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- 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.
- 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.
- Using mathematical magic to improve student’s motivation in mathematics classesPublication . Pais, Sónia; Hall, AndreiaOne of the problems identified in the failure of mathematics teaching is the lack of motivation that students feel towards the discipline. Considering that it is imperative to make the teaching and learning processses of mathematics more stimulating, taking into account modern society and student’s interests, 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. In order to develop this experience, the techniques of inquiry, direct observation and analysis of documents were applied and the following instruments were used: questionnaires and respective analysis grids; production of a battery of tasks of a diversified nature and field notes. The analysis of the collected data allows us to conclude that the use of mathematical magic tricks in the classroom, with the purpose of motivating the students to learn mathematics, revealed to be effective.
- The Mathematical Circus ProjectPublication . Hall, Andreia; Pais, SóniaMagic and mathematics appear hand in hand when it comes to promoting the interest and motivation for learning mathematics. Portugal, like other countries, has a high failure rate in school mathematics, which of course causes a negative attitude towards this subject in society. Mathematics is generally thought of as a difficult subject with little practical importance. Motivated by the need to fight this stigma, the Mathematical Circus Project emerged in 2012. Linking mathematics with the performing arts (theater and circus) is not as common as other connections such as with the visual arts. The Mathematical Circus team performs mathematical magic shows with a circus atmosphere in schools, science centers and other public spaces. In a traditional magic show, one often realizes that what causes the fantastic effects is the magician’s ability to manipulate objects combined with the art of controlling the perception of the spectators. The tricks performed in the Mathematical Circus are exclusively based on mathematical principles. In this paper we describe the Mathematical Circus project: its context, goals, contents and achievements
- Mathematical magic in the classroomPublication . Hall, A.; Pais, S.Mathematics, considered one of the basic areas of various formations, has been the subject of concern for many authors and researchers due to its enormous academic and educational failure [1]. Its importance in day-to-day life and the formation of individuals is irrefutable [2]. One of the problems identified in the failure of mathematics teaching is the lack of motivation that students feel towards the discipline. According to [3], motivation is an essential factor in any learning since the quality of learning is not only related to the capacity to learn, but also to the level of motivation that we have to carry out this same learning. 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 [4], the authors have developed a qualitative case study to evaluate how "mathematical magic" can contribute to increase students’ motivation for learning mathematics. In order to develop this experience, the techniques of inquiry, direct observation and analysis of documents were applied and the following instruments were used: questionnaires and respective analysis grids; production of a battery of tasks of a diversified nature; field notes and interviews. Although this project is still ongoing and therefore not yet completed, a previous analysis of the collected data allows us to conclude that the use of mathematical magic tricks in the classroom, with the purpose of motivating the students to learn mathematics, was revealed effective. Students were curious about the new tricks and were positively surprised at the relative simplicity of their explanation, as if saying to themselves, "How can such mathematical concepts bring so much surprise?" The students showed that the topics gained more meaning after performing the tricks because they witnessed real applications of the concepts, with an extremely attractive purpose. They often stated that they were going to play the tricks on their friends / family outside the classroom context, which meant that they were mastering the concepts involved.
- Mathematical circus clown tricksPublication . Hall, A.; Almeida, P.; Vettori, P.; Pais, S.The Mathematical Circus project was created in 2011 by the LUDUS association with the main goal of promoting the interest and motivation for learning mathematics. The Mathematical Circus team performs mathematical magic shows where complementary skills are merged to produce a high intervention capacity within a wide geographical range in Portugal. Some tricks are performed by a mathematical clown, a unique character in the circus world, who brings together the usual foolish characteristics of a clown and the rigorous mathematical knowledge. In this paper we will describe and explain some of the tricks of the Mathematical Circus repertoire involving the clown.