Vanda Santos - Academia.edu (original) (raw)
Papers by Vanda Santos
EDULEARN proceedings, Jul 1, 2023
Open Education Studies
This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic E... more 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.
Revista INFAD de Psicología. International Journal of Developmental and Educational Psychology.
The integral development of the child is nowadays one of the goals of the education, which implie... more The integral development of the child is nowadays one of the goals of the education, which implies the use of activities and strategies that involve the various dimensions of the human being in a comprehensive way. This paper aims to describe and analyse the potential of the pedagogical model of the Erasmus+ Vidukids project to develop ‘Heads-on’, ‘Hearts-on’, ‘Hands-on’ activities. The project aims to explore the use of video production about mathematics, by children aged 4-8 years old. The pedagogical matrix involves different levels of complexity in video production, mathematical topics such as numbers, shapes, space and tasks such as ‘An explorer mission’, ‘A story with mathematical content’, ‘Solving a mathematical problem’. Based on a Vidukids activity in which participated 60 trainees from bachelor courses in educational areas, there was immediate involvement in the video production task and the resources needed for the narrative. The analysis of the videos produced and the a...
Electronic Proceedings in Theoretical Computer Science, 2022
The introduction of automated deduction systems in secondary schools face several bottlenecks, th... more The introduction of automated deduction systems in secondary schools face several bottlenecks, the absence of the subject of rigorous mathematical demonstrations in the curricula, the lack of knowledge by the teachers about the subject and the difficulty of tackling the task by automatic means. Despite those difficulties we claim that the subject of automated deduction in geometry can be introduced, by addressing it in particular cases: simple to manipulate by students and teachers and reasonably easy to be dealt by automatic deduction tools. The subject is discussed by addressing four secondary schools geometry problems: their rigorous proofs, visual proofs, numeric proofs, algebraic formal proofs, synthetic formal proofs, or the lack of them. For these problems we discuss a lesson plan to address them with the help of Information and Communications Technology, more specifically, automated deduction tools.
EDULEARN21 Proceedings, 2021
Lecture Notes in Computer Science, 2021
European Journal of Engineering Education, 2014
ABSTRACT Concern has been expressed throughout Europe about the significant deficiencies in the b... more ABSTRACT Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into engineering education, such as projects or real-world problems. Every year, in the Dublin Institute of Technology (Ireland) and the Instituto Superior de Engenharia de Coimbra (Portugal), a diagnostic test is given to incoming first-year students. A comparison showed some potentially interesting differences between these students. In September 2013, a project was undertaken to compare mathematical competencies of incoming engineering students in both countries. A modified diagnostic test was devised and the results were then compared to ascertain if there are common areas of difficulty between students in Ireland and Portugal, or evidence of one group significantly outperforming the other in a particular area.
2008 Eighth IEEE International Conference on Advanced Learning Technologies, 2008
The study of geometry, with its formal and constructive nature, is, and will always be, very impo... more The study of geometry, with its formal and constructive nature, is, and will always be, very important for a mathematical practitioner. In this paper we describe an e-Learning course for Euclidean Geometry with a particular focus on the constructive nature of geometry: from basic objects: points and lines, and basic constructions that can be done with a ruler and a compass, to very complex constructions with well defined properties. For this purpose we have integrated in the e-Learning course a Web page that gives the student the ability to explore the constructions already built-in and to do new ones through the use of a dynamic geometry software. The e-Learning course was implemented as a SCORM activity allowing, in this way, the use of various LMSs as actual e-Learning platforms. We have used the Moodle, Claroline, and Dokeos LMSs as test beds.
EDULEARN proceedings, Jul 1, 2022
In recent times, the debate on active methodologies has been intensified with the emergence of st... more In recent times, the debate on active methodologies has been intensified with the emergence of strategies that can favor students' autonomy. The active, dynamic and constructive environment can positively influence the perception of teachers and students. One of the ways to achieve this is through the use of technologies that enhance learning. Due to the pandemic situation, the use of technologies was imperative and essential. Three higher education institutions were involved in an active learning project, involving diversified technologies and methodologies to enhance the learning of mathematics. The methodologies used were applied during three distinct phases and according to the students' profile, related to each course. The methodologies used were very diverse: team-based learning; flipped classroom; peer teaching; think-pair-share and exposition followed by exercise practice; problem-based learning and inquiry-based learning. The technologies were also very diversified: Desmos, Kahoot!, Quizizz, GeoGebra, Excel, OneNote, Google Docs, Zoom, Miro, Wolfram alpha, PowerPoint, calculators and videos. The use of a wide range of methodologies and technologies made it possible to teach during the lockdown imposed by the pandemic situation, and simultaneously motivated the students. In addition, they provided opportunities to adapt the learning process to the diverse knowledge and learning styles of students and increased their involvement.
International Conference on Intelligent Computer Mathematics, 2014
The Web Geometry Laboratory (WGL) project's goal is, to build an adaptive and collaborative blend... more The Web Geometry Laboratory (WGL) project's goal is, to build an adaptive and collaborative blended-learning Web-environment for geometry. In its current version (1.2) the WGL is already a collaborative blendedlearning Web-environment integrating a dynamic geometry system (DGS) and with some adaptive features. The building of the adaptive module is a two steps task, a first task, already almost completed, is the collection of data, textual, navigation and also geometric data. A second task will be, using the collected data, the construction of student profiles and/or learning paths. In this article the process of collection of the data and its visualisation will be described. The actual testing of the WGL platform by high-school teachers is underway and field-tests with high-school students are being prepared. The next steps in the development of this platform will be the construction of student profiles and/or learning paths. The integration of a geometric automated theorem prover, allowing the exploration of geometric reasoning in a learning environment is also planned.
Proof Technology in Mathematics Research and Teaching
EDULEARN21 Proceedings, 2021
A necessidade de desenvolver ferramentas educacionais de ensino para apoiar a aprendizagem da mat... more A necessidade de desenvolver ferramentas educacionais de ensino para apoiar a aprendizagem da matemaatica e bem reconhecida. As possibilidades abertas pelas utilizcao de ferramentas das tecnologias da informacao e comunicacao sao muitas, ambientes adaptativos, colaborativos, sincronos e assincronos, contribuem para reforcar a aprendizagem de materias complexas como a Matematica. A plataforma Laboratorio de Geometria na Rede (em Ingles, Web Geometry Laboratory, WGL) carateriza-se por ser um ambiente de ensino presencial/nao presencial, colaborativo, adaptativo e integrando um sistema de geometria dinâmica. A plataforma visa contribuir para o melhorar do nivel de raciocinio geometrico do aluno. Neste artigo descreve-se de forma breve a plataforma e, atraves da descricao de um estudo de caso, a sua utilizacao para a realizacao, de forma colaborativa, de trabalhos para casa.
Tese de Doutoramento em Didatica de Ciencias e Tecnologias, Especializacao em Didatica de Matematica
ICERI2019 Proceedings, 2019
s of Contributed Talks of the CADGME 2016 Conference 1. Vanda Santos, Perdo Quaresma Adaptive Str... more s of Contributed Talks of the CADGME 2016 Conference 1. Vanda Santos, Perdo Quaresma Adaptive Strategies in the Web Geometry Laboratory The Web Geometry Laboratory (WGL) platform is a collaborative and adaptive blended-learning Web-environment for geometry, it integrates a dynamic geometry system (DGS), it provides a collaborative environment for students and teachers and provide some adaptive features. Its use is possible in the context of a classroom or remotely (hilbert.mat.uc.pt/WebGeometryLab). To be able to build individual students profiles and/or individual learning paths, the system collects geometric information about the students' interactions when in the regular, stand-alone, mode. In the regular mode all the steps done be the students when using the DGS to complete a given task are recorded. An initial case study in Portugal was done, sustained through a qualitative approach, with a 15 years old student in an adaptive environment context. The teacher was able to see...
EDULEARN proceedings, Jul 1, 2023
Open Education Studies
This article presents the analysis and discussion of solving geometry tasks by Portuguese Basic E... more 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.
Revista INFAD de Psicología. International Journal of Developmental and Educational Psychology.
The integral development of the child is nowadays one of the goals of the education, which implie... more The integral development of the child is nowadays one of the goals of the education, which implies the use of activities and strategies that involve the various dimensions of the human being in a comprehensive way. This paper aims to describe and analyse the potential of the pedagogical model of the Erasmus+ Vidukids project to develop ‘Heads-on’, ‘Hearts-on’, ‘Hands-on’ activities. The project aims to explore the use of video production about mathematics, by children aged 4-8 years old. The pedagogical matrix involves different levels of complexity in video production, mathematical topics such as numbers, shapes, space and tasks such as ‘An explorer mission’, ‘A story with mathematical content’, ‘Solving a mathematical problem’. Based on a Vidukids activity in which participated 60 trainees from bachelor courses in educational areas, there was immediate involvement in the video production task and the resources needed for the narrative. The analysis of the videos produced and the a...
Electronic Proceedings in Theoretical Computer Science, 2022
The introduction of automated deduction systems in secondary schools face several bottlenecks, th... more The introduction of automated deduction systems in secondary schools face several bottlenecks, the absence of the subject of rigorous mathematical demonstrations in the curricula, the lack of knowledge by the teachers about the subject and the difficulty of tackling the task by automatic means. Despite those difficulties we claim that the subject of automated deduction in geometry can be introduced, by addressing it in particular cases: simple to manipulate by students and teachers and reasonably easy to be dealt by automatic deduction tools. The subject is discussed by addressing four secondary schools geometry problems: their rigorous proofs, visual proofs, numeric proofs, algebraic formal proofs, synthetic formal proofs, or the lack of them. For these problems we discuss a lesson plan to address them with the help of Information and Communications Technology, more specifically, automated deduction tools.
EDULEARN21 Proceedings, 2021
Lecture Notes in Computer Science, 2021
European Journal of Engineering Education, 2014
ABSTRACT Concern has been expressed throughout Europe about the significant deficiencies in the b... more ABSTRACT Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into engineering education, such as projects or real-world problems. Every year, in the Dublin Institute of Technology (Ireland) and the Instituto Superior de Engenharia de Coimbra (Portugal), a diagnostic test is given to incoming first-year students. A comparison showed some potentially interesting differences between these students. In September 2013, a project was undertaken to compare mathematical competencies of incoming engineering students in both countries. A modified diagnostic test was devised and the results were then compared to ascertain if there are common areas of difficulty between students in Ireland and Portugal, or evidence of one group significantly outperforming the other in a particular area.
2008 Eighth IEEE International Conference on Advanced Learning Technologies, 2008
The study of geometry, with its formal and constructive nature, is, and will always be, very impo... more The study of geometry, with its formal and constructive nature, is, and will always be, very important for a mathematical practitioner. In this paper we describe an e-Learning course for Euclidean Geometry with a particular focus on the constructive nature of geometry: from basic objects: points and lines, and basic constructions that can be done with a ruler and a compass, to very complex constructions with well defined properties. For this purpose we have integrated in the e-Learning course a Web page that gives the student the ability to explore the constructions already built-in and to do new ones through the use of a dynamic geometry software. The e-Learning course was implemented as a SCORM activity allowing, in this way, the use of various LMSs as actual e-Learning platforms. We have used the Moodle, Claroline, and Dokeos LMSs as test beds.
EDULEARN proceedings, Jul 1, 2022
In recent times, the debate on active methodologies has been intensified with the emergence of st... more In recent times, the debate on active methodologies has been intensified with the emergence of strategies that can favor students' autonomy. The active, dynamic and constructive environment can positively influence the perception of teachers and students. One of the ways to achieve this is through the use of technologies that enhance learning. Due to the pandemic situation, the use of technologies was imperative and essential. Three higher education institutions were involved in an active learning project, involving diversified technologies and methodologies to enhance the learning of mathematics. The methodologies used were applied during three distinct phases and according to the students' profile, related to each course. The methodologies used were very diverse: team-based learning; flipped classroom; peer teaching; think-pair-share and exposition followed by exercise practice; problem-based learning and inquiry-based learning. The technologies were also very diversified: Desmos, Kahoot!, Quizizz, GeoGebra, Excel, OneNote, Google Docs, Zoom, Miro, Wolfram alpha, PowerPoint, calculators and videos. The use of a wide range of methodologies and technologies made it possible to teach during the lockdown imposed by the pandemic situation, and simultaneously motivated the students. In addition, they provided opportunities to adapt the learning process to the diverse knowledge and learning styles of students and increased their involvement.
International Conference on Intelligent Computer Mathematics, 2014
The Web Geometry Laboratory (WGL) project's goal is, to build an adaptive and collaborative blend... more The Web Geometry Laboratory (WGL) project's goal is, to build an adaptive and collaborative blended-learning Web-environment for geometry. In its current version (1.2) the WGL is already a collaborative blendedlearning Web-environment integrating a dynamic geometry system (DGS) and with some adaptive features. The building of the adaptive module is a two steps task, a first task, already almost completed, is the collection of data, textual, navigation and also geometric data. A second task will be, using the collected data, the construction of student profiles and/or learning paths. In this article the process of collection of the data and its visualisation will be described. The actual testing of the WGL platform by high-school teachers is underway and field-tests with high-school students are being prepared. The next steps in the development of this platform will be the construction of student profiles and/or learning paths. The integration of a geometric automated theorem prover, allowing the exploration of geometric reasoning in a learning environment is also planned.
Proof Technology in Mathematics Research and Teaching
EDULEARN21 Proceedings, 2021
A necessidade de desenvolver ferramentas educacionais de ensino para apoiar a aprendizagem da mat... more A necessidade de desenvolver ferramentas educacionais de ensino para apoiar a aprendizagem da matemaatica e bem reconhecida. As possibilidades abertas pelas utilizcao de ferramentas das tecnologias da informacao e comunicacao sao muitas, ambientes adaptativos, colaborativos, sincronos e assincronos, contribuem para reforcar a aprendizagem de materias complexas como a Matematica. A plataforma Laboratorio de Geometria na Rede (em Ingles, Web Geometry Laboratory, WGL) carateriza-se por ser um ambiente de ensino presencial/nao presencial, colaborativo, adaptativo e integrando um sistema de geometria dinâmica. A plataforma visa contribuir para o melhorar do nivel de raciocinio geometrico do aluno. Neste artigo descreve-se de forma breve a plataforma e, atraves da descricao de um estudo de caso, a sua utilizacao para a realizacao, de forma colaborativa, de trabalhos para casa.
Tese de Doutoramento em Didatica de Ciencias e Tecnologias, Especializacao em Didatica de Matematica
ICERI2019 Proceedings, 2019
s of Contributed Talks of the CADGME 2016 Conference 1. Vanda Santos, Perdo Quaresma Adaptive Str... more s of Contributed Talks of the CADGME 2016 Conference 1. Vanda Santos, Perdo Quaresma Adaptive Strategies in the Web Geometry Laboratory The Web Geometry Laboratory (WGL) platform is a collaborative and adaptive blended-learning Web-environment for geometry, it integrates a dynamic geometry system (DGS), it provides a collaborative environment for students and teachers and provide some adaptive features. Its use is possible in the context of a classroom or remotely (hilbert.mat.uc.pt/WebGeometryLab). To be able to build individual students profiles and/or individual learning paths, the system collects geometric information about the students' interactions when in the regular, stand-alone, mode. In the regular mode all the steps done be the students when using the DGS to complete a given task are recorded. An initial case study in Portugal was done, sustained through a qualitative approach, with a 15 years old student in an adaptive environment context. The teacher was able to see...