Reading and writing mathematical notation in e-learning environments

How do students and teachers communicate mathematics via the internet? Why do they use these methods? Is there any better way of communicating mathematics via the internet? In addition to the time needed to understand a concept, it is also a challenge for students to write formulae in e-learning environments, since most computers and software are not designed to write formulae. Furthermore, most physics, mathematics and engineering students do most of all their initial analysis and calculations using pen and paper and then have to translate it into a computer environment. Does this extra time investment play a role in the academic results achieved?This paper presents exploratory research into the different methods used by teachers and students to communicate mathematics via the internet and to use appropriate patterns according to the different subjects and knowledge areas. It explores the reasons that make students choose one method or another and analyses the extreme case: when students write mathematical formulae on paper and then scan this electronically.The analysis is carried out on engineering subjects at the Universitat Oberta de Catalunya (UOC) in which mathematics plays an important role: 17,000 emails are analysed and five physics teachers are interviewed as part of a qualitative study about handwritten scanned exercises.This paper shows that the key to explaining students' behaviour is the time factor. In order to reduce the time required to write the required mathematical formulae, the paper proposes a speech-to-text tool, such as TalkMaths, to help students create and edit mathematical formulae, since speech is the fastest and most natural way of communicating

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