surrounding MKM, we analyse the metadata we have gathered from these papers, in an effort to cast more light on the field of MKM and its evolution.