Center for Research and Development in Mathematics and Applications

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Publications

Use of Desmos to engage students in calculus

Publication . Bastos, Nuno

In 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.

2022Journal article

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Exploring symmetry through portuguese tiles in historical monuments

Publication . Rita, Paula; Bastos, Nuno; Hall, Andreia

Portugal 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.

2022Journal article

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Activities with desmos and geogebra for formative and automatic feedback

Publication . Santos, V.; Bastos, Nuno

The 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.

2022Journal article

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Interlacing Islamic Art with the Teaching of Symmetry in Portuguese Schools

Publication . Rita, Paula; Hall, Andreia; Bastos, Nuno

After 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.

2022-07Journal article

Open access

Active learning during the covid-19 pandemic - A triple experiment

Publication . Santos, Vanda; Hall, Andreia; Bastos, Nuno; Caridade, CMR

In 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.

2022Journal article

Restricted access