A creative approach to isometries integrating Geogebra and Italc with ‘paper and pencil’ environments

Creativity is recognized nowadays as a basic skill. However, the educational system fails in promoting their development. On the other hand, a growing acknowledgement of the importance of geometry emerges. Conceptual renewal, namely on isometries, requires new approaches based on mathematically significant tasks. The digital revolution has brought powerful tools but demands changes in the educational process. The use of Dynamic Geometry Environments (DGE), complementing ‘paper and pencil’, can contribute to provide rich learning environments, enhanced by Classroom Management Systems (CMS) such as iTALC. Indeed, the qualitative case study we carried out suggests that: the creation of an "atmosphere" of cooperation, collaboration and sharing seems to increase creativity dimensions; the use of DGE can facilitate the emergence of more creative productions; development of knowledge and geometrical capabilities seems to benefit from a complementary approach that combines DGE and ‘paper and pencil’ environments. Different approaches, with a more technological and exploratory nature seem to promote more favourable attitudes towards mathematics in general, and geometry, in particular.

Management and Control of Water Supply Systems

The fast increase in the energy’s price has brought a growing concern about the highly expensive task of transporting water. By creating an hydraulic model of the Water Supply System’s (WSS) network and predicting its behaviour, it is possible to take advantage of the energy’s tariffs, reducing the total cost on pumping activities. This thesis was developed, in association with a technology transfer project called the E-Pumping. It focuses on finding a flexible supervision and control strategy, adaptable to any existent Water Supply System (WSS), as well as forecasting the water demand on a time period chosen by the end user, so that the pumping actions could be planned to an optimum schedule, that minimizes the total operational cost. The OPC protocol, associated to a MySQL database were used to develop a flexible tool of supervision and control, due to their adaptability to function with equipments from various manufacturers, being another integrated modular part of the E-Pumping project. Furthermore, in this thesis, through the study and performance tests of several statistical models based on time series, specifically applied to this problem, a forecasting tool adaptable to any station, and whose model parameters are automatically refreshed at runtime, was developed and added to the project as another module. Both the aforementioned modules were later integrated with an Graphical User Interface (GUI) and installed in a pilot application at the ADDP’s network. The implementation of this software on WSSs across the country will reduce the water supply companies’ running costs, improving their market competition and, ultimately, lowering the water price to the end costumer.