Integrating DGSs and GATPs in an Adaptative and Collaborative Blended-Learning Web-Environment

The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant way, the learning environments. The dynamic geometry software systems (DGSs) can be used to explore the visual contents of geometry. This already mature tools allows an easy construction of geometric figures build from free objects and elementary constructions. The geometric automated theorem provers (GATPs) allows formal deductive reasoning about geometric constructions, extending the reasoning via concrete instances in a given model to formal deductive reasoning in a geometric theory. An adaptative and collaborative blended-learning environment where the DGS and GATP features could be fully explored would be, in our opinion a very rich and challenging learning environment for teachers and students. In this text we will describe the Web Geometry Laboratory a Web environment incorporating a DGS and a repository of geometric problems, that can be used in a synchronous and asynchronous fashion and with some adaptative and collaborative features. As future work we want to enhance the adaptative and collaborative aspects of the environment and also to incorporate a GATP, constructing a dynamic and individualised learning environment for geometry.Comment: In Proceedings THedu'11, arXiv:1202.453

The value of learning geometry with ICT: lessons from innovative educational research

This chapter reviews research on using ICT to support the teaching of geometry. The research selected focuses on learners’ use of interactive geometry software, the design of suitable teaching and learning activities, and the nature of relevant teacher professional development. The central theme of the chapter is that while ICT has considerable potential in enlivening the teaching and learning of school mathematics (and geometry in particular), there is much to take account of in terms of enabling this potential to be fully realise

Prediction of the Atomization Energy of Molecules Using Coulomb Matrix and Atomic Composition in a Bayesian Regularized Neural Networks

Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and challenging machine learning problem. In this paper we embrace a learning from scratch approach where the quantum mechanical electronic properties of molecules are predicted directly from the raw molecular geometry, similar to some recent works. But, unlike these previous endeavors, our study suggests a benefit from combining molecular geometry embedded in the Coulomb matrix with the atomic composition of molecules. Using the new combined features in a Bayesian regularized neural networks, our results improve well-known results from the literature on the QM7 dataset from a mean absolute error of 3.51 kcal/mol down to 3.0 kcal/mol.Comment: Under review ICANN 201