O conhecimento profissional do professor e as investigações matemáticas na sala de aula: Um estudo nos 1º e 2º ciclos do ensino básico

Este estudo tem como objetivo contribuir para a compreensão do conhecimento profissional do professor de Matemática envolvido no desenvolvimento de tarefas de investigação na sala de aula, focando-se em quatro questões orientadoras: (i) como é que os professores colocam em prática as tarefas de investigação, considerando a planificação e condução das aulas? (ii) que dificuldades sentem os professores no desenvolvimento de tarefas de investigação na sala de aula? (iii) como é que o conhecimento didático dos professores influencia o desenvolvimento de tarefas de investigação? (iv) como é que o conhecimento didático dos professores é influenciado pelo desenvolvimento de tarefas de investigação? A fundamentação teórica assenta sobre as duas grandes temáticas do estudo: o conhecimento profissional do professor, sendo discutida a sua natureza, estrutura e conteúdo, e as tarefas de investigação, das quais se aprofunda a natureza e a utilização em sala de aula. Apresenta-se ainda investigação empírica referente ao conhecimento profissional do professor envolvido no desenvolvimento de tarefas de investigação. O estudo assumiu uma abordagem interpretativa, concretizando-se através dois estudos de caso, um de uma professora de 1. ° Ciclo e outro de um professor de Matemática do 2. ° Ciclo do Ensino Básico. Estes professores trabalharam em colaboração com a investigadora sobre tarefas de investigação, que até aí não conheciam, planificando, lecionado e refletindo acerca de um conjunto de aulas com tarefas desta natureza. Foram recolhidos dados durante as sessões de trabalho referidas, bem como nas aulas e ainda em entrevistas realizadas a cada um dos professores. Uma leitura transversal dos casos permite retirar algumas conclusões. A possibilidade de enquadramento nos conteúdos programáticos parece ser o principal critério de seleção das tarefas por parte dos professores. Na planificação, é a inventariação dos conteúdos que a tarefa mobiliza a principal prioridade, na busca da redução do grau de incerteza relacionado com as eventuais reações dos alunos. Quanto à condução de tarefas de investigação, a fase de introdução foi a mais breve, tendo servido o objetivo de conduzir à compreensão do propósito da tarefa por parte dos alunos e também reforçar alguns aspetos metodológicos do trabalho investigativo. A fase de desenvolvimento da tarefa foi aquela a que o professor de 2. ° Ciclo atribuiu maior importância, embora também valorizada pela professora de 1. ° Ciclo. Aqui, os professores consideram que o seu papel é acompanhar e orientar o trabalho dos alunos, ajudando a ultrapassar possíveis obstáculos, mantendo uma atitude questionadora. Quanto à fase de discussão, a grande preocupação dos professores é garantir a compreensão das ideias apresentadas pelos alunos. No entanto, existem duas estratégias distintas: enquanto a professora de 1. ° Ciclo, que muito valorizou esta fase, estimula a interação aluno-aluno, atribuindo-lhes a responsabilidade de validar/rejeitar as conjeturas apresentadas, o professor de 2. ° Ciclo centra em si toda esta fase, assumindo a responsabilidade de corrigir as ideias apresentadas. O desenvolvimento de tarefas de investigação é influenciado pelo conhecimento didático, revelando-se determinantes o conhecimento dos alunos e da forma como aprendem e o conhecimento do processo instrucional. O desenvolvimento de tarefas de investigação influencia várias componentes do conhecimento didático do professor, permitindo-lhe fortalecer o seu conhecimento matemático, desenvolver um conhecimento mais completo dos alunos e da forma como aprendem. Por último, a prática letiva com tarefas de investigação fornece ao professor dados importantes de como planificar e conduzir tarefas de natureza aberta, de forma a tirar o máximo partido das suas potencialidades. ABSTRACT: This study’s aim is to contribute to the understanding of the professional knowledge of the Maths teacher, involved in the development of investigative tasks in the classroom, focusing four guiding questions: (i) how do teachers give practical way to the investigative tasks, having in mind the lesson plans and lesson execution? (ii) Which difficulties do the teachers face when developing the investigative tasks in the classroom? (iii) How does the teachers' didactical knowledge influence the development of the investigative tasks? (iv) How is the teachers' didactical knowledge influenced by the development of the investigative tasks? The theorical framework is based on two broad themes of the study: teacher's professional knowledge (discussing its nature, structure and contents) and the investigative tasks (whose nature and use in the classroom is deepened). Besides, empirical research in what concerns to the professional knowledge of the teacher involved in the development of investigative tasks is also added. The study assumed an interpretative approach, materialised through two case studies, one of a primary school teacher, the other of a preparatory school Maths teacher. The teachers worked in cooperation with the researcher on the investigative tasks, which, until then, they weren't familiar with, planning, teaching and thinking about a set of lessons with tasks of this kind. Data were collected during the work meetings, as well as in the lessons and also in interviews to each one of the teachers. A transversal appreciation of the cases allows us to draw some conclusions. The possibility of integrating the programmatic contents seems to be the main criteria for the selection of the tasks by the teachers. ln the planning, the main priority of the task is the inventory of contents, aiming to reduce the level of uncertainty in what concerns to eventual reactions of the students. ln what concerns to the conduction of the investigative tasks, the introduction phase was the shortest, fulfilling the aim of leading to the understanding of the proposal of the task by the students and also to reinforce some methodological aspects of the investigative work. The task's development phase was the one the preparatory school teacher dedicated more importance, though it was also valued by the primary school teacher. ln this aspect, the teachers consider that their role is to follow and lead the students’ work, helping them to overtake eventual obstacles, keeping the questioning attitude. ln what concerns the discussion phase, the big concern of the teachers is to reassure the understanding of the ideas presented by the students. However, there are two different strategies: while the primary school teacher, who really valued this phase, stimulates the student-student interaction, giving them the responsibility of validating/rejecting the presented conjectures; the preparatory school teacher centers around himself all this phase, assuming the responsibilities of correcting the presented ideas. The development of the investigative tasks is influenced by the didactical knowledge, and it is determinant the knowledge about the students and about the way they learn and the instructional knowledge. The development of the investigative tasks influences several components of the didactical knowledge of the teacher, allowing him/her to reinforce his mathematical knowledge, developing a more complete knowledge about the students and the way they learn. Finally, the lessons execution with investigative tasks provides the teacher with important data about how to plan and conduct open nature tasks, in order to take the biggest advantage of their potential.

The impact of personal background and school contextual factors on academic competence and mental health functioning across the primary-secondary school transition

Students negotiate the transition to secondary school in different ways. While some thrive on the opportunity, others are challenged. A prospective longitudinal design was used to determine the contribution of personal background and school contextual factors on academic competence (AC) and mental health functioning (MHF) of 266 students, 6-months before and after the transition to secondary school. Data from 197 typically developing students and 69 students with a disability were analysed using hierarchical linear regression modelling. Both in primary and secondary school, students with a disability and from socially disadvantaged backgrounds gained poorer scores for AC and MHF than their typically developing and more affluent counterparts. Students who attended independent and mid-range sized primary schools had the highest concurrent AC. Those from independent primary schools had the lowest MHF. The primary school organisational model significantly influenced post-transition AC scores; with students from Kindergarten--Year 7 schools reporting the lowest scores, while those from the Kindergarten--Year 12 structure without middle school having the highest scores. Attending a school which used the Kindergarten--Year 12 with middle school structure was associated with a reduction in AC scores across the transition. Personal background factors accounted for the majority of the variability in post-transition AC and MHF. The contribution of school contextual factors was relatively minor. There is a potential opportunity for schools to provide support to disadvantaged students before the transition to secondary school, as they continue to be at a disadvantage after the transition.

ESL teacher profiles of ICT integration in their classroom practices and assessment activities : a portrait viewed through the lens of some Quebec teachers’ social representations

Abstract : Information and communication technologies (ICTs, henceforth) have become ubiquitous in our society. The plethora of devices competing with the computer, from iPads to the Interactive whiteboard, just to name a few, has provided teachers and students alike with the ability to communicate and access information with unprecedented accessibility and speed. It is only logical that schools reflect these changes given that their purpose is to prepare students for the future. Surprisingly enough, research indicates that ICT integration into teaching activities is still marginal. Many elementary and secondary schoolteachers are not making effective use of ICTs in their teaching activities as well as in their assessment practices. The purpose of the current study is a) to describe Quebec ESL teachers’ profiles of using ICTs in their daily teaching activities; b) to describe teachers’ ICT integration and assessment practices; and c) to describe teachers’ social representations regarding the utility and relevance of ICT use in their daily teaching activities and assessment practices. In order to attain our objectives, we based our theoretical framework, principally, on the social representations (SR, henceforth) theory and we defined most related constructs which were deemed fundamental to the current thesis. We also collected data from 28 ESL elementary and secondary school teachers working in public and private sectors. The interview guide used to that end included a range of items to elicit teachers’ SR in terms of ICT daily use in teaching activities as well as in assessment practices. In addition, we carried out our data analyses from a textual statistics perspective, a particular mode of content analysis, in order to extract the indicators underlying teachers’ representations of the teachers. The findings suggest that although almost all participants use a wide range of ICT tools in their practices, ICT implementation is seemingly not exploited to its fullest potential and, correspondingly, is likely to produce limited effects on students’ learning. Moreover, none of the interviewees claim that they use ICTs in their assessment practices and they still hold to the traditional paper-based assessment (PBA, henceforth) approach of assessing students’ learning. Teachers’ common discourse reveals a gap between the positive standpoint with regards to ICT integration, on the one hand, and the actual uses of instructional technology, on the other. These results are useful for better understanding the way ESL teachers in Quebec currently view their use of ICTs, particularly for evaluation purposes. In fact, they provide a starting place for reconsidering the implementation of ICTs in elementary and secondary schools. They may also be useful to open up avenues for the development of a future research program in this regard.

Talent in first, second, and third graders: teachers’ perspectives vs. educational reality

The article addresses the subject of talent by emphasizing different conceptions about talent and by proposing an approach to this theme, from the point of view of talent in boys and girls. It also provides an analysis of research conducted with first, second, and third graders in public and private schools of the Costa Rican Education System. Using questionnaires and observations of the dynamics of the classroom as measurement tools, this study contrasts teachers` expectations about their students’ talent with the reality of the class environment, pointing out the existing abyss between teachers’ beliefs and their professional practices.

Proposal for Labor Market Integration of Teachers in Contexts of High Social Vulnerability

The purpose of this paper is to share a proposal for teacher’s labor market integration in contexts of high social5 vulnerability. This paper is the result of a research conducted in a priority attention primary school6 of the central canton of Heredia7. It explored the labor market integration process of teachers, considering the community, family and student reality of a population social risk. The research that supports this proposal is based on a qualitative approach, since the diagnosis process is not intended to provide answers that could be commonly applied to other education centers in similar contexts, but to make an exploratory approach of teachers’ reality and their integration process into education institutions of high social vulnerability. Therefore, although this paper intends to share this experience, it does not aim to unify integration practices, but to be an input in carrying out similar processes.  (5) The concept of high social vulnerability is understood based on Sojo’s approach (2003), which defines it as marginal urban communities in areas considered by the Costa Rican government as priority areas with the greatest social, economic backwardness in the country, and high rates of violence, leisure, unemployment and drug addiction. (6) Translator’s note: The Costa Rican education system is composed of primary education (1st-6th grade) and secondary education (7th-11th grade). (7)A public primary school in the circuit 02 of the Province of Heredia.

A Low Cost Controller Board for Teaching Robotics

This paper presents the Smarty Board; a new micro-controller board designed specifically for the robotics teaching needs of Australian schools. The primary motivation for this work was the lack of commercially available and cheap controller boards that would have all their components including interfaces on a single board. Having a single board simplifies the construction of programmable robots that can be used as platforms for teaching and learning robotics. Reducing the cost of the board as much as possible was one of the main design objectives. The target user groups for this device are the secondary and tertiary students, and hobbyists. Previous studies have shown that equipment cost is one of the major obstacles for teaching robotics in Australia. The new controller board was demonstrated at high-school seminars. In these demonstrations the new controller board was used for controlling two robots that we built. These robots are available as kits. Given the strong demand from high-school teachers, new kits will be developed for the next robotic Olympiad to be held in Australia in 2006.

Secondary teachers’ conceptions of teaching and learning

This paper presents a phenomenographic analysis of the conceptions of teaching and learning held by a sample of 16 secondary school teachers in two Australian schools. It provides descriptions of four categories, derived from pooled data, of the ways in which these teachers thought about teaching and about learning, their teaching strategies, and their focus on student or content. The categories for teaching and learning are described with each teacher allocated to the category most typical of their conceptions of teaching and of learning. The lack of congruence, in some cases, between the conceptions of teaching and of learning held by these teachers is discussed.

Students' and teachers' perceptions of adolescents' problems and coping strategies

In an investigation of the problems and coping strategies of Australian high school students, comparisons were made between the responses of 1664 students enrolled in years 8 to 12 in 1988, 1620 students enrolled in the same year levels in 1993, and 178 high school teachers in 1993. The subjects completed the High School Stressors Scale and the Adolescent Coping Strategies Scale. Data analyses using MANOVAs, ANOVAs, and t- tests revealed close similarities between the responses of the 1993 students and those of the 1988 students, but a considerable amount of incongruence between the responses of the students and those of the teachers. In particular, the teachers generally seemed to regard their students' problems as being more serious than was acknowledged by the students, and the teachers generally seemed to project a less positive view of adolescents' coping strategies than did the students. These discrepancies are discussed in terms of the different orientations that students and teachers bring to the student- teacher relationship. It is suggested that teachers and counsellors need to take cognisance of the differences between adolescents' perspectives and their own if they are going to be effective in assisting students to develop positive coping strategies and in creating more positive learning environments.

Transition into high school : a phenomenological study

Transition is a process of moving from the known to the unknown (Green, 1997) and transition from primary school to high school can be described in this way. In Australia, there is a two tiered system of primary and secondary schooling operating where school students typically undergo at least two transitions. Firstly, when they leave home to attend pre-school/primary school; and secondly, when they leave primary school to enter secondary school. Potentially some students may experience up to four transitions: from home to kindergarten to pre-school to primary school to secondary school while for a smaller number of students who attend P-12 schools, there may be only one transition: from home to preschool.

The future face of school guidance and counselling : what will it look like in 25 years?

The author undertook a qualitative and quantitative survey of 130 guidance counsellors and primary school principles focusing on perceptions of what school guidance and counselling will be like in 25 years. Generally the participants held similar beliefs and were bullish about employment prospects.

An investigation of the social learning and symbolic interaction models for the development of self-concepts and self-esteem

Two studies were conducted to investigate empirical support for two models relating to the development of self-concepts and self-esteem in upper-primary school children. The first study investigated the social learning model by examining the relationship between mothers' and fathers' self-reported self-concepts and self-esteem and the self-reported self-concepts and self-esteem of their children. The second study investigated the symbolic interaction model by examining the relationship between children's perception of the frequency of positive and negative statements made by parents and their self-reported self-concepts and self-esteem. The results of these studies suggested that what parents say to their children and how they interact with them is more closely related to their children's self-perceptions than the role of modelling parental attitudes and behaviours. The findings highlight the benefits of parents talking positively to their children.

Re-imagining school through young people’s drawings

Children’s drawings provide rich qualitative data (Walker, 2008) and “valuable information for the assessment of children's environmental perceptions” (Barraza, 1999, p. 49). They are the primary data source being used to re-imagine school from a student perspective (Schratz & Steiner-Löffler, 1998) in a research project being carried out with primary school students in Queensland, Australia. This paper will report on the progress of this project which addresses a mostly unmet need for students’ perspectives to be included in school design (Rudduck & Flutter, 2004). Grade 5/6 students in a number of primary schools have been invited to submit annotated drawings with up to 200 words of text illustrating their ideal educational spaces. Using purpose-designed analytical tools, the submissions will be compared across student backgrounds and school types to obtain a better understanding of the needs and educational desires of young people in relation to changing learning environments. The findings will inform consideration of the design and use of educational spaces with all work exhibited through a dedicated website. The term ‘educational spaces’ avoids restrictive notions of what the concept of ‘school’ means, referring to any real or virtual space in which teaching and learning may occur or, as Ferguson and Seddon (2007) have referred to it, “the shifting imagery of education” that includes red brick schools and dispersed learning networks. The theoretical framework for this study is grounded in the work of Greene (1995) and Wright-Mills (2001) who cited the deployment of critical and empathic imagination in addressing education reform.

Mainstreaming sustainability into pre-service teacher edcuation in Australia

There is a growing interest in and support for education for sustainability in Australian schools. Australian Government schemes such as the Australian Sustainable Schools Initiative (AuSSI), along with strategies such as Educating for a Sustainable Future: A National Environmental Education Statement for Australian Schools(NEES(Australian Government and Curriculum Corporation (2005) and Living Sustainably: The Australian Government’s National Action Plan for Education for Sustainability (Australian Government 2009), recognise the need and offer support for education for sustainability in Australian schools. The number of schools that have engaged with AuSSI indicates that this interest also exists within Australian schools. Despite this, recent research indicates that pre-service teacher education institutions and programs are not doing all they can to prepare teachers for teaching education for sustainability or for working within sustainable schools. The education of school teachers plays a vital role in achieving changes in teaching and learning in schools. Indeed, the professional development of teachers in education for sustainability has been identified as ‘the priority of priorities’. Much has been written about the need to ‘reorient teacher education towards sustainability’. Teacher education is seen as a key strategy that is yet to be effectively utilised to embed education for sustainability in schools. Mainstreaming sustainability in Australian schools will not be achieved without the preparation of teachers for this task. The Mainstreaming Sustainability model piloted in this study seeks to engage a range of stakeholder organisations and key agents of change within a system to all work simultaneously to bring about a change, such as the mainstreaming of sustainability. The model is premised on the understanding that sustainability will be mainstreamed within teacher education if there is engagement with key agents of change across the wider teacher education system and if the key agents of change are ‘deeply’ involved in making the change. The model thus seeks to marry broad engagement across a system with the active participation of stakeholders within that system. Such a systemic approach is a way of bringing together diverse viewpoints to make sense of an issue and harness that shared interpretation to define boundaries, roles and relationships leading to a better defined problem that can be acted upon more effectively. Like action research, the systemic approach is also concerned with modelling change and seeking plausible solutions through collaboration between stakeholders. This is important in ensuring that outcomes are useful to the researchers/stakeholders and the system being researched as it creates partnerships and commitments to the outcomes by stakeholder participants. The study reported on here examines whether the ‘Mainstreaming Sustainability’ model might be effective as a means to mainstream sustainability in pre-service teacher education. This model, developed in an earlier study, was piloted in the Queensland teacher education system in order to examine its effectiveness in creating organisational and systemic change. The pilot project in Queensland achieved a number of outcomes. The project: • provided useful insights into the effectiveness of the Mainstreaming Sustainability model in bringing about change while also building research capacity within the system • developed capacities within the teacher education community: o developing competencies in education for sustainability o establishing more effective interactions between decision-makers and other stakeholders o establishing a community of inquiry • changed teaching and learning approaches used in participating teacher education institutions through: o curriculum and resource development o the adoption of education for sustainability teaching and learning processes o the development of institutional policies • improved networks within the teacher education system through: o identifying key agents of change within the system o developing new, and building on existing, partnerships between schools, teacher education institutions and government agencies • engaged relevant stakeholders such as government agencies and non-government organisations to understand and support the change Our findings indicate that the Mainstreaming Sustainability model is able to facilitate organisational and systemic change – over time – if: • the individuals involved have the conceptual and personal capacities needed to facilitate change, that is, to be a key agent of change • stakeholders are engaged as participants in the process of change, not simply as ‘interested parties’ • there is a good understanding of systemic change and the opportunities for leveraging change within systems. In particular, in seeking to mainstream sustainability in pre-service teacher education in Queensland it has become clear that one needs to build capacity for change within participants such as knowledge of education for sustainability, conceptual skills in systemic thinking, action research and organisational change, and leadership skills. It is also of vital importance that key agents of change – those individuals who are ‘hubs’ within a system and can leverage for change across a wide range of the system – are identified and engaged with as early as possible. Key agents of change can only be correctly identified, however, if the project leaders and known participants have clearly identified the boundary to their system as this enables the system, sub-system and environment of the system to be understood. Through mapping the system a range of key organisations and stakeholders will be identified, including government and nongovernment organisations, teacher education students, teacher education academics, and so on. On this basis, key agents of change within the system and sub-system can be identified and invited to assist in working for change. A final insight is that it is important to have time – and if necessary the funding to ‘buy time’ – in seeking to bring about system-wide change. Seeking to bring about system-wide change is an ambitious project, one that requires a great deal of effort and time. These insights provide some considerations for those seeking to utilise the Mainstreaming Sustainability model to bring about change within and across a pre-service teacher education system.

A pilot study utilising cross-age peer tutoring as a method of intervention for anxious adolescents

Anxiety disorders are the most common psychopathology experienced by young people, with up to 18% of adolescents developing an anxiety disorder. The consequences of these disorders, if left untreated, include impaired peer relationships, school absenteeism and self-concept problems. In addition, anxiety disorders may play a causal role in the development of depression in young people, precede eating disorders and predispose adolescents to substance abuse disorders. While the school is often chosen as a place to provide early intervention for this debilitating disorder, the fact that excessive anxiety is often not recognised in school and that young people are reluctant to seek help, makes identifying these adolescents difficult. Even when these young people are identified, there are problems in providing sensitive programs which are not stigmatising to them within a school setting. One method which may engage this adolescent population could be cross-age peer tutoring. This paper reports on a small pilot study using the “Worrybusters” program and a cross-age peer tutoring method to engage the anxious adolescents. These anxious secondary school students planned activities for teacher-referred anxious primary school students for a term in the high school setting and then delivered those activities to the younger students weekly in the next term in the primary school. Although the secondary school students decreased their scores on anxiety self-report measures there were no significant differences for primary school students’ self-reports. However, the primary school parent reports indicated a significant decrease in their child’s anxiety.