Browsing by Author "Bastos, Nuno"
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- Active learning during the covid-19 pandemic - A triple experimentPublication . Santos, Vanda; Hall, Andreia; Bastos, Nuno; Caridade, CMRIn recent times, the debate on active methodologies has been intensified with the emergence of strategies that can favor students' autonomy. The active, dynamic and constructive environment can positively influence the perception of teachers and students. One of the ways to achieve this is through the use of technologies that enhance learning. Due to the pandemic situation, the use of technologies was imperative and essential. Three higher education institutions were involved in an active learning project, involving diversified technologies and methodologies to enhance the learning of mathematics. In the University of Aveiro, the experiment involved all the 1st-year students enrolled in the course “Complementary Mathematics II” during the second semester of the academic year 2020-21. These are students of a master’s program for pre-service teachers, preparing to become primary school teachers and mathematics and science teachers, grades 5 and 6. At the Institute of Engineering in Coimbra, the students who attended this experiment were students of Mathematical Analysis I, from the undergraduate degree in Electrical Engineering. In the Polytechnic Institute of Viseu, the students involved in this experiment were students from the Preparation Course in Mathematics (which aims to prepare candidates over 23 who wish to apply to an undergraduate degree in Business). The methodologies used were applied during three distinct phases and according to the students’ profile, related to each course. The methodologies used were very diverse: team-based learning; flipped classroom; peer teaching; think-pair-share and exposition followed by exercise practice; problem-based learning and inquiry-based learning. The technologies were also very diversified: Desmos, Kahoot!, Quizizz, GeoGebra, Excel, OneNote, Google Docs, Zoom, Miro, Wolfram alpha, Powerpoint, calculators and videos. The use of a wide range of methodologies and technologies made it possible to teach during the lockdown imposed by the pandemic situation, and simultaneously motivated the students. In addition they provided opportunities to adapt the learning process to the diverse knowledge and learning styles of students, and increased their involvement.
- 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.
- 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.
- Breakout rooms: a collaborative space that worksPublication . Bastos, NunoIn this paper it’s described a study of the use of breakout rooms for small group work in synchronous online classes. Since the lockdown started, due to the pandemic COVID-19, higher education institutions needed to adapt to the new realities and start using, most frequently, remote learning. In the universe of the most common platforms (e.g. Zoom, Cisco WebEx, Microsoft Teams), the Zoom platform has been the selected one in the institution where I teach. This study was done over the second semester of 2020/2021 in a freshman math class. While teaching large class the interaction and participation of students becomes more difficult and can lead to consequences such as demotivation and lack of involvement of those students. One of the strategies for all students to have (and be) an active part during the learning process in a class is to put them to work in groups. Breakout rooms is a feature in Zoom that allows split large groups into smaller groups. The teacher has different options to create the rooms, fixed number of groups or randomly. One of the benefits of using breakout rooms is that it facilitates collaborative learning and interaction (between the students in each breakout room and between students and teacher). This study was with the use of breakout rooms, randomly created, with a maximum of 5 participants. During that period the classes were mainly divided into three main parts: an introductory part where some theoretical concepts were complemented with examples, a second part where students were placed in breakout rooms to solve specific group tasks and a last part, a spokesperson, selected by each group, presented the work done by the group to the whole class. During the time where students are working in separate breakout rooms, I go to each room, see the work that was done until that moment and notice if they need help. Beside those moments participants can, at any moment, click the “Ask for Help” button to call the teacher to that room. As all this process was very interactive, students worked in small groups and the collaboration was huge, at the end, I noticed that every group concluded, mostly with success, the exercises and they mentioned that the classes was very productive. This study will also offer some insights for educators in higher education who wish to incorporate breakout rooms as a collaborative learning tool.
- Cálculo fraccional em escalas temporaisPublication . Bastos, Nuno; Torres, Delfim Fernando MaradoIntroduzimos um cálculo das variações fraccional nas escalas temporais ℤ e (hℤ)!. Estabelecemos a primeira e a segunda condição necessária de optimalidade. São dados alguns exemplos numéricos que ilustram o uso quer da nova condição de Euler–Lagrange quer da nova condição do tipo de Legendre. Introduzimos também novas definições de derivada fraccional e de integral fraccional numa escala temporal com recurso à transformada inversa generalizada de Laplace.
- 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.
- Professional Development for Higher Education Teaching Staff: An Experience of Peer Learning in a Portuguese PolytechnicPublication . Figueiredo, Maria Pacheco; Matias, Rogério; Alves, Valter; Bastos, Nuno; P. Duarte, Rui; Ferreira, Bruno; Cunha, CarlosSeveral challenges have been tackled by Portuguese (Fernandes, 2016; Mendes et al., 2016) and European Higher Education, many of which are in the pedagogical arena. Although Pedagogy in Higher Education is not an invested area, there are studies, initiatives, projects, and structures of great quality in the national context (Costa, 2019; Fernandes, 2016; Gonçalves et al., 2010; Vieira et al., 2016; Pêgo & Mouraz, 2017; Vieira, 2017). An important part of the advances in the area has resulted from the systematic analysis, sharing, and discussion of practices that have embodied several publications and sustained several interventions in Portugal and internationally. The EQuIPES - Study of Quality and Pedagogical Innovation in Higher Education aims to contribute to this body of experiences and studies that allows to understand and improve teaching and learning in Higher Education institutions, based on the analysis of practices in the Polytechnic of Viseu (PV) in communication with external partners. The PV has five schools with a teaching staff of 400 members for 5400 students. The programs range from professional learning (level 5, no degree) to Masters level, with a large percentage of students enrolled in Bachelor degrees from different areas (teacher education, social work, and education, nursing, community health, engineering, arts, design and multimedia, marketing, management, tourism, media studies, agriculture, public relations, information and communication technologies, and sports). The majority of PV’s study programs are professionally oriented, in line with the mission of the polytechnic Higher Education system. This holds true for EQF level 5 programs but also for the BAs and MAs. Each program is designed in close proximity and alignment with professional contexts and practices. The supervised practical training in professional contexts is combined with project-based learning throughout the programs and there is a strong emphasis on active learning strategies. These pose challenges for Pedagogy and pedagogical knowledge and competencies, developed in the workplace through action, but also through reflection (Kuh et al., 2010). Peer learning and discussion groups are important for supporting those processes. Pedagogical action becomes something that is shared, regardless of scientific areas (Behrens & Junges, 2018). In the discussion of pedagogical practices, a focus on the learning and the students is important and technology has been highlighted as facilitating that shift (Sharples, 2016). In the past year, a group of seven professors developed a set of opportunities to share and discuss practices, named “Apps & Things”, that ran 10 workshops. In this paper, we will present the set of workshops and analyze the pedagogical elements of each one, as well as how the technology was articulated with the pedagogical elements. The pedagogical elements identified were: assessment and evaluation; communication and interaction; planning and monitoring work; distance learning; students’ participation; and trust. The results also include how the colleagues that participated in the workshops (around 25 in each) valued the pedagogical elements and what challenges were shared regarding them The experience is discussed in terms of the EQuIPES framework, intending to contribute to the visibility of Pedagogy in Higher Education, associated with peer-to-peer training opportunities and experiences.
- Use of Desmos to engage students in calculusPublication . Bastos, NunoIn the Spring of 2020, Portugal was one of the countries that experienced the first lockdown at all their school levels system and it resulted in a new challenge also for teachers. During the second semester of 2020/2021 a new lockdown was imposed and, with a variety of tools available to teach, it was important to try different approaches at classes. From one hand it is desired to use digital tools accessible through the devices that students are most familiar with and, from another hand, that those tools were able to create a stimulating environment. Desmos, a free platform, was used in a different way since Desmos combines features of graphic calculators and classroom activities (Activity Builder). This platform was initially thought for use in mathematics, there are already many activities carried out on this platform ranging from the area of history to the area of languages. This platform allows the creation of free digital activities that are elaborated according to a pedagogical philosophy. One of the ideas behind that philosophy is the fact that students can be right or wrong in different ways since not all responses in the learning process need to have the usual "right" or "wrong" label. This platform allows students to give personalized feedback (and the quality of feedback can allow students to remain motivated); allows anonymous sharing of some student responses in a sequence created by the teacher, and it can enhance the debate of concepts and opinions. Compared with several quizzes platforms (e.g. Kahoot!, Quizizz, etc) Desmos have the possibility of writing mathematical expressions by the students in their answers and, in fact, facilitate students' answers during that semester. In this paper is presented some activities in calculus topics such as integration, sequences and ordinary differential equations using some of the Desmos Activity Builder tools. One of those tools is the “card sort” that transpose to the digital the easy activity to stack cards. Some analysis is made about the students' responses. At the end, the students considered the Desmos environment as dynamic and attractive, and mentioned that it facilitates learning.