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

A teachable semi-automatic web information extraction system based on evolved regular expression patterns

This thesis explores Web Information Extraction (WIE) and how it has been used in decision making and to support businesses in their daily operations. The research focuses on a WIE system based on Genetic Programming (GP) with an extensible model to enhance the automatic extractor. This uses a human as a teacher to identify and extract relevant information from the semi-structured HTML webpages. Regular expressions, which have been chosen as the pattern matching tool, are automatically generated based on the training data to provide an improved grammar and lexicon. This particularly benefits the GP system which may need to extend its lexicon in the presence of new tokens in the web pages. These tokens allow the GP method to produce new extraction patterns for new requirements