Results 1 
8 of
8
ActiveMath: A Generic and Adaptive WebBased Learning Environment
 International Journal of Artificial Intelligence in Education
, 2001
"... ActiveMath is a generic webbased learning system that dynamically generates interactive (mathematical) courses adapted to the students goals, preferences, capabilities, and knowledge. The content is represented in an semantic xmlbased format. For each user, the appropriate content is retrieved fr ..."
Abstract

Cited by 92 (28 self)
 Add to MetaCart
ActiveMath is a generic webbased learning system that dynamically generates interactive (mathematical) courses adapted to the students goals, preferences, capabilities, and knowledge. The content is represented in an semantic xmlbased format. For each user, the appropriate content is retrieved from a knowledge base and the course is generated individually according to pedagogical rules. Then the course is presented to the user via a standard webbrowser. One of the exceptional features of ActiveMath is its integration of standalone mathematical service systems. This offers the means for exploratory learning, realistically complex exercises as well as for learning proof methods. The article provides a comprehensive account of the current version of ActiveMath.
Adaptable mixedinitiative proof planning for educational interaction
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2004
"... Today, most theorem proving systems are either used by their developers or by a (small) group of particularly trained and skilled users. In order to make theorem proving functionalities useful for a larger clientele we have to ask “What does an envisioned group of users need?” For educational purpos ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Today, most theorem proving systems are either used by their developers or by a (small) group of particularly trained and skilled users. In order to make theorem proving functionalities useful for a larger clientele we have to ask “What does an envisioned group of users need?” For educational purposes a theorem prover can be used in different scenarios and can serve students with different needs. Therefore, the user interface as well as the choice of functionalities of the underlying prover have to be adapted to the context and the learner. In this paper, we present proof planning as backengine for interactive proof exercises as well as an interaction console, which is part of our graphical user interface. Based on the proof planning situation, the console offers suggestions for proof steps to the learner. These suggestions can dynamically be adapted, e.g., to the user and to pedagogical criteria using pedagogical knowledge on the creation and presentation of suggestions.
Adaptive access to a proof planner
 In Proceedings of Third International Conference on Mathematical Knowledge Management (MKM2004), number 3119 in LNCS, Bialowieza
, 2004
"... Abstract. Mathematical tools such as computer algebra systems and interactive and automated theorem provers are complex systems and can perform difficult computations. Typically, such tools are used by a (small) group of particularly trained and skilled users to assist in mathematical problem solvin ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
(Show Context)
Abstract. Mathematical tools such as computer algebra systems and interactive and automated theorem provers are complex systems and can perform difficult computations. Typically, such tools are used by a (small) group of particularly trained and skilled users to assist in mathematical problem solving. They can also be used as backengines for interactive exercises in learning environments. This, however, suggests the adaptation of the choice of functionalities of the tool to the learner. This paper addresses the adaptive usage of the proof planner Multi for the learning environment ActiveMath. The proof planner is a backengine for interactive proof exercises. We identify different dimensions in which the usage of such a service system can be adapted and investigate the architecture realizing the adaptive access to Multi. 1
ActiveMath  Learning Environment System Description
 In Calculemus Workshop at IJCAR
, 2001
"... ActiveMath is a webbased learning environment that dynamically generates interactive mathematical courses adapted to the student 's goals, preferences, capabilities, and knowledge. It integrates several mathematical service systems. The course content is represented in OMDoc, an extension of O ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
ActiveMath is a webbased learning environment that dynamically generates interactive mathematical courses adapted to the student 's goals, preferences, capabilities, and knowledge. It integrates several mathematical service systems. The course content is represented in OMDoc, an extension of OpenMath. For each user, the appropriate content is retrieved from a knowledge base and the actual course is generated individually according to pedagogical rules. The course is presented to the user via a standard webbrowser. During a course the learner can interactively practice problem solving by using mathematical services such as computer algebra system or a proof planner. The article provides a brief account of the current state of ActiveMath.
User interface for adaptive suggestions for interactive proof
 IN PROCEEDINGS OF THE INTERNATIONAL WORKSHOP ON USER INTERFACES FOR THEOREM PROVERS (UITP
, 2003
"... We describe an interaction console for interactive proof exercises using proof planning as backengine. Based on the proof planning situation, the console offers suggestions for proof steps. These suggestions can dynamically be adapted, e.g. to the user and to pedagogical criteria. This adaptive con ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
We describe an interaction console for interactive proof exercises using proof planning as backengine. Based on the proof planning situation, the console offers suggestions for proof steps. These suggestions can dynamically be adapted, e.g. to the user and to pedagogical criteria. This adaptive configuration is possible because the suggestion mechanism and proof planning are clearly separated. Therefore, a configuration can represent pedagogical knowledge which would not be possible by using proof planning alone.
UITP 2003 Preliminary Version Adaptable MixedInitiative Proof Planning for Educational Interaction
"... Abstract Today, most theorem proving systems are either used by their developers or by a (small) group of particularly trained and skilled users. In order to make theorem proving functionalities useful for a larger clientele we have to ask "What does an envisioned group of users need?&q ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract Today, most theorem proving systems are either used by their developers or by a (small) group of particularly trained and skilled users. In order to make theorem proving functionalities useful for a larger clientele we have to ask &quot;What does an envisioned group of users need?&quot; For educational purposes a theorem prover can be used in different scenarios and can serve students with different needs. Therefore, the user interface as well as the choice of functionalities of the underlying prover have to be adapted to the context and the learner. In this paper, we present proof planning as backengine for interactive proof exercises as well as an interaction console, which is part of our graphical user interface. Based on the proof planning situation, the console offers suggestions for proof steps to the learner. These suggestions can dynamically be adapted, e.g., to the user and to pedagogical criteria using pedagogical knowledge on the creation and presentation of suggestions. Key words: mathematics education, adaptive GUI, adaptive theorem proving 1 Motivation So far, the main goal of developing automated theorem proving systems has been to output true/false for a statement formulated in some logic or to deliver a proof object. Interactive theorem proving systems aim to support the proof construction done by a user in different ways, they restrict the search space (the choices) by making valid suggestions for proof steps, they suggest applicable lemmas, or they produce a whole subproof automatically. These functionalities are useful, e.g., for checking a student's proof for validity or for verifying a program. They are not particularly helpful, when the goal is to This is a preliminary version. The final version will be published in
Automated Deduction Systems for Real Mathematicians
"... Abstract. Automated deduction systems currently have a low uptake (or even recognition) amongst mathematicians. This paper takes a human computer interaction perspective on the role of automated deduction in mathematics. We first dismiss the fallacy that making systems easy to use will make them use ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. Automated deduction systems currently have a low uptake (or even recognition) amongst mathematicians. This paper takes a human computer interaction perspective on the role of automated deduction in mathematics. We first dismiss the fallacy that making systems easy to use will make them used by heuristically comparing Microsoft Word and L ATEX systems in mathematical authoring. Through considering the goals of mathematicians, we propose ways to develop automated deduction systems that mathematicians actually want. There are clearly considerable technological and even philosophical barriers but it is hoped that these can be surmounted in time. 1