Learning through patterns: a powerful approach to algebraic thinking

We are engaged in a project named Mathematics and patterns in elementary schools: perspectives and classroom experiences of students and teachers. Our aim is to analyze the impact of an intervention centered on the study of patterns in the learning of mathematics concepts and on the development of communication and development of higher order thinking skills. In this paper we present part of an ongoing research with pre-service teachers concerning the development of teachers’ algebraic thinking, in particular how they move through pattern tasks involving generalization. We will present some of the tasks used in the didactical experience and some preliminary conclusions of its implementation in the mathematics didactics classes of a mathematics elementary teachers’ course of a School of Education

Evaluation of the implementation process of a new mathematics curriculum for Grades 1-­‐9: A discussion of the main results

Recently, a new Mathematics curriculum for basic education (Grades 1-9) has been introduced in the Portuguese educational system. This curriculum was designed to bring together some disperse curricular documents and to substitute the former one that was being used since the early 90s. But, above all, the new curriculum was aimed at providing a more sustained development of students’ mathematical learning based upon recent international recommendations for mathematics teaching and learning. The new curriculum implementation was strongly supported by a special designed programme aimed at providing scientific and pedagogical support to all teachers of Grades 1-9 throughout all the schools of the country. Before its generalization to all basic education schools of the country, the new curriculum had been put into practice by 40 teachers of the different grade levels for a three-year period. These teachers had the opportunity to attend a number of workshops and to share their experiences in a variety of contexts. In fact, they functioned as a true network, working in close collaboration. Besides they were also in touch with the authors of the new curriculum to insure that it was put into practice according to the authors’ proposal. At the same time the Ministry of Education appointed a team of three mathematics educators to conduct a three-year evaluation study of the whole process of implementation of the new curriculum. An overview of this evaluation study will be presented: Besides, teachers’ classroom practices as well as the ideas they shared through their collaborative work, will be also presented and discussed. This discussion will illustrate some of the features of the new curriculum. As a matter of fact, data seem to suggest that some improvements are already visible, namely regarding students’ attitudes and competences and teachers’ practices. Tasks selected and used by the teachers, teaching strategies they used, and students’ work on those tasks will also be presented and analysed

Patterns in the city: a mathematics project

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Isometries and patterns: a creative approach

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Mathematics outside the classroom: examples with pre-service teachers

The classroom is only one of the "homes" where education takes place. The use of non-formal teaching contexts, such as the surrounding environment, constitutes an educational context that can promote positive attitudes among students and an additional motivation for the study of mathematics. Teaching should be enriched with challenging tasks, aimed at developing cognitive abilities, such as problem posing and solving, and also encourage creative thinking. Thus, arise the trails, which consist of a sequence of tasks that the students have to solve, along a preplanned route. In this process, teacher education has a fundamental role, providing (future) teachers with the same experiences they are expected to offer their own students. The trails have great potential for all the students who experience them. Thus, we will discuss some of that potential developed in the context of pre-service teacher training.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

Paper folding for an active learning of mathematics: an experience with preservice teachers

Students are active individuals that build, modify and integrate ideas, interacting with the physical world, materials and other students. Furthermore, not all students learn in the same way, some learn better by seeing, others by listening, others by moving. So, we developed an exploratory study of qualitative nature, with elementary preservice teachers, where the emphasis was on a teaching approach based on problem solving, mathematical communication and collaborative work that involved the manipulation of a sheet of paper. We intended to identify the relevance of this approach with preservice teachers and what were the main difficulties revealed, related to the proposed tasks. Preliminary results allowed to identify several difficulties in terms of mathematical communication and the manipulation of the sheet of paper to solve a problem. However, they reacted positively to the tasks, expressing interest, motivation and recognition of its importance in mathematical learning at any level.Les étudiants sont des individus actifs, qui construisent, modifient et intègrent des idées, en interaction avec le monde physique, des matériaux et d’autres étudiants. En outre, tous n'apprennent pas de la même manière: certains apprennent mieux en regardant, d'autres en écoutant, d'autres en bougeant. Nous avons donc développé une étude exploratoire de nature qualitative, avec des futures instituteurs, promouvant une approche pédagogique basée sur la résolution de problèmes, la communication mathématique et le travail collaboratif impliquant la manipulation d’une feuille de papier. Nous voulions déterminer la pertinence de cette approche pour les futures enseignants et identifier les les principales difficultés révélées face aux tâches proposées. Les résultats préliminaires ont permis d'identifier plusieurs difficultés relevant de la communication mathématique et de la manipulation de la feuille de papier pour résoudre un problème. Cependant, les participants ont réagi positivement aux tâches, exprimant leur intérêt et motivation et reconnaissant leur importance pour l’apprentissage des mathématiques à tous les niveaux.publishe

Preservice teachers' knowledge on elementary geometry concepts

This text is based on a research, which is still in progress, whose main objective is to identify and understand what are the main difficulties of future mathematics teachers of basic education are, regarding their content knowledge in geometry in the context of the curricular unit of Geometry during their undergraduate degree. We chose a qualitative approach in the form of case study, in which data collection was done through observation, interviews, a diverse set of tasks, a diagnostic test and other documents. This paper focuses on the test given to prospective teachers at the beginning of the course. The preliminary analysis of the data points to a weak performance of preservice teachers in the test issues addressing elementary knowledge of Geometr

O pensamento algébrico e a descoberta de padrões na formação de professores

Este texto incide sobre o tema do pensamento algébrico nos primeiros anos de escolaridade ao nível da formação contínua de professores. Na abordagem apresentada o tema dos padrões surge como contexto estruturante para o desenvolvimento do pensamento algébrico. Começa-se por fazer um enquadramento dos referenciais teóricos que fundamentam a adoção de uma proposta didática desenvolvida nesse âmbito, recorrendo em seguida a um estudo empírico que foi desenvolvido, do qual se relata aqui uma parte centrada nas práticas de sala de aula de uma professora do primeiro ciclo em formação, de modo a poder confirmar a eficácia da proposta no ensino e desenvolvimento do pensamento algébrico dos alunos. Os resultados permitem concluir que a professora interiorizou e projetou na sua prática os aspetos essenciais que conduziram ao desenvolvimento do pensamento algébrico nos alunos. O texto termina com algumas conclusões e implicações para a formação de professores.Abstract: This article deals with the subject of algebraic thinking in early years of schooling and at the level of continuous teacher education. In the presented approach, the subject of patterns serves as a structuring context for the development of algebraic thinking. It begins by creating a theoretical frame of reference which substantiates the adoption of a didactic proposal developed in this field. It then uses an empirical study that was carried out, of which reference is made here to a part focusing on the classroom practices of a third cycle teacher in training, with a view to confirming the effectiveness of the proposal in the teaching and development of algebraic thinking in the pupils. The outcomes allow us to conclude that the teacher had absorbed and incorporated in her practice the essential aspects leading to the development of algebraic thinking in her pupils. The article ends with some conclusions and implications for teacher education.Résumé: Ce texte met l'accent sur le thème de la pensée algébrique dans les premières années de scolarisation au niveau de la formation continue des enseignants. Dans l'approche présentée, le thème des patrons apparaît comme un contexte structurant pour le développement de la pensée algébrique. Nous commençons par présenter les cadres théoriques de référence qui sous-tendent l'adoption d'une proposition didactique développée dans ce contexte, puis nous exposons une étude empirique qui a été développée , et dont nous rapportons ici la partie centrée sur les pratiques de salle de classe d'un enseignant du premier cycle en formation , afin de pouvoir confirmer l'efficacité de la proposition pour l’enseignement et le développement de la pensée algébrique des élèves. Les résultats permettent de conclure que la professeure a intériorisé et projeté dans sa pratique les aspects essentiels qui ont conduit au développement de la pensée algébrique chez les élèves. Le texte se termine par quelques conclusions et implications pour la formation des professeurs