Symbol detection in online handwritten graphics using Faster R-CNN

Symbol detection techniques in online handwritten graphics (e.g. diagrams and mathematical expressions) consist of methods specifically designed for a single graphic type. In this work, we evaluate the Faster R-CNN object detection algorithm as a general method for detection of symbols in handwritten graphics. We evaluate different configurations of the Faster R-CNN method, and point out issues relative to the handwritten nature of the data. Considering the online recognition context, we evaluate efficiency and accuracy trade-offs of using Deep Neural Networks of different complexities as feature extractors. We evaluate the method on publicly available flowchart and mathematical expression (CROHME-2016) datasets. Results show that Faster R-CNN can be effectively used on both datasets, enabling the possibility of developing general methods for symbol detection, and furthermore, general graphic understanding methods that could be built on top of the algorithm.Comment: Submitted to DAS-201

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