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College-bound young people and first-year engineering students should be informed about the unique opportunity for meaningful public service available through a career in civil engineering. Civil engineering students ought to be made aware of the distinction between the engineer and technician so as to better prepare them for the full range of functions and responsibilities awaiting them in their chosen careers. The formal education of civil engineers can be effectively enhanced by the integration of practitioners into the teaching program. Effective oral, written, graphic, and mathematical communication should be given increased emphasis throughout the civil engineering curriculum. Civil engineering practitioners and educators should continuously strive to narrow the gap between what they say and what they do, thereby providing worthy examples for students and young civil engineers.

In Malaysia and also elsewhere in the world the demands for graduates who have employability skills such as ability to think critically, solve problems and can communicate are highly sought in the workplace. In the early 2006, the development of such skills was recognized as integral goals of undergraduate education at Universiti Teknologi Malaysia. Since then rigorous efforts have been made to inculcate these skills amongst the undergraduates. In this paper, we will share some of our experiences in coping with the challenges of changing our teaching practices to accommodate this quest though focusing on communication. For mathematics learning to occur, we believed that students should participate actively in the knowledge construction and be able to take charge of their own learning. Taking these aspects into consideration, we had developed a framework of active learning and used it to guide our instruction in engineering mathematics at UTM. Here we will discuss the strategies that we had designed and employed in engaging students with the subject matter as well as to initiate and support student's thinking and communication in the language of mathematics. Some student's responses that gave indications of their struggle, progress and growth encountered in the research implementation will also be presented.

Relatório de Estágio apresentado à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Ensino do 1º e 2º ciclo do Ensino Básico O presente relatório é mais um instrumento de avaliação da unidade curricular de Prática de Ensino Supervisionada II (PES II), no Mestrado em Ensino do 1.º e do 2.º Ciclo do Ensino Básico e surge na sequência de oito semanas de intervenção pedagógica numa turma do 2.º ano do 1.º Ciclo do Ensino Básico, numa escola de Lisboa. Durante a intervenção, realizou-se uma investigação centrada nas estratégias que os professores podem usar para fomentar a comunicação matemática na sala de aula, com a finalidade de analisar o impacto que estas tinham na evolução da capacidade dos alunos se expressarem matematicamente. Assim sendo, este relatório tem como principal objetivo apresentar todo o percurso da intervenção, com especial destaque para o tema investigado. Através de observação participante e não participante e de análise documental foi possível caracterizar a turma, avaliar os seus crescimentos e tirar conclusões relativamente às perguntas investigadas. As atividades foram planeadas com base nas estratégias de implementação de rotinas, implementação de atividades práticas, implementação de atividades que promoveram a comunicação oral (enfoque na matemática), implementação de trabalho cooperativo e na exploração de conteúdos promovendo a interdisciplinaridade. O balanço é bastante positivo, no que respeita à avaliação das aprendizagens dos alunos e à avaliação dos objetivos previstos para a intervenção. A investigação permitiu concluir que as estratégias implementadas para fomentar a comunicação matemática devem ser cuidadosa e intencionalmente orientadas pelo professor, o qual deve ter um papel de questionador e de moderador da discussão matemática. Os alunos são levados a esclarecer os seus conhecimentos e a contribuir para o esclarecimento das ideias dos pares, refletindo, o que contribui de forma positiva para o desenvolvimento do seu raciocínio matemático. No entanto estas estratégias devem ser continuadas senão os alunos tendencionalmente deixam de participar ativamente nas tarefas propostas para este efeito. ABSTRACT The final report of supervised teaching practice is part of the course of Supervised Teaching Practice II for the Masters in Teaching 1st and 2nd Cycle. This report was developed during eight weeks of teaching practice in a 2nd year class in a primary school in Lisbon. During the intervention it was performed an investigation centred in the strategies that teachers could use to implement mathematical communication in the class room, with the goal of analysing the impact of the strategies in the evolution of the capacity of the pupils express themselves. Therefore, the major goal of this report is to show the entire route of intervention, with special emphasis on the theme investigated. Through the participant observation and non-participant as also the documentary analysis, it was possible to characterize the class, evaluate their growth and draw conclusions concerning the questions investigated. The activities were planned on the basis of strategies for implementing routines, implementation of practical activities, implementation of activities that promote the development of oral communication (focus on mathematics), implementation of cooperative work and the development of content promoting interdisciplinarity. The balance is very positive, regarding the appreciation of the learning of the students and the evaluation of the objectives established for the intervention. The investigation concluded that the strategies implemented to promote mathematical communication, should be careful and intentionally oriented by the teacher, which should have a role of inquirer and moderator of mathematical discussions. The students are taken to clarify their knowledge and to contribute to the clarification of ideas of peers, reflecting, what contributes positively to the development of their mathematical thinking. However, these strategies should be continued because students tend to be cease to participate actively in tasks proposed for this purpose

This paper discusses the difficulties, reactions and conceptions of future teachers in relation to tasks that privilege different forms of communication in visual contexts. The tasks proposed focus on seeing the information directly or listening to the information without seeing. This research is of qualitative nature and was developed with forty-five future teachers of basic education. Data emerged from classroom observations, a questionnaire, written productions and photographic registers of students solving the tasks. The results show that students reacted positively to the proposed tasks, manifesting interest and motivation despite of some difficulties revealed in communication. They recognized the potential of the tasks to develop/improve mathematical knowledge.

Mestrado (PES II), Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico, 1 de Julho de 2014, Universidade dos Açores. No presente trabalho, procurou-se perceber de que modo a utilização de uma metodologia baseada na resolução de problemas, com o recurso ao cálculo mental, ao raciocínio e à comunicação matemática, potencia a aprendizagem da Matemática no Pré-Escolar e no 1.º Ciclo do Ensino Básico. O gosto do mestrando pela Matemática foi o ponto de partida, mas a responsabilidade de um futuro professor pelo ensino desta disciplina aos seus alunos, despertando neles o gosto pelas aprendizagens que ela promove, foi o verdadeiro impulsionador de toda a ação que este trabalho espelha. As práticas aqui analisadas e a reflexão que delas decorre constituem, muito possivelmente, o embrião de uma forma de estar na profissão docente que obriga o professor a um olhar atento à sua ação e a um reajuste constante das suas práticas em proveito do desenvolvimento dos seus alunos. As práticas realizaram-se em pequenos períodos ao longo do ano de 2013, com crianças do Pré-Escolar e do 1º. Ciclo do Ensino Básico. A sua análise e reflexão foi sendo feita ao longo desse tempo, tendo amadurecido e tomado forma nos últimos quatro meses. O resultado é o trabalho que aqui se apresenta. Trata-se, pois, de um documento que seleciona práticas levadas a cabo pelo estagiário com a finalidade de, a partir de uma reflexão aprofundada, construir conhecimento sobre o ser educador/professor que ensina Matemática. Essa reflexão deixa transparecer o potencial didáctico resultante do entrecruzar das tarefas de resolução de problemas com a comunicação e o raciocínio matemáticos, destacando igualmente os benefícios daí decorrentes para o desenvolvimento da autonomia das crianças. Focam-se, ainda, tarefas promotoras do desenvolvimento do cálculo mental e analisam-se as suas potencialidades na resolução de problemas. ABSTRACT: The present study aims at providing a broader understanding of how a problem-solving methodology, using mental arithmetic, mathematical reasoning and communication, promotes mathematics learning in Preschool and Primary school. The joy and beauty of mathematics was the starting point of this study; however, the real catalyst was without a doubt the responsibility a future teacher has to awaken in his/her students a taste for mathematics. The practice described and analysed in the study and subsequent reflection may be the basis for the development of a reflexive teacher, as it makes him/her be attentive to what goes on in the classroom in order to make the necessary adjustments to promote effective learning. This study was carried out in 2013 and was performed with children in Preschool and Primary School during short-periods of time. The analysis and reflection on the teaching practice have been done throughout this timeframe, however, only in the last four months have they culminated in the current study, which presents a student teacher’s practice, looked at from a distance, with the aim of obtaining a clearer conception of what it means to be a teacher who teaches Mathematics. With this study, it is possible to give a glimpse of the connection between problem-solving tasks, mathematical reasoning and communication, and its potential for developing students’ autonomy. The potential of using tasks for promoting mental arithmetic in problem-solving is also highlighted.

Dissertação apresentado à Escola Superior de Educação do Instituto Politécnico de Castelo Branco para cumprimento dos requisitos necessários à obtenção do grau de Mestre em Educação Pré-Escolar e Ensino do 1º Ciclo do Ensino Básico. Submitted by iria pinto (iria@ipcb.pt) on 2014-01-08T15:19:28Z No. of bitstreams: 1 relatório tese.pdf: 11932537 bytes, checksum: a00de6a2eadf2328a65140d38b3a9f2d (MD5) Approved for entry into archive by Maria Eduarda Pereira Rodrigues (erodrigues@ipcb.pt) on 2014-01-08T16:25:21Z (GMT) No. of bitstreams: 1 relatório tese.pdf: 11932537 bytes, checksum: a00de6a2eadf2328a65140d38b3a9f2d (MD5) Made available in DSpace on 2014-01-10T10:30:26Z (GMT). No. of bitstreams: 1 relatório tese.pdf: 11932537 bytes, checksum: a00de6a2eadf2328a65140d38b3a9f2d (MD5)

Komunikasi matematis merupakan salah satu hal penting dalam menyelesaikan masalah pada studi PISA. Komunikasi matematis adalah kemampuan mengekspresikan ide-ide matematika secara koheren kepada teman, guru, dan lainnya melalui bahasa lisan maupun tulisan yang disertai dengan penjelasan dan justifikasi. Karena pentingnya kemampuan komunikasi yang dimiliki oleh siswa, maka muncul gagasan untuk menganalisis tingkat kemampuan komunikasi matematis siswa dalam menyelesaikan soal PISA konten space dan shape. Tujuan penelitian ini adalah untuk mendeskripsikan kemampuan komunikasi matematis siswa dalam menyelesaikan soal PISA konten space and shape. Penelitian ini menggunakan pendekatan kualitatif, dengan jenis penelitian deskriptif. Hasil penelitian ini menunjukkan bahwa 1) siswa dengan kemampuan matematika tinggi memiliki kemampuan komunikasi matematis sangat baik dengan hampir memenuhi seluruh indikator; 2) siswa yang memiliki kemampuan matematika sedang memiliki komunikasi matematis baik dengan memenuhi indikator hingga dapat menjelaskan suatu permasalahan dengan baik. Kata Kunci: komunikasi matematis, Soal PISA, space and shape Abstract Mathematical communication is one of the important things in solving problems on the PISA study. Mathematical communication is the ability to express mathematical ideas coherently to friends, teachers, and others through spoken and written language accompanied by explanations and justifications. Because of the importance of communication skills possessed by students, then the idea arises to analyze the level of mathematical communication skills of students in solving PISA questions of space and shape content. The purpose of this study is to describe the mathematical communication skills of students in solving PISA questions on space and shape content. This research uses a qualitative approach, with descriptive research type. The results of this study indicate that 1) students with high mathematical abilities have excellent mathematical communication skills with almost all the indicators; 2) students who have mathematical abilities are having good mathematical communication by meeting the indicators so that they can explain a problem well. Keyword: Mathematical communication, PISA question, space and shape

Dissertação de Mestrado em Didáctica da Matemática e das Ciências apresentada na Escola Superior de Educação do Instituto Politécnico de Viana do Castelo A aprendizagem da Matemática necessita que os alunos trabalhem de diversas formas tanto na escola como em casa. O TPC pode ser entendido como um meio de ajudar os alunos a reforçar e a desenvolver uma atitude positiva face à aprendizagem realizada (Cooper, 2001) e de aumentar o envolvimento da família nas aprendizagens escolares das suas crianças (Epstein, 2001; Paiva & Gaspar, 2005). A presente dissertação centra-se no estudo do envolvimento dos pais no TPC de matemática e no seu contributo para o desenvolvimento da comunicação matemática dos alunos. Para orientar o estudo definiram-se várias questões: a) como se carateriza o envolvimento dos pais participantes no TPC de matemática?, b) como se descreve e como evolui a comunicação matemática de alunos no início da escolaridade?, c) como se carateriza a motivação dos alunos quanto ao TPC de matemática proposto?, d) que dificuldades manifestam os alunos na resolução de tarefas matemáticas (TPC) e como é que se podem superar?, e) que apreciações fazem estes pais do seu envolvimento no TPC de matemática e que conceções manifestam sobre o ensino e aprendizagem da Matemática? O estudo realizado situa-se no paradigma de investigação qualitativa, optando-se pelo formato de estudo de caso longitudinal, tendo sido realizados três estudos de caso. Os participantes foram três alunas e as respetivas mães. Os dados foram recolhidos durante a frequência do 1º ano e 2º anos de escolaridade com recurso a tarefas, entrevistas semiestruturadas, observação participante, gravação áudio e análise documental. A análise dos dados permitiu evidenciar uma associação positiva entre o envolvimento parental e o desempenho académico das crianças. Registaram-se evoluções na qualidade da comunicação matemática de todas as alunas. As mães mostraram interesse e vontade em motivar as filhas para a resolução de tarefas matemáticas (TPC) e as alunas sentiram-se mais motivadas para o realizar com a contribuição do envolvimento das mães. As alunas manifestaram dificuldades na resolução dessas tarefas mas, ao longo do tempo, foram sendo superadas. Com este tipo de envolvimento, as mães reconheceram que construíram possibilidades das suas filhas aumentarem os seus saberes e competências matemáticas e admitiram que contribuíram e podem continuar a contribuir para o desenvolvimento da comunicação matemática das alunas, pretendendo continuar a envolver-se no TPC das suas filhas. Learning mathematics requires that students work in different ways both at school and at home. Homework can be understood as a means of helping students to strengthen and develop a positive attitude towards learning (Cooper, 2001) and to increase family involvement in their childrens’ school learning (Epstein, 2001; Paiva & Gaspar, 2005). This dissertation focuses on the study of parental involvement in math homework and its contribution to the development of students' mathematical communication. The following research questions were defined: a) how can be characterized the involvement of parents in the math homework?, b) how can be described and how evolves the mathematical communication of students at the beginning of school?, c) how can be characterized student’s motivation at the assigned math homework?, d) how did students overcome difficulties in solving mathematical tasks (homework)?, e) how did parents assessed their involvement in math homework and what are their perceptions about teaching and learning mathematics? Within a qualitative approach, the present study adopted a longitudinal case study methodology, having conducted three case studies. Participants were three students and their mothers. Data were collected during the 1st year and 2nd year of schooling, using tasks, interviews, participant observation, audio recording and document analysis. Data analysis evidenced a positive association between parental involvement and childrens’ academic performance. It was evidenced a positive evolution in the quality of mathematical communication for all students. The mothers expressed interest and willingness to motivate their children in solving mathematical tasks at homework, and students felt more motivated to perform with the contribution of their mothers’ involvement. Students expressed difficulties in solving these tasks, but they were overcome. Mothers recognized that this type of involvement enlarged the possibilities for their daughters to increase their mathematical knowledge and skills. They also admitted that they may have contributed and will continue to contribute to the development of students' mathematical communication, and were intending to continue engaging in their daughters’ homework.