Patterns in the city: a mathematics project

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Posters: a tool to foster visual and communication skills through mathematical challenging tasks using a gallery walk

The society is evolving posing continuous challenges that demand the development of a specific set of skills and knowledge of its citizens. These core competencies involve problem solving, creativity, communication, critical thinking, collaboration, that must be incorporated in the teachers’ practice and developed by students. So, teachers must orchestrate productive discussions around the solution of tasks that allow multiple solutions (including visual ones). Students don’t all have the same types of thinking, some are more analytical, others prefer visual approaches. This implies the use of strategies that meet the different types of thinking displayed by the students, confronting them with tasks that challenge them to see outside of the box. We introduced posters to foster students’ learning as a tool that enable visualization and stimulate communication, through a Gallery Walk (GW), as an active learning instructional strategy. The GW allows students to solve a task, collaboratively, given them the opportunity to present, discuss and assess solutions in a poster placed around the classroom, in a similar perspective to that used by artists when they expose their works in a gallery. In this paper we share an ongoing study carried out with future elementary teachers (6-12 years old) where a GW was implemented that aims to characterize the strategies used by the students (future teachers) when solving tasks with multiple solutions, in particular to identify the visual solutions, and to characterize the reaction during their engagement in this GW strategy. An exploratory qualitative approach was adopted, collecting data through written productions (solutions, posters, comments to the posters), observations and a written report. The results showed that students enjoyed this experience, allowed to identify that students privileged visuals solutions of the tasks, and posters are a potential tool for assessment, through peer feedback, and allowed to verify the potentialities of the GW for a more effective teaching and learning of mathematics.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

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

Mobile Math Trails: An Experience in Teacher Training with Mathcitymap

Background: Studies show that the outdoors can be a privileged context to promote positive attitudes towards mathematics. Objectives: We aim to address the following questions: 1) Which pros and cons are pointed out by pre-service teachers of elementary education to the use of MathCityMap (MCM)? 2) How can we characterise the participants’ engagement in a math trail performed with MCM? Design: We followed a qualitative, interpretative methodology. The paradigm choice was because the main goal was to understand the perspective and reactions of the participants to a particular situation. Setting and Participants: The participants were 48 pre-service teachers of elementary education attending the first semester of the 3rd year of an undergraduate course at a public higher education institution in Portugal. Data collection and analysis: Data were collected during the classes of a unit course on Didactics of Mathematics. The pre-service teachers answered a questionnaire, followed by the implementation of a mobile math trail. At the end of this experience, the participants filled out another questionnaire. Participant observation and audio-visual records were also applied. Thus, the analysis involved a qualitative and inductive approach, resorting to content analysis. Results: The pre-service teachers were actively engaged during the math trail, showing interest in solving the tasks, using MCM, and focused on finishing the activity, evidencing persistence and will to be involved in the discussions. We also identified anxiety and frustration related to the outcome of a particular task. Strategies of different nature were used, mainly associated to the level of cognitive demand of the tasks. As pros, they considered the app intuitive, promoting autonomy, spatial orientation and collaborative work and highlighted as cons the inaccessibility to Wi-Fi, younger students’ not having smartphones/tablets, and the limitation of answer formats in task design. Conclusions: Results encourage the use of MCM as a valuable tool in outdoor mathematics education

Early mathematical experiences: the importance of curricular integration

In this paper we explore the implications of some tasks that promote integrated activities in a preschool context. In early years education, children should have meaningful experiences, involving discovery, experimenting and solving challenging problems, based on their interests. All of this should be regarded in an articulated way, intertwining contents, knowledge and processes from different areas. Our main goal is to explore the potential of this approach from were mathematics stands, perceiving the kind of mathematics pre-schoolers should learn, operationalizing it through different types of connections.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

The impact of visualization on functional reasoning: the ability to generalize

Com este estudo pretende-se compreender de que forma alunos da forma??o inicial de professores, do ensino b?sico (alunos 3-12 anos de idade), resolvem problemas que envolvem a generaliza??o de padr?es em contextos visuais, identificando: as estrat?gias que usam; as dificuldades que apresentam; o papel da visualiza??o no seu racioc?nio; e os fatores que influenciam as suas generaliza??es. Considerando os objetivos do estudo, seguimos uma metodologia qualitativa. Os participantes foram 80 alunos da forma??o inicial de professores. Durante as aulas de uma disciplina de Did?tica da Matem?tica, estes alunos resolveram uma sequ?ncia de tarefas que envolviam a generaliza??o de padr?es em contextos figurativos. Os resultados mostraram que os alunos foram capazes de usar diferentes tipos de estrat?gias de generaliza??o, mas tamb?m que algumas dimens?es das tarefas (e.g. tipo de padr?o, a natureza das figuras) podem ter impacto no racioc?nio dos alunos, fazendo com que, em alguns casos, haja uma mudan?a nas estrat?gias utilizadas e a emerg?ncia de dificuldades de tipo diferente. ABSTRACT: With this study we try to understand how pre-service teachers, from basic education (for 3 to 12-year-old students), solve problems involving the generalization of patterns in visual contexts, identifying: the strategies they use; the difficulties they present; the role of visualization in their reasoning; and the factors that influence their generalizations. Considering the aims of this study, we followed a qualitative methodology. The participants were 80 pre-service teachers. During the classes of a Mathematics unit course, these students solved a sequence of tasks involving pattern generalization in figurative contexts. Our results showed that students were able to use different types of generalization strategies, but also that some dimensions of the tasks (e.g. type of pattern, nature of the figures) can have impact in students? reasoning, causing, in some cases, a shift on the strategies used and the emergence of difficulties of different kind.0D1E-4824-1244 | Ana Cristina Coelho Barbosainfo:eu-repo/semantics/publishedVersio

Feedback and written mathematics communication: a pen pal exchange

This paper describes a study that aims to understand and characterize the written communication of future primary education teachers in a context of a pen pal exchange with 3rd grade students (8 years old), in particular the nature of the feedback. We followed a qualitative methodology, where data were collected through observation, written productions (letters) and an interview with the participants. Each future teacher was paired with two students, and four letters were written by the participants over the course of ten weeks. The first letter had the intent of presenting themselves and knowing the recipient. In the following letters the dialogue was continued and the pre-service teachers posed challenging mathematical tasks for the students to solve and for them to give feedback. We focused our analysis in the quality of written communication/feedback, the perceptions of future teachers about the potential of this experience and difficulties experienced. The dynamics of the correspondence exchange allowed the records to be prepared with great commitment. When selecting the tasks, they realized the importance of knowing the curricular guidelines, as well as the contents that the students were addressing. The tasks posed varied from exercises/problems centred on contents addressed by the students. The feedback sent was quite diverse. In some cases, it was not informative, and was even quite superficial; in other situations, the comments provided indicated hints for future action, seeking to promote learning. The exchange of correspondence by letter enabled the sharing of ideas, access to mathematical knowledge, the formulation of tasks, promoting the development of written communication.0D1E-4824-1244 | Ana Cristina Coelho BarbosaN/

The relevance of psychological capital on individual's perceptions of performance, motivation, work-engagement and job-satisfaction

The concept of psychological capital (PsyCap) has been a great focus of interest and curiosity from academics and practitioners. The principal purpose of the present research is to study the relevance of PsyCap and its influence in employees’ attitudes, behaviors and performance. This investigation also aims to understand the importance of an authentic leader (leaders with power to influence their followers and to develop their capabilities) and the impact that the leader’s PsyCap may have on their followers’ dimensions (performance, motivation, work-engagement and job-satisfaction). Data was collected from both Linkedin and from a small company operating in the transportation sector, through a customized survey. The results support the literature showing that: (a) the individual psychological capital has an influence on individuals’ perceptions of performance, motivation, work-engagement and job-satisfaction; (b) the leaders’ PsyCap and the goodwill between the leader and followers may cause some positive impacts on followers’ perceptions of performance, motivation, work-engagement and job-satisfaction; and (c) the leaders’ psychological capital may affect the followers’ level of PsyCap.O conceito de capital psicológico (PsyCap) tem sido alvo de grande atenção e interesse por parte de diversos investigadores. O presente estudo tem como principal objetivo analisar a relevância do PsyCap e a sua respectiva influência nas atitudes, comportamentos e performance dos trabalhadores. Esta investigação tem também interesse em compreender a importância de um líder autêntico (líder com poder para influenciar os seus colaboradores e desenvolvendo as suas capacidades), bem como o impacto que o capital psicológico do líder poderá ter nas principais componentes dos seus colaboradores (performance, motivação, work-engagement e satisfação com o trabalho). Os dados foram recolhidos numa pequena empresa que opera no setor dos transportes e no site Linkedin através de um questionário comum a ambas as amostras. Os resultados encontrados no presente estudo académico coincidem com o que tem sido apresentado na literatura, concluindo assim que: (a) o capital psicológico individual influencia as perceções dos indivíduos relativas à sua performance, motivação, work-engagement e satisfação com o trabalho; (b) o capital psicológico dos líderes e a boa relação estabelecida com os seus colaboradores poderá causar impactes positivos nas perceções dos colaboradores relativas à sua performance, motivação, work-engagement e satisfação com o trabalho; e (c) o capital psicológico dos líderes poderá afetar o nível de PsyCap apresentado pelos seus colaboradores