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- Exploring symmetry through portuguese tiles in historical monumentsPublication . Rita, Paula; Bastos, Nuno; Hall, AndreiaPortugal has a rich and long cultural heritage which can be used to promote the teaching of Mathematics in schools. Geometry can be explored through the analysis of decorative art found in Portuguese historical buildings, in particular through the analysis of ceramic tile panels and facades used extensively throughout several centuries. Through the analysis of decorative art found using ceramic tiles in two Portuguese monuments, we propose several teaching activities to explore the topics of isometry and symmetry in schools. We give some examples of rosettes, friezes and wallpapers found in the monuments, classified according to their symmetry groups. We also give an example of an applied activity using GeoGebra and exploring Islamic patterns.
- Interlacing Islamic Art with the Teaching of Symmetry in Portuguese SchoolsPublication . Rita, Paula; Hall, Andreia; Bastos, NunoAfter five centuries of Muslim presence in Portugal, it would be unthinkable to assume that, apart from the naming of regions, towns, and villages (Algarve, Ourém, Alcabideche), Islamic culture has not left its mark on Portuguese society. It is not possible to ignore the impact of Islamic art on Portuguese art and architecture, especially in decorative arts such as tiles or crockery. That rich and long cultural heritage can be used to promote the teaching of Mathematics in schools. Ge- ometry can be explored through the analysis of decorative art found in Portuguese historical build- ings, in particular through the analysis of ceramic tile panels and facades used extensively throughout several centuries. Through the analysis of decorative art found using ceramic tiles in two Portuguese monuments, we propose several didactical activities to explore the topics of isome- try and symmetry in schools. We give some examples of rosettes, friezes and wallpapers found in the monuments, classified according to their symmetry groups. We also give some examples of ap- plied activities using GeoGebra and exploring Islamic motives/patterns.
- An experience with Desmos in the study of the quadratic functionPublication . Dias, Lucília; Oliveira, Paula; Bastos, NunoAt a time when students have multiple demands in terms of technology and the resources and tools available are more and more varied, the school must respond with more attractive activities. It is, therefore, essential to provide students with digital tools accessible through the devices they are most familiar with, mobile phones and computers. By using these tools, we are creating a stimulating environment capable of engaging the students, providing them with the means to build their knowledge. In this paper we present a didactic experience in the subject of Mathematics carried out in a distance learning context, on the topic Quadratic Function, using the digital and free platform Desmos. Desmos has a very intuitive interface where you can create sets of interactive activities and tasks that facilitate learning mathematics, in order to make it more meaningful. The use of this tool was determinant for the teaching and learning of quadratic function since its teaching took place in distance education and students didn't have, at that time, a graphing calculator or any simulator in their computers. Ten activities on the quadratic function were constructed, involving various parameters so that the students, observing the changes on the graphs, were able to understand the concepts underlying this subject, namely vertical and horizontal translations of the graph, domain, range, injectivity, zeros, monotony, extremes, axis of symmetry and coordinates of the vertex of the parabola representing the graph of the quadratic function. This didactic experience was applied to two classes of 10th grade in Portuguese Educational System, involving forty-seven students, 76.7% of whom highlighted the fact that it facilitated learning in the study of functions, followed by 74.4% who considered the environment dynamic and attractive as well as the feedback given in the answers to the exercises. The use of digital tools should always be complemented with the teacher’s human component. The profile of each student is unique and specific, and the pace of learning differs from student to student. A tool like Desmos, which students are enthusiastic about using, allows monitoring of individual performance and timely and appropriate intervention by the teacher. In a pandemic context, the use of tools to gauge student learning was a necessity, but practices such as the one described in this paper should be incorporated into a normal classroom environment, promoting discovery through graphical and algebraic manipulation.
- Activities with desmos and geogebra for formative and automatic feedbackPublication . Santos, V.; Bastos, NunoThe study developed here was carried out within the scope of a National Meeting “19.º MatViseu” with secondary school mathematics teachers in a workshop entitled Desmos and GeoGebra: activities with automatic feedback and formative”. The objectives were to articulate the mathematics curriculum and essential learning program, and to explore activities that use some of the strengths of Desmos and GeoGebra to provide feedback to students and develop some activities with feedback appropriate to the level of education they teach. This National Meeting was organized with plenary sessions (invited speakers) and parallel sessions (workshops). In-service teacher training is an essential element to help them to adapt to different curricula and new methods and resources in their professional careers. This study aims to understand how the use of these two platforms can allow a different approach in their classes. The research methodology adopted consists of a case study, relating to a group of teachers who worked autonomous in this workshop. Essentially, a qualitative approach was adopted through the interpretation of data collected through observation, interaction in these platforms and a brief questionary. We can conclude that using the GeoGebra platform requires prior preparation, essentially with GeoGebraScript and with the Desmos platform it was easier to work with the Computation Layer language, although GeoGebraScript and Computation Layer language are new for most of them. Thus, it is recommended that in future training, the creation of strategies and dynamics of preparation for work in the GeoGebraScript and in the Desmos language, to carry out a complete work. However, it is important to keep in mind that the GeoGebra platform was known to most of the participants, but Desmos was not and that the sample is not significant to draw general conclusions.