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Sonia Pais

Since 1989, the Mathematics Education Project (PmatE–Projecto Matemática Ensino) has developed several strategies to improve the success of students in Mathematics. The most important of these are mathematical games for all grades above... more
Since 1989, the Mathematics Education Project (PmatE–Projecto Matemática Ensino) has developed several strategies to improve the success of students in Mathematics. The most important of these are mathematical games for all grades above primary school. The online evaluation of Mathematics subjects is one of PmatE's goals. The implementation of an on-line diagnosis test–TDmat (Teste Diagnóstico de Matemática), mandatory for all
Resumo A era da informação e o desenvolvimento das tecnologias de informação e comunicação vêm colocar novos desafios e oportunidades às instituições de Ensino Superior, nomeadamente, ao nível do processo educativo, que deve ser mais... more
Resumo A era da informação e o desenvolvimento das tecnologias de informação e comunicação vêm colocar novos desafios e oportunidades às instituições de Ensino Superior, nomeadamente, ao nível do processo educativo, que deve ser mais centrado no aluno e nas suas aprendizagens. Assim, desenvolveu-se um estudo de caso, envolvendo alunos do curso de Engenharia Alimentar, que perseguiu como principal objetivo avaliar o impacto da exploração diferenciada da plataforma de ensino assistido, desenvolvida pelo Projeto Matemática Ensino (PmatE), como complemento à abordagem didática da unidade temática "Cálculo Integral em IR". Neste artigo, discute-se a sua ressonância ao nível do desenvolvimento de apetências relativamente à matemática, manifestadas através dum maior interesse por parte dos alunos em relação à unidade curricular e concluiu-se que o uso da plataforma contribuiu para aumentar o gosto pela Matemática. Palavras-chave: Ensino Superior; Matemática; Ensino Assistido por ...
This 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... more
This 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...
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.... more
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. 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 di...
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.... more
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.
Magic 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... more
Magic 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 ...
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.... more
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. 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 di...
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... more
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.
Nowadays we live in an ever-changing society, changes that are reflected, not only, but also, in the educational community. Thus renewal of paradigms in the educational context is demanded. The challenge that teachers face today is to... more
Nowadays we live in an ever-changing society, changes that are reflected, not only, but also, in the educational community. Thus renewal of paradigms in the educational context is demanded. 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, thus increasing their motivation to learn. The questions underlying this work are: How can teachers know the students' differences and their individual learning characteristics? How can teachers understand their students and design effective instruction? What teaching strategies are recommended to help teachers meet the different learning needs of all their students? The empirical part of the case study, in an investigation-action context, encompassed students of the curricular unit of Mathematical Analysis I (2008/2009 1st semester), of the plan of studies of the Science Food Engineering of the Superior School of Tourism and Sea Technology (ESTM), of Leiria's Polytechnical Institute. Preliminary analysis of the data collected trough several techniques - surveys, content analysis and participant observation - indicates that instruction designed to address a broad spectrum of learning styles has proven more effective than traditional instruction (almost exclusively magisterial and based on the transmission of knowledge), which focuses on a narrow range of styles. Moreover, it allows us to reflect on the conditions that will enhance the implementation of a model that has the learning of the students as the basis, respecting their individual rhythm and learning style preferences, and favoring an education centered in the pupil's body of work.
Nowadays we live in an ever-changing society, changes that are reflected, not only, but also, in the educational community. Thus renewal of paradigms in the educational context is demanded. The challenge that teachers face today is to... more
Nowadays we live in an ever-changing society, changes that are reflected, not only, but also, in the educational community. Thus renewal of paradigms in the educational context is demanded. 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, thus increasing their motivation to learn. The questions underlying this work are: How can teachers know the students' differences and their individual learning characteristics? How can teachers understand their students and design effective instruction? What teaching strategies are recommended to help teachers meet the different learning needs of all their students? The empirical part of the case study, in an investigation-action context, encompassed students of the curricular unit of Mathematical Analysis I (2008/2009 1st semester), of the plan of studies of the Science Food Engineering of the Superior School of Tourism and Sea Technology (ESTM), of Leiria's Polytechnical Institute. Preliminary analysis of the data collected trough several techniques - surveys, content analysis and participant observation - indicates that instruction designed to address a broad spectrum of learning styles has proven more effective than traditional instruction (almost exclusively magisterial and based on the transmission of knowledge), which focuses on a narrow range of styles. Moreover, it allows us to reflect on the conditions that will enhance the implementation of a model that has the learning of the students as the basis, respecting their individual rhythm and learning style preferences, and favoring an education centered in the pupil's body of work.
Research Interests:
The educational context requires a renewal of paradigms. Profound changes in the roles and functions of teachers and students are particularly vital. More active, cooperative and participative methodologies of learning must be privileged,... more
The educational context requires a renewal of paradigms. Profound changes in the roles and functions of teachers and students are particularly vital. More active, cooperative and participative methodologies of learning must be privileged, breaking with magisterial education and the mere ‘transmission’ of knowledge.
Informatics tools can become a major element in the educational context, promoting significant and self-regulated learning for the student, always under the adequate orientation of the teacher.
In this context, the Mathematics Education Project (PmatE) was created in the University of Aveiro, with the main objective of identifying and counteracting the causes of school failure in mathematics in an innovative approach.
However, the PmatE platform has not yet been subjected to the kind of systematic evaluation, especially in higher education, that would allow us to understand in what conditions the goals can be achieved.
Thus, the question underlying this explanatory research is: “What impact does the platform of assisted education developed by PmatE have in the process of learning math subjects at university level?”
A previous analysis (still ongoing) of the data collected through several techniques – inquiry, documental analysis and participant observation – suggests there are interesting and innovative alternatives to the dominant pedagogies in higher education (where teaching assumes almost exclusively a magisterial form), with significant advantages for the construction of knowledge and for the development of the students’ capabilities.
A era da informação e o desenvolvimento das tecnologias de informação e comunicação vêm colocar novos desafios e oportunidades às instituições de Ensino Superior, nomeadamente, ao nível do processo educativo, que deve ser mais centrado no... more
A era da informação e o desenvolvimento das tecnologias de informação e comunicação vêm colocar novos desafios e oportunidades às instituições de Ensino Superior, nomeadamente, ao nível do processo educativo, que deve ser mais centrado no aluno e nas suas aprendizagens. Assim, desenvolveu-se um estudo de caso, envolvendo alunos do curso de Engenharia Alimentar, que perseguiu como principal objetivo avaliar o impacto da exploração diferenciada da plataforma de ensino assistido, desenvolvida pelo Projeto Matemática Ensino (PmatE), como complemento à abordagem didática da unidade temática “Cálculo Integral em IR”. Neste artigo, discute-se a sua ressonância ao nível do desenvolvimento de apetências relativamente à matemática, manifestadas através dum maior interesse por parte dos alunos em relação à unidade curricular e concluiu-se que o uso da plataforma contribuiu para aumentar o gosto pela Matemática.
The educational context requires a renewal of paradigms. More active, cooperative and participative methodologies of learning must be privileged. Profound changes to the role and function of the professor and the students are particularly... more
The educational context requires a renewal of paradigms. More active, cooperative and participative methodologies of learning must be privileged. Profound changes to the role and function of the professor and the students are particularly vital. Active, cooperative and participative methodologies must be privileged, breaking with magisterial education and the mere transmission of knowledge. Informatics tools can become a major element in the educational context, promoting significant and self-regulated learning for the student, always under the adequate orientation of the teacher. Being aware of this need, the Mathematics Education Project (PmatE) was created in the University of Aveiro, with the main objective of identifying and counteracting the causes of school failure in mathematics in an innovative approach. However, the PmatE platform has not yet been subjected to the kind of systematic evaluation, especially in higher education, that would allow us to understand in what conditions the goals can be achieved. Thus, the question underlying this explanatory research is: “What impact does the platform of assisted education developed by PmatE have, as a complement of the didactic approach, in the process of learning math subjects at university level?”, regarding the develoopment of autonomy abilities, the ability to transfer acquired knowledge to other mathematical situations and the development of appetence towards mathematics. The study encompassed students enrolled in the curricular unit of Mathematical Analysis I (2008/2009 1st semester), integrated in the plan of studies of Food Engineering of a Portuguese Polytechnic Institute. In parallel with the lessons, the students explored the platform and worked with it. Thus, inside the classroom was possible to work with another type of tasks. For the data collection, we privileged the inquiry techniques, direct observation and documental analysis and the following instruments: an initial and a final questionnaire, assessments tests (in versions: pre-test, post-test1 and post-test2), a battery of tasks of diverse nature, computerized records of the students’ performance on PmatE’s platform, field notes and interviews. The results obtained indicate that students who are more autonomous, more persistent and who get better results are the students who used the platform frequently and that the use of PmatE platform contributed to increase the liking for mathematics. It also allowed us to obtain important information about aspects to improve the platform, in particular concerning the nature of tasks and the resolution of the proposed exercises.