O recurso à magia matemática para aumentar a motivação dos estudantes nas aulas de Matemática

One 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 processes 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.Um dos problemas identifcados no fracasso do processo de aprendizagem da Matemática é a falta de motivação que os estudantes sentem em relação à disciplina. Sendo evidente que é imperativo que o processo de ensino da Matemática se torne mais estimulante, tendo em conta a sociedade moderna e os interesses dos estudantes, as autoras desenvolveram diversas estratégias para aumentar o interesse e promover o sucesso dos estudantes relativamente à Matemática. Assim, decidiram, nas suas aulas, recorrer a truques de magia matemática para aumentar a motivação dos estudantes, cativando-os e estimulando o seu interesse pela Matemática. Neste artigo, é apresentado um estudo de caso para avaliar como a magia matemática pode contribuir para aumentar a motivação dos estudantes para aprenderem Matemática. Para desenvolver a experiência referida, privilegiaram-se as técnicas de inquirição, observação direta e análise de documentos e os seguintes instrumentos: questionários e respetivas grelhas de análise; produções de uma bateria de tarefas de natureza diversificada e notas de campo. A análise dos dados recolhidos permite concluir que o recurso a truques de magia matemática em contexto de sala de aula, com o intuito de motivar os alunos para a aprendizagem da Matemática, se revelou eficaz.Uno de los problemas identificados en el fracaso del proceso de enseñanza-aprendizaje de las matemáticas es la falta de motivación que los estudiantes sienten en relación a la disciplina. Siendo evidente que es imperativo que el proceso de enseñanza y aprendizaje de las matemáticas se vuelva más estimulante, teniendo en cuenta la sociedad moderna y los intereses de los estudiantes, las autoras desarrollaron diversas estrategias para aumentar el interés y promover el éxito de los estudiantes con respecto a las matemáticas. Así, decidieron, en sus clases, recurrir a trucos de magia matemática para aumentar la motivación de los estudiantes, cautivándolos y estimulando su interés por las matemáticas. En este artículo, se presenta un estudio de caso para evaluar cómo la magia matemática puede contribuir a aumentar la motivación de los estudiantes para aprender matemáticas. Para desarrollar esta experiencia, favoreció a las técnicas de investigación, la observación directa y el análisis de los documentos y las siguientes herramientas: cuestionarios y las respectivas rejillas de análisis; producciones de una batería de tareas diversificadas y notas de campo. El análisis de los datos recogidos muestran que el uso de trucos de magia matemática en el contexto del aula, con el fin de motivar a los estudiantes para el aprendizaje de las matemáticas, ha demostrado ser eficaz.publishe

Using Kahoot! to enhance the motivation of undergraduate students of tourism in mathematics classes: a case study

Nowadays 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.publishe

On the extremes of randomly sub-sampled time series

In this paper, we investigate the extremal properties of randomly sub-sampled stationary sequences. Motivation comes from the need to account for the effect of missing values on the analysis of time series and the comparison of schemes for monitoring systems with breakdowns or systems with automatic replacement of devices in case of failures

Beautiful geometry: a STEAM experience in a professional development course for mathematics teachers

Mathematics and art have a connection that goes far beyond proximity. In fact, they are two symbiotic areas shaping a beautiful, logical, systematic, and breathtaking world. One of the works that exposes their intrinsic connection, in a clear, rigorous and simple way, is the book Beautiful Geometry by Eli Maor and Eugen Jost. To a greater or lesser degree, we all feel the power that art exerts on our minds, both at a sensory and at a cognitive level. In fact, art is one of the privileged areas for the emergence of creativity. Combining beauty with rigor and reason, and based on the book mentioned above, we designed a professional development course for mathematics teachers, following a STEAM approach. The description of this course, illustrated with part of the graphic/artistic material produced by the participants, is the main object of this paper.publishe

Interlacing mathematics and art: hands-on non-Euclidean geometry

Elliot 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.publishe

Exploring symmetry through portuguese tiles in historical monuments

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.publishe

Arte modular com azulejos de Truchet

A construção de obras de arte baseadas num módulo - arte modular - está presente ao longo de toda a história da humanidade. A recombinação do módulo pode ser mais ou menos flexível dando origem a resultados com diferentes graus de regularidade. Naturalmente, a modularidade é um campo fértil para a ocorrência de simetrias e também de antissimetrias. Neste apresentação consideramos a utilização de um módulo particular que consiste num quadrado dividido por uma das suas diagonais em dois triângulos de cores diferentes, que designamos por \textit{azulejo de Truchet}. A partir deste módulo considerámos rosáceas e frisos de diferentes dimensões e estudámos as suas propriedades quanto às possíveis simetrias e antissimetrias. Fizemos também contagens das configurações distintas que se podem obter para diferentes dimensões das rosáceas e dos frisos. Para terminar apresentam-se alguns trabalhos realizados por professores do ensino básico/secundário no contexto de uma ação de formação de professores realizada na Universidade de Aveiro nos meses de fevereiro a abril de 2017

Simetria e antissimetria de rosáceas e frisos

Pretende-se com este curso aprender (ou recordar) a classificar rosáceas e frisos quanto ao seu grupo de simetria. Pretende-se também abordar o conceito de antissimetria e com ele identificar e criar figuras de diversos tipos. O conceito de antissimetria é um conceito simples e apelativo que pode ajudar os alunos a assimilar e consolidar o conceito de simetria. Estes conceitos são explorados durante o curso através de diversos exemplos com especial incidência em figuras construídas a partir dum módulo simples, um quadrado dividido por uma das suas diagonais em dois triângulos de cores diferentes

Interlacing mathematics and art in the classroom: teaching symmetry and antisymmetry using Truchet tiles

The construction of art works based on a module --- \textit{modular art} --- is present throughout all human history. Naturally, modularity is a fertile field for the occurrence of symmetries. In this paper we consider the use of a particular module consisting of a square divided by one of its diagonals into two triangles of different colors, known as a \textit{Truchet tile}. From this module we considered rosettes and friezes of different dimensions and studied their properties regarding possible symmetries and antisymmetries. We have also counted the different configurations that can be obtained for different dimensions of rosettes and friezes. Symmetry and antissymmetry can be useful when creating art works and interlacing mathematics with the arts in the classroom can be a successful way to promote the interest for both subjects. We present some works carried out by primary and secondary school students and teachers.publishe

Cross-Cultural Adaption of the GRBAS and CAPE-V Scales for Portugal and a New Training Programme for Perceptual Voice Evaluation

Several methods have been proposed for the perceptual evaluation of voice quality, but the GRBAS and Consensus Auditory-Perceptual Evaluation of Voice (CAPE-V) scales are the most widely used and recommended as part of standardised voice evaluation protocols. In this study, cross-cultural adaptation and translation of the GRBAS (the first translation from the original Japanese version) and CAPE-V scales to European Portuguese were carried out following international guidelines. Results from a study of the intra- and inter-rater reliability of the perceptual evaluation of voices with the GRBAS and CAPE-V scales, before and after a training programme, designed according to the most recent American Speech-Language-Hearing Association and Japan Society of Logopedics and Phoniatrics guidelines, are also reported