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- Mathematics classes for tourism undergraduate students and pre-service teachers with active methodologies using technologiesPublication . Santos, Vanda; Pais, Sónia; Hall, AndreiaIn the last few decades, technology has advanced in multiple fields, including Education. Some of its benefits include improving student performance and motivation, fostering active learning and tracking student progress. Game-based learning platforms, like Kahoot!, can be used for reviewing content and motivating students for learning. The participants in the study are undergraduate and postgraduate students from two Portuguese public higher education institutions. The aim of the study is to investigate students’ perceptions of how Kahoot! can be used as a tool for reviewing class content or designing warm-up activities. A quantitative survey is being conducted to gather information about students’ insights on the use of Kahoot!. Other studies have also shown that higher education students are usually receptive to the use of this tool, finding it useful to increase their motivation and considering that technology can positively impact learning.
- Using an interdisciplinary approach to the teaching of solid geometry in a professional development course for preschool and primary school teachersPublication . Hall, Andreia; Pais, SóniaThis paper presents some results of a professional development course for teachers where the participants studied basic solid geometry and developed applied projects in an interdisciplinary context. The course took place in a Portuguese university, from February to May 2020, and involved 19 teachers of preschool and primary levels (grades 1 to 4). The authors have developed a qualitative case study to evaluate how an interdisciplinary approach to the teaching of solid geometry is perceived, by the mathematics teachers, as a contribution to the teaching/learning process of geometry. Overall, the activities developed have proved to be successful examples of interdisciplinary methodologies. Moreover, the approach followed during the course helped the teachers develop their geometric competences concerning solid geometry in a more consistent appropriation and application of the geometric concepts involved.
- The use of diversified active learning methodologies in mathematics classes: A case study with pre-service teachersPublication . Hall, A.; Pais, S.Mathematics is one of the school subjects where demotivation, dislike and failure are frequent concerns. It is necessary to engage students in the classroom and look for resources that make classes attractive and engaging, thus leading to meaningful learning experiences in mathematics. Active learning methodologies provide alternative options to traditional lecturing, actively engaging students in the learning process. The use of a single methodology may not be the best option to address this problem. A diversified approach that incorporates various methodologies and their combinations appears to be a preferable solution, as diversity not only leads to a more dynamic teaching style but also attends to the variety of preferences and needs of the students. In this work, we present a case study where we implemented and combined a range of active learning strategies to enhance student engagement and success in mathematics. Across one semester of undergraduate coursework, we emphasized collaborative group work and discussion groups, integrated peer teaching, flipped classroom, and role-play methodologies, used game-based learning through Kahoot! and Quizizz, and regularly incorporated mathematical magic tricks. The participants in the study are pre-service teachers from a Portuguese higher education institution enrolled in a first year mathematics course. In order to understand how these methodologies were perceived by the students, a survey was conducted. Our findings suggest that this multi-faceted approach effectively increased student interest and improved learning outcomes in mathematics.
- Taking school outdoors: Mathematical trails as a teaching resourcePublication . Ambrósio, H.; Hall, A.; Pais, S.Everybody should have opportunities to experience mathematical learning, solve challenges, and become more knowledgeable. Indeed, governmental recommendations present in the introduction of the mathematics Portuguese curriculum state that “No human being should be deprived of the opportunity to learn and benefit from the unique scientific and cultural heritage that mathematics represents” [1, p. 2]. We have designed a mathematical trail, in the village of Vieira de Leiria, in which geometric /mathematical elements stand out. Our aim is, first of all, to promote the interest in the study of mathematics, through observation of the surrounding environment, in particular of outdoor elements with decorative art. We also intend to establish mathematical links that make mathematics a useful, important subject, with connections to the world around us. The trail has an educational component and explores specific topics of the mathematics curriculum of the 5th and 6th years: isometries and symmetry. This activity, in the form of a rally-paper with a sequence of challenges and problems along the trail, encourages students to explore the concepts in a different, more playful and interactive way. Furthermore, it involves students in the discovery, preservation and enhancement of Portuguese heritage. In order to assess the perceptions of the students regarding the pedagogical approach used in the experience, a questionnaire was applied. This paper describes this teaching experience and the main results of the applied questionnaire. We conclude that this teaching experience had a very positive impact on the students, contributing to a better understanding of the covered curriculum, the importance of mathematics and its relation to everyday life, as well as feeling more motivated to study mathematics.
- Interlacing mathematics and art: hands-on non-Euclidean geometryPublication . Hall, Andreia; Brás, Isabel; Pais, SóniaElliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education. One such topic is the study of non-Euclidean geometry. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied non-Euclidean geometry concepts. The participants created ceramic pieces using the Poincaré disk and styrofoam balls covered with fabrics using spherical geometry.
- Learning and teaching symmetry by creating ceramic panels with Escher type tessellationsPublication . Hall, Andreia; Pais, SóniaElliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning. This is true for any subject, including mathematics. Some topics of the mathematics school curriculum make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of symmetry and isometry, present throughout the school mathematics curriculum from elementary to secondary levels. We believe that the learning and teaching of symmetry and isometry can be greatly facilitated by taking the role of an artist and creating works of art, eventually inspired by renowned artists. In this paper, we present some results of a professional development course for mathematics teachers where the participants created ceramic panels using the same techniques as the Dutch artist M.C. Escher did in his tessellation drawings.
- Using Kahoot! to enhance the motivation of undergraduate students of tourism in mathematics classes: A case studyPublication . Pais, Sónia; Hall, AndreiaNowadays we live in an ever-changing society. The educational context is no exception and requires a renewal of paradigms. Profound changes to the role and function of the professor and the students are particularly vital. Active, cooperative and participative methodologies of learning must be privileged, breaking with magisterial education and the mere transmission of knowledge. Mathematics is one of the school subjects where demotivation is a frequent concern. Relating mathematics with other areas usually draws students’ attention and increases their involvement in the classes. It is necessary to go beyond the traditional; the teacher must look for resources that make his classes flow, so that the students acquire or increase their interest in mathematics. In the last few decades, technology has advanced in multiple fields, including education. Some of its benefits include improving student performance and motivation, fostering active learning, and tracking student progress. Kahoot! is an example of a platform that can be used for reviewing content and motivating students for learning. The main reasons for choosing this tool are related to the fact that the application is accessible online free of charge, allows an intuitive use, both by the teacher/author and by the student/player and allows the participation of the whole class in an interactive, stimulating, and playful way. The teachers involved in this study began using Kahoot! in their classes as an alternative teaching methodology. The participants in the study are undergraduate students from a Portuguese higher education institution and encompassed the curricular unit of Statistics. The aim of the study is to investigate students’ perceptions of how Kahoot! can be used as a tool for reviewing class content or designing warm-up activities. A survey was conducted to gather information about students’ insights on the use of Kahoot!. Similar studies have shown that higher education students are usually receptive to the use of this tool, finding it useful to increase their motivation and consider technology can positively impact learning.
- Using an artistic approach to the teaching of non-Euclidean geometry in a professional development course for mathematics teachersPublication . Hall, Andreia; Brás, Isabel; Pais, SóniaElliot Eisner (1933-2014), a pioneer in arts education, suggested that an artistic approach to education could improve its quality and lead to a new vision for teaching and learning [1]. This is true for any subject, including mathematics. Geometry related topics make a perfect setting for a deeper contribution of art to education and allow for a complete symbiosis between the teaching of mathematics and an artistic education. One such topic is the study of non-Euclidean geometry which is now briefly addressed in the middle school mathematics curriculum in Portugal [2]. We believe that the learning and teaching of non-Euclidean geometry can be facilitated by taking the role of an artist and creating works of art, eventually inspired by renowned artists such as M.C. Escher. In this paper, we present some results of a professional development course for mathematics teachers where the participants studied basic non-Euclidean geometry concepts and created ceramic pieces using the Poincaré disk. The course took place in a Portuguese university, from January to March 2018, and involved 20 teachers of grades 1 to 12. The authors have developed a qualitative case study to evaluate how an artistic approach to the teaching of non-Euclidean geometry is perceived, by the mathematics teachers, as a contribution to the learning process. Overall, the activities developed have proved to be successful examples of interdisciplinary methodologies that bring into the teaching of mathematics usual procedures in the teaching of the arts. Moreover, the artistic approach followed during the course helped the teachers develop their geometric competences concerning non-Euclidean geometry in a more solid appropriation and application of the geometric concepts involved.
- Mathematical magic in undergraduate mathematical classes for pre-service teachersPublication . Hall, Andreia; Pais, SóniaNowadays we live in an ever-changing society. The educational context is no exception, and requires a renewal of paradigms. Profound changes to the role and function of the teacher and the students are particularly vital [1], [2], [3]. The current University students have different motivations, different attitudes towards the teaching and learning process, and different responses to specific classroom environments and instructional practices [4]. The challenge that teachers face today is to motivate students to learn, get them to commit to and have an active role in their learning [5]. Considering that it is imperative to make the teaching and learning process of mathematics more stimulating, taking into account modern society and student’s interests [6], the authors have developed several strategies to increase the interest and improve the success of students in mathematics. Thus, they decided to use mathematical magic tricks in their classes to raise the motivation of the students, captivating them and stimulating their interest in mathematics. In this work, a case study to evaluate how mathematical magic can contribute to increase students' motivation for learning mathematics is presented. The paper describes how it is conceived as well as the main results.
- Volume of geometric solids on the Desmos platform: A didactic experience in Cape VerdePublication . Machado, Daniel; Bastos, Nuno; Hall, Andreia; Pais, SóniaThis work intends to disseminate a didactic experience in mathematics, in times of pandemic, in an emergency remote teaching situation, at the Portuguese School of Cape Verde, using the Desmos digital platform. The topic addressed was the study of the volume of geometric solids. The main objective was to contribute to the learning of mathematical concepts, using digital tools that promote students’ autonomy while respecting their learning pace, thus improving teaching practices through more assertive methodologies and more innovative resources. In order to understand how the Desmos platform contributes to improve the learning of geometry an explanatory case study was conducted. The participants in the study are 9th grade students from a Cape Verde school. Preliminary analysis of the data collected through several techniques, using diverse data collecting mechanisms, indicates that the contribution is very positive with clear advantages in the construction of knowledge on the part of the students, centered in a logic of skill development.