Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

IMPACTS in natural language generation NLG between technology and applications : workshop at Schloss Dagstuhl, Germany July 26-28, 2000

Instructional text, because it is a useful and relatively constrained sub-Ianguage, has been a popular target for research-oriented generation systems. This work has demonstrated that existing technology is adequate for generating draft instructions; the problem, as is typical of generation work in general, has been with the acquisition of domain and lexicogrammatical knowledge. This acquisition task is a formidable barrier to the practical use of generation technology. The Isolde project attempts to address this problem by extracting parts of the required knowledge from existing models and by building tools to tailor what is extracted into a form suitable for generation

IMPACTS in natural language generation NLG between technology and applications : workshop at Schloss Dagstuhl, Germany July 26-28, 2000

Instructional text, because it is a useful and relatively constrained sub-Ianguage, has been a popular target for research-oriented generation systems. This work has demonstrated that existing technology is adequate for generating draft instructions; the problem, as is typical of generation work in general, has been with the acquisition of domain and lexicogrammatical knowledge. This acquisition task is a formidable barrier to the practical use of generation technology. The Isolde project attempts to address this problem by extracting parts of the required knowledge from existing models and by building tools to tailor what is extracted into a form suitable for generation

A survey on perceived speaker traits: personality, likability, pathology, and the first challenge

The INTERSPEECH 2012 Speaker Trait Challenge aimed at a unified test-bed for perceived speaker traits – the first challenge of this kind: personality in the five OCEAN personality dimensions, likability of speakers, and intelligibility of pathologic speakers. In the present article, we give a brief overview of the state-of-the-art in these three fields of research and describe the three sub-challenges in terms of the challenge conditions, the baseline results provided by the organisers, and a new openSMILE feature set, which has been used for computing the baselines and which has been provided to the participants. Furthermore, we summarise the approaches and the results presented by the participants to show the various techniques that are currently applied to solve these classification tasks