É com grande satisfação que apresentamos esta edição especial da Indagatio Didactica, dedicada à Conferência Internacional Joga-Mate, realizada na Universidade de Aveiro nos dias 21 e 22 de fevereiro de 2025. Este encontro reuniu professores, investigadores e educadores para explorar a integração de estratégias e metodologias baseadas em jogos no ensino da Matemática. Os nove artigos selecionados nesta edição especial, redigidos em inglês ou português por 21 autores, apresentam uma variedade de atividades, tanto digitais como físicas, que utilizam jogos e abordagens lúdicas para enriquecer o ensino da Matemática. As iniciativas destacam-se por promoverem a motivação dos alunos, o trabalho em equipa, a resolução de problemas e o desenvolvimento de competências essenciais. Estes contributos refletem práticas inovadoras que combinam o rigor dos conteúdos matemáticos com metodologias interativas, tornando a aprendizagem mais significativa e eficaz.

In the context of 21st-century education, the integration of computational thinking, robotics, programming, digital literacy, and artificial intelligence (AI) into mathematics, science, and technology curriculum is essential to effectively prepare students. This paper explores these themes within the framework of Sustainable Development Goals (SDGs), emphasizing universal access and equitable quality education for all. It examines how these technologies and methodologies can enhance teaching and learning experiences, fostering critical thinking and problem-solving skills from kindergarten through higher education. Drawing on current research and educational practices, the discussion includes insights into continuous teacher training initiatives and interdisciplinary collaboration to support the implementation of these innovations in educational settings. By addressing these topics, this paper contributes to the ongoing discourse on modernizing education to meet the demands of a technology-driven society and prepares students for future challenges in mathematics, science, and technology. The integration of computational thinking and AI into the mathematics curriculum not only enhances students’ learning experiences but also equips them with essential skills for navigating an increasingly complex and interconnected world.

This study was developed in the scope of the Poly-Universe in Teacher Training Education project and explores how to promote interdisciplinary and STEAM approaches in teacher education with Poly-Universe, a game based on materials of different geometric shapes and different colours, that obey certain characteristics that allow for various constructions. The aim of this study is to examine how Poly-Universe can be used in teacher education to promote interdisciplinary and STEAM education. Participants were preservice teachers enrolled in master courses, the third cycle of basic education and secondary education, focusing on different subject areas such as sciences, mathematics, geography, biology, history, philosophy, humanities, and sports. The study involved activities that required participants to construct and replicate models as well as propose their own ideas. Data were collected through observation, documentary analysis, and the intrinsic motivation inventory. Diverse ideas and proposals emerged, participants were actively engaged. The study highlights the potential of Poly-Universe as a tool for enhancing motivation and engagement as well as a resource for developing key competencies in problem-solving, creativity, and collaboration among preservice teachers. Furthermore, the research provides insights into how future educators can integrate Poly-Universe into their curricula to strengthen interdisciplinary connections.

Due to its formal, logical and spatial properties, geometry is well suited for the exploration of new knowledge, new properties that arise from different constructions and new insights into already known constructions, to the exploration of proofs of new conjectures, to the exploration of new proofs of known theorems. With a Dynamic Geometry System (DGS) we get an environment where new conjectures can be easily formulated and visually verified (but not proven). With a Geometry Automated-Theorem-Prover (GATP) we get an environment where conjectures/theorems can be formally proved. We explore some environments where DGS and GATP are combined, analysing their possibilities for the exploration of new conjectures and proofs, having in mind their use in a learning situation.

Using a Dynamic Geometry System (DGS) students can engage in a dynamic learning process that allows them to experiment, create strategies, make conjectures, argue, and deduce mathematical properties. A DGS enables the introduction of proofs, by providing visual aids. The proof of the conjectures made emerges as the next step towards formalising and understanding the contents covered and the introduction of automated deduction systems at schools can be an added value. The implementation of automated deduction systems in schools faces several challenges, such as curriculum-issues, teacher knowledge and the discrepancy between automated theorem provers and traditional practices of proving in schools. Synthetic provers based on a set of inference rules and forward chaining reasoning may provide a possible help to these challenges. With the aim of introducing formal proofs and inspiring students towards this goal, a geometric conjecture was chosen for 7th grade students to engage with, based on a rule set discussed in a previous work, “A rule based theorem prover: an introduction to proofs in secondary schools”. The study also aimed to showcase the application of a Geometry Automated Theorem Prover within the classroom setting. A sequence of tasks was created for students to complete using GeoGebra Classroom. In the first phase, they were asked to identify quadrilaterals, construct a parallelogram, and measure sides and angles until they formulated a conjecture, which was strengthened by the dynamic possibility of changing the constructed parallelogram. In the second phase, the students were provided with four rules and were asked to justify their results using these rules. By the end of these justifications, the students had a complete proof of the initial conjecture. A short video of the proof made using JGEx (Java Geometry Expert) was also shown to the students.

Este estudo abordou o desafio de preparar estudantes com habilidades relevantes para o século XXI, focando no papel das metodologias ativas na educação. O objetivo geral foi investigar como essas metodologias contribuem para o desenvolvimento de competências essenciais, como pensamento crítico, criatividade, colaboração, comunicação, e alfabetizações informacional e digital. Adotou-se uma metodologia de revisão bibliográfica, analisando estudos de caso e literatura acadêmica sobre aprendizagem baseada em problemas (PBL), aprendizagem baseada em projetos (PjBL), e sala de aula invertida. Os resultados apontaram que as metodologias ativas promovem um aprendizado mais engajador e significativo, estimulando a participação ativa dos alunos na construção do conhecimento. Enfrentaram-se desafios como resistência à mudança e a necessidade de infraestrutura adequada, mas as soluções passaram por capacitação docente e adaptação dos espaços de aprendizagem. As considerações finais destacaram a importância das metodologias ativas na formação de indivíduos aptos a navegar pela complexidade dos desafios contemporâneos, sugerindo a continuidade da pesquisa na área.

In educational environments, technology is present as a resource that facilitates teaching and learning. In higher education, modern education in science, technology, engineering and mathematics (STEM) faces fundamental challenges. The objective of the present study is to analyse, the learning strategy with the use of technologies in mathematical activities, analyse mathematical activities and ways of thinking in Higher Education. The research methodology adopted consists of a case study, relating to a group of pre-service teachers in a public Higher Education Institution. A qualitative approach was adopted with the interpretation of data collected through the activities on GeoGebra Classroom, brief questionnaire and conducting individual interviews. It is concluded that technologies have a significant participation in the educational environment and support teaching and learning. The teacher, when perfecting his pedagogical practice, will be able to insert the technological tools in teaching and learning, to improve the interaction with students and further the improvement of learning with the modelled use of technology in the classroom.

1 Research Centre on Didactics and Technology in the Education of Trainers (CIDTFF), Department of Education and Psychology, University of Aveiro (PORTUGAL)2 Research Centre on Didactics and Technology in the Education of Trainers (CIDTFF), Aveiro Institute of Accounting and Administration (PORTUGAL)

Abstract This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic Education students, using material from the Poly-UNiverse in Teacher Training Education (PUNTE) project. The teaching experience developed was aimed at testing and disseminating new resources, and innovative and transdisciplinary methodologies in the areas of Science, Technology, Engineering, Art and Mathematics (STEAM). The adopted methodology involved two phases. The first phase was exploratory, followed by a second phase where the exploration of geometry concepts in the plane (namely, the perimeter and the similarity of triangles) was carried out using the Poly-Universe material. The results of the study show that the Poly-Universe materials constituted an important teaching resource in solving the proposed tasks. Its manipulation allowed the visualisation of the situations involved in the tasks, as well as contributed to an implication in the activities developed by the students.

The twenty-first century presents fundamental challenges for education systems focused on skills development. With this requirement, the training of teachers is changing little by little. Where the learning of the knowledge to be taught seeks to articulate itself in different modalities. Teachers can use various resources, from manipulative materials to technological resources, which can make the class more attractive and contribute to the student’s interest in the content being worked on, thus building knowledge. The Poly-Universe in Teacher Training Education (PUNTE) project aims to develop innovative and transdisciplinary pedagogical methods that are mainly related to a revolutionary educational tool called Poly-Universe. This work aims to describe and analyse the material of the PUNTE project, which allows the development of a new methodology for visual mathematics education in the physical and digital aspects to improve the quality of students’ learning. Based on classroom observations and workshops for prospective teachers, the results have shown that this tool can be used in a science, technology, engineering, art, and mathematics (STEAM) context.

The introduction of automated deduction systems in secondary schools face several bottlenecks. Beyond the problems related with the curricula and the teachers, the dissonance between the outcomes of the geometry automated theorem provers and the normal practice of conjecturing and proving in schools is a major barrier to a wider use of such tools in an educational environment. Since the early implementations of geometry automated theorem provers, applications of artificial intelligence methods, synthetic provers based on inference rules and using forward chaining reasoning are considered to be more suited for education proposes. Choosing an appropriate set of rules and an automated method that can use those rules is a major challenge. We discuss one such rule set and its implementation using the geometry deductive databases method (GDDM). The approach is tested using some chosen geometric conjectures that could be the goal of a 7th year class (approx. 12-year-old students). A lesson plan is presented, its goal is the introduction of formal demonstration of proving geometric theorems, trying to motivate students to that goal

The introduction of games as a teaching and learning strategy in the classroom is a pedagogical resource that presents excellent results, as it creates situations that allow the students to develop problem solving methods, stimulate their creativity and at the same time generate motivation. The theories of learning are used to describe the motives and processes of learning and teaching methods. In order to analyse the cognitive dimensions inherent in the teaching and learning process, we can consider Bloom's taxonomy. The present study was with students of 1st cycle studies, Bachelor's Degree, in the 2nd semester in the curricular unit Learning and Teaching Models. Several games were developed by the students based on the Poly-Universe material, with the objective of being used in classroom contexts with students. The conclusions of this study are very positive, as the students got involved in creatively playing games, drawing up a document with the rules of their created game.

Learning with understanding is essential to enabling students to solve problems that they will inevitably face in the future. Students will be more successful, if they are engaged in thought-provoking activities that encourage them to grow in their mathematical understanding and identity. With this study we intended to understand how the application of exploratory tasks for teaching and learning mathematics in primary school, using the Poly-Universe tool, promotes a comprehensive learning of mathematics. We concluded that the activities involving the Poli-Universe, a tool to teach mathematics are motivating, as the students' interest and motivation during this study was notorious. The use of objects with such attractive characteristics, that appeal to visualisation, permitted the exploration of different figures and its characteristics and the comprehension of some geometric concepts. As well as positive interaction and collaboration of the students, the discussion and the development of their geometric reasoning were remarkable.

Appears in: EDULEARN23 Proceedings Publication year: 2023Pages: 3100-3105ISBN: 978-84-09-52151-7ISSN: 2340-1117doi: 10.21125/edulearn.2023.0863Conference name: 15th International Conference on Education and New Learning TechnologiesDates: 3-5 July, 2023Location: Palma, Spain

1 Research Centre on Didactics and Technology in the Education of Trainers (CIDTFF), Department of Education and Psychology, University of Aveiro (PORTUGAL)2 Polytechnic Institute of Viseu / Center for Research & Development in Mathematics and Applications (CIDMA), University of Aveiro (PORTUGAL)