Adaptation model for PCMAT – Mathematics collaborative learning platform

The aim of this paper is to present an adaptation model for an Adaptive Educational Hypermedia System, PCMAT. The adaptation of the application is based on progressive self-assessment (exercises, tasks, and so on) and applies the constructivist learning theory and the learning styles theory. Our objective is the creation of a better, more adequate adaptation model that takes into account the complexities of different users.

e-Math Workshops : a forum for exchanging experiences of mathematics e-learning at university level

We report here about a series of international workshops on e-learning of mathematics at university level, which have been jointly organized by the three publicly funded open universities in the Iberian Peninsula and which have taken place annually since 2009. The history, achievements and prospects for the future of this initiative will be addressed.

The development of an eBook for teaching and learning mathematics

Mobile devices, smartphones, phablets and tablets, are widely avail‐ able. This is a generation of digital natives. We cannot ignore that they are no longer the same students for which the education system was designed tradition‐ ally. Studying math is many times a cumbersome task. But this can be changed if the teacher takes advantage of the technology that is currently available. We are working in the use of different tools to extend the classroom in a blended learning model. In this paper, it is presented the development of an eBook for teaching mathematics to secondary students. It is developed with the free and open standard EPUB 3 that is available for Android and iOS platforms. This specification supports video embedded in the eBook. In this paper it is shown how to take advantage of this feature, making videos available about lectures and problems resolutions, which is especially interesting for learning mathematics.

Learning of shared attention in sociable robotics

Sociable robots are embodied agents that are part of a heterogeneous society of robots and humans. They Should be able to recognize human beings and each other, and to engage in social, interactions. The use of a robotic architecture may strongly reduce the time and effort required to construct a sociable robot. Such architecture must have structures and mechanisms to allow social interaction. behavior control and learning from environment. Learning processes described oil Science of Behavior Analysis may lead to the development of promising methods and Structures for constructing robots able to behave socially and learn through interactions from the environment by a process of contingency learning. In this paper, we present a robotic architecture inspired from Behavior Analysis. Methods and structures of the proposed architecture, including a hybrid knowledge representation. are presented and discussed. The architecture has been evaluated in the context of a nontrivial real problem: the learning of the shared attention, employing an interactive robotic head. The learning capabilities of this architecture have been analyzed by observing the robot interacting with the human and the environment. The obtained results show that the robotic architecture is able to produce appropriate behavior and to learn from social interaction. (C) 2009 Elsevier Inc. All rights reserved.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

Understanding Teacher and Student Learning Situated in a School-wide Implementation of Fractions Instruction

Thesis (Ph.D.)--University of Washington, 2016-06

O ensino e aprendizagem do gráfico da função quadrática com e sem auxílio do Software Winplot

RESUMO: A utilização adequada das TIC no ensino da Matemática, nos dias de hoje é considerada por alguns como justificada e inevitável, esperando que a sua utilização melhore o ensino e a aprendizagem da Matemática. Nesta investigação, pretende-se testar o Software Winplot), no ensino e aprendizagem do gráfico da função quadrática com alunos do 10ºano, da Escola do segundo ciclo do Ensino Secundário nº9099, de modo a verificar se melhora o ensino e na aprendizagem desta temática.Para a nossa investigação Seleccionámos dois grupos de alunos do 10º ano que funcionaram como grupo de controlo e grupo experimental; depois de ambos os grupos terem realizado dois pré-testes, o grupo experimental realizou as aprendizagens no laboratório de informática com auxílio do Software Winplot, ao longo de 8 semanas, durante o 2º trimestre do ano lectivo de 2009/2010. O grupo de controlo realizou as aprendizagens, ao mesmo tempo que o grupo experimental, na sala normal de aulas sem auxílio do Software Winplot.Ao compararmos os dois grupos, o teste T de pares para amostras independentes, mostra-nos que estatisticamente não há diferenças significativas entre os dois grupos, porque os níveis de significância são maiores que p=0,05, desta feita podemos dizer que o grupo experimental, não obteve melhores resultados que o grupo de controlo, logo o Software Winplot não resultou o efeito desejado nas aprendizagens com alunos da 10ºano da Escola do segundo ciclo do ensino Secundário nº9099, sita no município de Viana (Luanda/Angola). ABSTRACT:The appropriate use of ICTs in teaching mathematics, today is considered by somo to be justified and inevitable, hoping that their use will improve the teaching and learning of mathematics.In this investigation, we intend to test the Software Winplot, teaching and learning of the graph of quadratic functions with students of grade 10, attending the second cycle of secondary School nº9099 in order to verify that improves teaching and learning of this subject.For our research selected two groups of students in 10th grade who acted as the controlo group and experimental group, after both group had undergone two pre-test, the experimental group performed the learning in the computer lab with the aid of Software Winplot, over 8 weeks during the second quarter of the academic year 2009/2010. Thr control gropu performed the learning, while the experimental group, in rregular class room without help of the Software Winplot.Comparing the two groups, the t test for independent samples pairs, shows us that there is no statistically significant differences between the two groups, because the significance levels are greater than p=0,05, this time we can say that experimental group, not yielded better results than the control group, so the Software did not result the desired effect on the learning with students from 10th grade of the School of the second cycle of Secondary nº9099, located in Viana (Luanda/Angola).

Content adaptation for an adaptive hypermedia system

The aim of this paper is presenting the recommendation module of the Mathematics Collaborative Learning Platform (PCMAT). PCMAT is an Adaptive Educational Hypermedia System (AEHS), with a constructivist approach, which presents contents and activities adapted to the characteristics and learning style of students of mathematics in basic schools. The recommendation module is responsible for choosing different learning resources for the platform, based on the user's characteristics and performance. Since the main purpose of an adaptive system is to provide the user with content and interface adaptation, the recommendation module is integral to PCMAT’s adaptation model.

Providing Adaptation for an Adaptive Hypermedia System

O ensino à distância cresceu consideravelmente nos últimos anos e a tendência é para que continue a crescer em anos vindouros. No entanto, enquanto que a maioria das plataformas de ensino à distância utilizam a mesma abordagem de ensino para todos os utilizadores, os estudantes que as usam são na realidade pessoas de diferentes culturas, locais, idades e géneros, e que possuem diferentes níveis de educação. Ao contrário do ensino à distância tradicional, os sistemas de hipermédia adaptativa educacional adaptam interface, apresentação de conteúdos e navegação, entre outros, às características, necessidades e interesses específicos de diferentes utilizadores. Apesar da investigação na área de sistemas de hipermédia adaptativa já estar bastante desenvolvida, é necessário efetuar mais desenvolvimento e experimentação de modo a determinar quais são os aspetos mais eficazes destes sistemas e avaliar o seu sucesso. A Plataforma de Aprendizagem Colaborativa da Matemática (PCMAT) é um sistema de hipermédia adaptativa educacional com uma abordagem construtivista, que foi desenvolvido com o objetivo de contribuir para a investigação na área de sistemas de hipermédia adaptativa. A plataforma avalia o conhecimento do utilizador e apresenta conteúdos e atividades adaptadas às características e estilo de aprendizagem dominante de estudantes de matemática do segundo ciclo. O desenvolvimento do PCMAT tem também o propósito de auxiliar os alunos Portugueses com a aprendizagem da matemática. De acordo com o estudo PISA 2012 da OCDE [OECD, 2014], o desempenho dos alunos Portugueses na área da matemática melhorou em relação à edição anterior do estudo, mas os resultados obtidos permanecem abaixo da média da OCDE. Por este motivo, uma das finalidades deste projeto é desenvolver um sistema de hipermédia adaptativa que, ao adequar o ensino da matemática às necessidades específicas de cada aluno, os assista com a aquisição de conhecimento. A adaptação é efetuada pelo sistema usando a informação constante no modelo do utilizador para definir um grafo de conceitos do domínio específico. Este grafo é adaptado do modelo do domínio e utilizado para dar resposta às necessidades particulares de cada aluno. Embora a trajetória inicial seja definida pelo professor, o percurso percorrido no grafo por cada aluno é determinado pela sua interação com o sistema, usando para o efeito a representação do conhecimento do aluno e outras características disponíveis no modelo do utilizador, assim como avaliação progressiva. A adaptação é conseguida através de alterações na apresentação de conteúdos e na estrutura e anotações das hiperligações. A apresentação de conteúdos é alterada mostrando ou ocultando cada um dos vários fragmentos que compõe as páginas dum curso. Estes fragmentos são compostos por diferentes objetos de aprendizagem, tais como exercícios, figuras, diagramas, etc. As mudanças efetuadas na estrutura e anotações das hiperligações têm o objetivo de guiar o estudante, apontando-o na direção do conhecimento mais relevante e mantendo-o afastado de informação inadequada. A escolha de objectos de aprendizagem adequados às características particulares de cada aluno é um aspecto essencial do modelo de adaptação do PCMAT. A plataforma inclui para esse propósito um módulo responsável pela recomendação de objectos de aprendizagem, e um módulo para a pesquisa e recuperação dos mesmos. O módulo de recomendação utiliza lógica Fuzzy para converter determinados atributos do aluno num conjunto de parâmetros que caracterizam o objecto de aprendizagem que idealmente deveria ser apresentado ao aluno. Uma vez que o objecto “ideal” poderá não existir no repositório de objectos de aprendizagem do sistema, esses parâmetros são utilizados pelo módulo de pesquisa e recuperação para procurar e devolver ao módulo de recomendação uma lista com os objectos que mais se assemelham ao objecto “ideal”. A pesquisa é feita numa árvore k-d usando o algoritmo k-vizinhos mais próximos. O modelo de recomendação utiliza a lista devolvida pelo módulo de pesquisa e recuperação para seleccionar o objecto de aprendizagem mais apropriado para o aluno e processa-o para inclusão numa das páginas Web do curso. O presente documento descreve o trabalho desenvolvido no âmbito do projeto PCMAT (PTDS/CED/108339/2008), dando relevância à adaptação de conteúdos.

A calculadora gráfica na promoção da escrita matemática na aprendizagem de modelos contínuos não lineares: um estudo com alunos do 11.º ano de Matemática B

Relatório de estágio de mestrado em Ensino de Matemática no 3.º Ciclo do Ensino Básico e no Ensino Secundário

Le développement d’une séquence d’enseignement/apprentissage basée sur l’histoire de la numération pour des élèves du troisième cycle du primaire

Notre contexte pratique — nous enseignons à des élèves doués de cinquième année suivant le programme international — a grandement influencé la présente recherche. En effet, le Programme primaire international (Organisation du Baccalauréat International, 2007) propose un enseignement par thèmes transdisciplinaires, dont un s’intitulant Où nous nous situons dans l’espace et le temps. Aussi, nos élèves sont tenus de suivre le Programme de formation de l’école québécoise (MÉLS Ministère de l'Éducation du Loisir et du Sport, 2001) avec le développement, notamment, de la compétence Résoudre une situation-problème et l’introduction d’une nouveauté : les repères culturels. Après une revue de la littérature, l’histoire des mathématiques nous semble tout indiquée. Toutefois, il existe peu de ressources pédagogiques pour les enseignants du primaire. Nous proposons donc d’en créer, nous appuyant sur l’approche constructiviste, approche prônée par nos deux programmes d’études (OBI et MÉLS). Nous relevons donc les avantages à intégrer l’histoire des mathématiques pour les élèves (intérêt et motivation accrus, changement dans leur façon de percevoir les mathématiques et amélioration de leurs apprentissages et de leur compréhension des mathématiques). Nous soulignons également les difficultés à introduire une approche historique à l’enseignement des mathématiques et proposons diverses façons de le faire. Puis, les concepts mathématiques à l’étude, à savoir l’arithmétique, et la numération, sont définis et nous voyons leur importance dans le programme de mathématiques du primaire. Nous décrivons ensuite les six systèmes de numération retenus (sumérien, égyptien, babylonien, chinois, romain et maya) ainsi que notre système actuel : le système indo-arabe. Enfin, nous abordons les difficultés que certaines pratiques des enseignants ou des manuels scolaires posent aux élèves en numération. Nous situons ensuite notre étude au sein de la recherche en sciences de l’éducation en nous attardant à la recherche appliquée ou dite pédagogique et plus particulièrement aux apports des recherches menées par des praticiens (un rapprochement entre la recherche et la pratique, une amélioration de l’enseignement et/ou de l’apprentissage, une réflexion de l’intérieur sur la pratique enseignante et une meilleure connaissance du milieu). Aussi, nous exposons les risques de biais qu’il est possible de rencontrer dans une recherche pédagogique, et ce, pour mieux les éviter. Nous enchaînons avec une description de nos outils de collecte de données et rappelons les exigences de la rigueur scientifique. Ce n’est qu’ensuite que nous décrivons notre séquence d’enseignement/apprentissage en détaillant chacune des activités. Ces activités consistent notamment à découvrir comment différents systèmes de numération fonctionnent (à l’aide de feuilles de travail et de notations anciennes), puis comment ces mêmes peuples effectuaient leurs additions et leurs soustractions et finalement, comment ils effectuaient les multiplications et les divisions. Enfin, nous analysons nos données à partir de notre journal de bord quotidien bonifié par les enregistrements vidéo, les affiches des élèves, les réponses aux tests de compréhension et au questionnaire d’appréciation. Notre étude nous amène à conclure à la pertinence de cette séquence pour notre milieu : l’intérêt et la motivation suscités, la perception des mathématiques et les apprentissages réalisés. Nous revenons également sur le constructivisme et une dimension non prévue : le développement de la communication mathématique.

Pedagogia etnomatemática : ações e reflexões em matemática do Ensino Fundamental com um grupo sócio cultural específico

mongst the trends in Mathematics Education, which have as their object a more significant and criticallearning, is the Ethnomathematics. This field of knowledge, still very recent amongst us, besides analyzing an externalist history of the sciences in a search for a relationship between the development of the scientific disciplines and the socio-cultural context, goes beyond this externalism, for it also approaches the intimate relationships betwe_n cognition and culture. In fact, the Ethnomathematics proposes an alternative epistemological approach associated with a wider historiography. It struggles to understand the reality and come to the pedagogical action by means of a cognitive approach with strong cultural basis. But the difficulty of inserting the Ethnomathematics into the educational context is met by resistance from some mathematics educators who seem indifferent to the influence of the culture on the understanding of the mathematics ideas. It was with such concerns in mind that I started this paper that had as object to develop a curricular reorientation pedagogical proposal in mathematics education, at the levei of the 5th grade of the Ensino Fundamental (Elementary School), built from the mathematical knowledge of a vegetable farmers community, 30 km away from the center of Natal/RN, but in accordance with the teaching dimensions of mathematics of the 1 st and 2nd cycles proposed by the Parâmetros Curriculares Nacionais - PCN: Numbers and Operations, Space and Form, Units and Measures, and Information Treatment. To achieve that, I developed pedagogical activities from the mathematical concepts of the vegetable farmers of that community, explained in my dissertation research in the period 2000 through 2002. The pedagogical process was developed from August through Oecember 2007 with 24 students of the 5th Grade of the Ensino Fundamental (Elementary School) of the school of that community. The qualitative analysis of the data was conducted taking into account three categories of students: one made up of students that helped their parents in the work with vegetables. Another one by students whose parents and relatives worked with vegetables, though they did not participate directly of this working process and one third category of students that never worked with vegetables, not to mention their parents, but lived adjacent to that community. From the analyses and results of the data gathered by these three distinct categories of students, I concluded that those students that assisted their parents with the daily work with vegetables solved the problem-situations with understanding, and, sometimes, with enriching contributions to the proposed problems. The other categories of students, in spite of the various field researches to the gardens of that community, before and during the pedagogical activities, did not show the same results as those students/vegetable farmers, but showed interest and motivation in ali activities of the pedagogical process in that period

Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well