O papel das representações na resolução de problemas de Matemática: um estudo no 1º ano de escolaridade

Este estudo tem como objectivo investigar o papel que as representações, construídas por alunos do 1.o ano de escolaridade, desempenham na resolução de problemas de Matemática. Mais concretamente, a presente investigação procura responder às seguintes questões: Que representações preferenciais utilizam os alunos para resolver problemas? De que forma é que as diferentes representações são influenciadas pelas estratégias de resolução de problemas utilizadas pelos alunos? Que papéis têm os diferentes tipos de representação na resolução dos problemas? Nesta investigação assume-se que a resolução de problemas constitui uma actividade muito importante na aprendizagem da Matemática no 1.o Ciclo do Ensino Básico. Os problemas devem ser variados, apelar a estratégias diversificadas de resolução e permitir diferentes representações por parte dos alunos. As representações cativas, icónicas e simbólicas constituem importantes ferramentas para os alunos organizarem, registarem e comunicarem as suas ideias matemáticas, nomeadamente no âmbito da resolução de problemas, servindo igualmente de apoio à compreensão de conceitos e relações matemáticas. A metodologia de investigação segue uma abordagem interpretativa tomando por design o estudo de caso. Trata-se simultaneamente de uma investigação sobre a própria prática, correspondendo os quatro estudos de caso a quatro alunos da turma de 1.0 ano de escolaridade da investigadora. A recolha de dados teve lugar durante o ano lectivo 2007/2008 e recorreu à observação, à análise de documentos, a diários, a registos áudio/vídeo e ainda a conversas com os alunos. A análise de dados que, numa primeira fase, acompanhou a recolha de dados, teve como base o problema e as questões da investigação bem como o referencial teórico que serviu de suporte à investigação. Com base no referencial teórico e durante o início do processo de análise, foram definidas as categorias de análise principais, sujeitas posteriormente a um processo de adequação e refinamento no decorrer da análise e tratamento dos dados recolhidos -com vista à construção dos casos em estudo. Os resultados desta investigação apontam as representações do tipo icónico e as do tipo simbólico como as representações preferenciais dos alunos, embora sejam utilizadas de formas diferentes, com funções distintas e em contextos diversos. Os elementos simbólicos apoiam-se frequentemente em elementos icónicos, sendo estes últimos que ajudam os alunos a descompactar o problema e a interpretá-lo. Nas representações icónicas enfatiza-se o papel do diagrama, o qual constitui uma preciosa ferramenta de apoio ao raciocínio matemático. Conclui-se ainda que enquanto as representações activas dão mais apoio a estratégias de resolução que envolvem simulação, as representações icónicas e simbólicas são utilizadas com estratégias diversificadas. As representações construídas, com papéis e funções diferentes entre si, e que desempenham um papel crucial na correcta interpretação e resolução dos problemas, parecem estar directamente relacionadas com as caraterísticas da tarefa proposta no que diz respeito às estruturas matemáticas envolvidas. ABSTRACT; The objective of the present study is to investigate the role of the representations constructed by 1st grade students in mathematical problem solving. More specifically, this research is oriented by the following questions: Which representations are preferably used by students to solve problems? ln which way the strategies adopted by the students in problem solving influence those distinct representations? What is the role of the distinct types of representation in the problems solving process? ln this research it is assumed that the resolution of problems is a very important activity in the Mathematics learning at the first cycle of basic education. The problems must be varied, appealing to diverse strategies of resolution and allow students to construct distinct representations. The active, iconic and symbolic representations are important tools for students to organize, to record and to communicate their mathematical ideas, particularly in problem solving context, as well as supporting the understanding of mathematical concepts and relationships. The adopted research methodology follows an interpretative approach, and was developed in the context of the researcher classroom, originating four case studies corresponding to four 1 st grade students of the researcher's class. Data collection was carried out during the academic year of 2007/2008 and was based on observation, analysis of documents, diaries, audio and video records and informal conversations with students. The initial data analysis was based on the problems and issues of research, as well in the theoretical framework that supports it. The main categories of analysis were defined based on the theoretical framework, and were subjected to a process of adaptation and refining during data processing and analysis aiming the -case studies construction. The results show that student's preferential representations are the iconic and the symbolic, although these types of representations are used in different ways, with different functions and in different contexts. The symbolic elements are often supported by iconic elements, the latter helping students to unpack the problem and interpret it. ln the iconic representations the role of the diagrams is emphasized, consisting in a valuable tool to support the mathematical reasoning. One can also conclude that while the active representations give more support to the resolution strategies involving simulation, the iconic and symbolic representations are preferably used with different strategies. The representations constructed with distinct roles and functions, are crucial in the proper interpretation and resolution of problems, and seem to be directly related to the characteristics of the proposed task with regard to the mathematical structures involved.

Trabalhar com a matemática em educação de infância

Este estudo tem como principal objetivo compreender e analisar o modo como crianças de creche e jardim-de-infância resolvem problemas matemáticos e o que pode constranger a resolução. Em particular, procurei analisar a atividade matemática que as crianças desenvolvem quando se confrontam com problemas matemáticos e os desafios com que se deparam. Do ponto de vista metodológico, o estudo enquadra-se numa abordagem qualitativa de investigação e num paradigma interpretativo. Além disso, trata-se de uma investigação-ação orientada pela questão “como otimizar a atividade de resolver problemas matemáticos em contextos de educação de infância?”. Neste âmbito, propus a quatro crianças de creche e a 21 de jardim-de-infância um conjunto de tarefas selecionadas para, potencialmente, terem, para si, algum grau de desafio. Os principais métodos de recolha de dados foram a observação participante, a análise documental e um inquérito por questionário realizado às educadoras cooperantes. O estudo ilustra que é possível envolver crianças de creche e de jardim-de-infância numa atividade de resolução de problemas matemáticos e que esta atividade é favorecida se o contexto dos problemas estiver próximo do que fazem no dia-a-dia da sala. Durante o processo de resolução das tarefas propostas, foram mobilizadas e trabalhadas diversas noções matemáticas. Na creche, todas as crianças evidenciaram possuir conhecimentos acerca da noção topológica “dentro de” e “fora de” e algumas foram bem-sucedidas no uso do processo de classificação, tendo em conta um critério. Neste âmbito, recorreram a representações ativas. No jardim-de-infância, todas as crianças conseguiram fazer a contagem sincronizada das letras do seu nome, de indicar a quantidade de letras, o que indicia o conhecimento da noção de cardinal, e de representar esta quantidade recorrendo tanto a numerais como a representações icónicas. Além disso, foram capazes de interpretar uma tabela de modo a construir um gráfico com barras e de elaborar um pictograma, o que revela possuírem conhecimentos ao nível da literacia estatística. Por último, algumas crianças foram bem-sucedidas na descoberta de estratégias de resolução de problemas que lhes permitiram inventariar exaustivamente todas as possibilidades de resolução e contar, organizadamente, estas possibilidades. No decurso desta atividade surgiram tentativas de generalização, embora nem sempre corretas, sobressaindo o recurso a representações ativas nomeadamente à dramatização de situações. Quanto aos desafios com que se depararam destacam-se, no caso da creche, o uso correto do processo de classificação. No caso do jardim-de-infância, as crianças demonstraram dificuldades em distinguir a legenda do pictograma dos dados, em resolver um problema em que estava em jogo o sentido combinatório da multiplicação e em encontrar estratégias de generalização. O estudo indicia, ainda, que é essencial que o educador proponha tarefas diversificadas e desafiantes que, partindo sempre da curiosidade e interesse das crianças, lhes permitam trabalhar com ideias matemáticas importantes e representar adequadamente o conhecimento com que lidam.

Social identity and engagement: an exploratory study at university

Within the framework of research on students' active performance in their study habits, the aim of this study is to analyze a model predicting the effect of social identity and personal initiative on engagement in university students. We conducted a cross-sectional study on 266 students from different Spanish universities. The resulting data were analyzed using SPSS Macro MEDIATE. Evidence was found for the proposed model. Only group-identity predicted personal initiative and engagement. Analysis revealed the mediating role of proactive behavior on engagement in university students. It is concluded that the university management may intervene, from an organizational-culture approach, promoting guidelines to reinforce students' sense of belonging by enhancing initiative and autonomous problem solving in learning behaviors.

Conexões matemáticas na educação pré-escolar

Dissertação de Mestrado, Educação Pré-Escolar, Escola Superior de Educação e Comunicação, Universidade do Algarve, 2016

Identification of nurses` competencies in primary health care through a Delphi study in southern Brazil

Objective: This investigation aimed to identify and analyze the general and specific competencies of nurses in the primary health care practice of Brazil. Design: The Delphi Technique was used as the method of study. Sample: 2 groups of participants were selected: One contained primary health care nurses (n=52) and the other specialists (n=57), including public health nurses and public or community health faculty. Measurements: 3 questionnaires were developed for the study. The first asked participants to indicate general and specific competencies, which were compiled into a list for each group. A Likert scale of 1-5 was added to these 2 lists in the second and third questionnaires. A consensus criterion of 75% for score 4 or 5 was adopted. Results: In the nurses` group, 17 general and 8 specific competencies reached the consensus criterion; 19 general and 9 specific competencies reached the criterion in the specialists` group. These competencies were classified into 10 domains: professional values, communication, teamwork, management, community-oriented, health promotion, problem solving, health care, and education and basic public health sciences. Conclusions: These competencies reflect Brazilian health policy and constitute a reference for health professional practice and education.

Group decision making and Quality-of-information in e-Health systems

Knowledge is central to the modern economy and society. Indeed, the knowledge society has transformed the concept of knowledge and is more and more aware of the need to overcome the lack of knowledge when has to make options or address its problems and dilemmas. One’s knowledge is less based on exact facts and more on hypotheses, perceptions or indications. Even when we use new computational artefacts and novel methodologies for problem solving, like the use of Group Decision Support Systems (GDSSs), the question of incomplete information is in most of the situations marginalized. On the other hand, common sense tells us that when a decision is made it is impossible to have a perception of all the information involved and the nature of its intrinsic quality. Therefore, something has to be made in terms of the information available and the process of its evaluation. It is under this framework that a Multi-valued Extended Logic Programming language will be used for knowledge representation and reasoning, leading to a model that embodies the Quality-of-Information (QoI) and its quantification, along the several stages of the decision-making process. In this way, it is possible to provide a measure of the value of the QoI that supports the decision itself. This model will be here presented in the context of a GDSS for VirtualECare, a system aimed at sustaining online healthcare services.

Modes of acquisition of health literacy skills in informal learning contexts

In this article we try to analyze the learning processes of health literacy skills in informal contexts. We intend to broaden the understanding of the learning process beyond the formal contexts, thus contributing to the elucidation of health professionals on how individuals acquire and manage their knowledge in health matters. Given our goal, we use an analytic corpus constituted by one hundred autobiographical narratives written between 2006 and 2011, in educational contexts but with recognized potential for use in different scientific fields, including health. The results reveal the existence of three different types of modes of learning health literacy skills in informal context: : i) learning that takes place in action, in achieving daily tasks; ii) learning processes that result from problem solving; iii) learning that occurs in an unplanned manner, resulting from accidental circumstances and, in some cases, devoid of intentionality.

Assessing positive mental health in people with chronic physical health problems: correlations with socio-demographic variables and physical health status

Background: A holistic perspective on health implies giving careful consideration to the relationship between physical and mental health. In this regard the present study sought to determine the level of Positive Mental Health (PMH) among people with chronic physical health problems, and to examine the relationship between the observed levels of PMH and both physical health status and socio-demographic variables. Methods: The study was based on the Multifactor Model of Positive Mental Health (Lluch, 1999), which comprises six factors: Personal Satisfaction (F1), Prosocial Attitude (F2), Self-control (F3), Autonomy (F4), Problem-solving and Self-actualization (F5), and Interpersonal Relationship Skills (F6). The sample comprised 259 adults with chronic physical health problems who were recruited through a primary care center in the province of Barcelona (Spain). Positive mental health was assessed by means of the Positive Mental Health Questionnaire (Lluch, 1999). Results: Levels of PMH differed, either on the global scale or on specific factors, in relation to the following variables: age: global PMH scores decreased with age (r=-0.129; p=0.038); b) gender: men scored higher on F1 (t=2.203; p=0.028) and F4 (t=3.182; p=0.002), while women scored higher on F2 (t -3.086; p=0.002) and F6 (t=-2.744; p=0.007); c) number of health conditions: the fewer the number of health problems the higher the PMH score on F5 (r=-0.146; p=0.019); d) daily medication: polymedication patients had lower PMH scores, both globally and on various factors; e) use of analgesics: occasional use of painkillers was associated with higher PMH scores on F1 (t=-2.811; p=0.006). There were no significant differences in global PMH scores according to the type of chronic health condition. The only significant difference in the analysis by factors was that patients with hypertension obtained lower PMH scores on the factor Autonomy (t=2.165; p=0.032). Conclusions: Most people with chronic physical health problems have medium or high levels of PMH. The variables that adversely affect PMH are old age, polypharmacy and frequent consumption of analgesics. The type of health problem does not influence the levels of PMH. Much more extensive studies with samples without chronic pathology are now required in order to be able to draw more robust conclusions.

InGen of creative production in the health sciences: A workbook companion to innovation generation

InGen of Creative Production in the Health Sciences is a compendium of innovative thinking exercises for individuals and groups, derived from an eclectic array of practical guides for professionals in a variety of fields. Segmented into five subcategories across twenty two chapters, the effort seeks to make techniques for increasing innovative problem solving more accessible to a diverse audience of problem solvers. The chapters of Roberta Ness. Innovation Generation (2012, Oxford University Press) provide the themes for each of the chapters in the workbook. It is intended that those who read Ness. Innovation Generation will benefit from practicing the constructs of innovative thinking exemplified in each exercise.^ The methods used to gather data, in this case mostly innovative thinking exercises, included literature reviews of existing innovative thinking tools, classroom materials, and theory-driven exploration of exercises to fill in gaps in extant materials. Specifically, Google.com and Amazon.com searches were conducted using the terms “innovation,” “innovative,” “innovator,” “creative,” “novelty,” “thinking,” together with some variance of “book,” “workbook,” and “exercise.” The results were sorted thematically to show correspondence with the themes in Ness (2012) and compared to suggested best practices of 50 years of scientific research on innovative thinking. Where themes were suggested by Ness (2012) and peer-reviewed research on innovation but unavailable in published innovation thinking workbooks, new exercises were developed. The five type subcategories into which these results were organized are: individual direct, individual indirect, group direct, group indirect and probing question. It is anticipated that the five type subcategories and spectrum of themes will equip problem solvers in a variety of capacities.^

Transition from community dwelling to retirement village in older adults:cognitive functioning and psychological health outcomes

Supported living and retirement villages are becoming a significant option for older adults with impairments, with independence concerns or for forward planning in older age, but evidence as to psychological benefits for residents is sparse. This study examined the hypothesis that the multi-component advantages of moving into a supported and physically and socially accessible “extra care” independent living environment will impact on psychological and functioning measures. Using an observational longitudinal design, 161 new residents were assessed initially and three months later, in comparison to 33 older adults staying in their original homes. Initial group differences were apparent but some reduced after three months. Residents showed improvement in depression, perceived health, aspects of cognitive function, and reduced functional limitations, while controls showed increased functional limitations (worsening). Ability to recall specific autobiographical memories, known to be related to social-problem solving, depression and functioning in social relationships, predicted change in communication limitations, and cognitive change predicted changes in recreational limitations. Change in anxiety and memory predicted change in depression. Findings suggest that older adults with independent living concerns who move to an independent but supported environment can show significant benefits in psychological outcomes and reduction in perceived impact of health on functional limitations in a short period. Targets for focussed rehabilitation are indicated, but findings also validate development of untargeted general supportive environments.

Subject -centered and problem -based approaches to teaching clinical competence in physical therapy

Physical therapy students must apply the relevant information learned in their academic and clinical experience to problem solve in treating patients. I compared the clinical cognitive competence in patient care of second-year masters students enrolled in two different curricular programs: modified problem-based (M P-B; n = 27) and subject-centered (S-C; n = 41). Main features of S-C learning include lecture and demonstration as the major teaching strategies and no exposure to patients or problem solving learning until the sciences (knowledge) have been taught. Comparatively, main features of M P-B learning include case study in small student groups as the main teaching strategy, early and frequent exposure to patients, and knowledge and problem solving skills learned together for each specific case. Basic and clinical orthopedic knowledge was measured with a written test with open-ended items. Problem solving skills were measured with a written case study patient problem test yielding three subscores: assessment, problem identification, and treatment planning. ^ Results indicated that among the demographic and educational characteristics analyzed, there was a significant difference between groups on ethnicity, bachelor degree type, admission GPA, and current GPA, but there was no significant difference on gender, age, possession of a physical therapy assistant license, and GRE score. In addition, the M P-B group achieved a significantly higher adjusted mean score on the orthopedic knowledge test after controlling for GRE scores. The S-C group achieved a significantly higher adjusted mean total score and treatment management subscore on the case study test after controlling for orthopedic knowledge test scores. These findings did not support their respective research hypotheses. There was no significant difference between groups on the assessment and problem identification subscores of the case study test. The integrated M P-B approach promoted superior retention of basic and clinical science knowledge. The results on problem solving skills were mixed. The S-C approach facilitated superior treatment planning skills, but equivalent patient assessment and problem identification skills by emphasizing all equally and exposing the students to more patients with a wider variety of orthopedic physical therapy needs than in the M P-B approach. ^

Ecological Literacy And Beyond: Problem-based Learning For Future Professionals.

Ecological science contributes to solving a broad range of environmental problems. However, lack of ecological literacy in practice often limits application of this knowledge. In this paper, we highlight a critical but often overlooked demand on ecological literacy: to enable professionals of various careers to apply scientific knowledge when faced with environmental problems. Current university courses on ecology often fail to persuade students that ecological science provides important tools for environmental problem solving. We propose problem-based learning to improve the understanding of ecological science and its usefulness for real-world environmental issues that professionals in careers as diverse as engineering, public health, architecture, social sciences, or management will address. Courses should set clear learning objectives for cognitive skills they expect students to acquire. Thus, professionals in different fields will be enabled to improve environmental decision-making processes and to participate effectively in multidisciplinary work groups charged with tackling environmental issues.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Teen Triple P: A universal approach to reducing risk factors for behavioural and emotional problems in adolescents at the transition to high school

Teen Triple P is a multilevel system of intervention that is designed to provide parents with specific strategies to promote the positive development of their teenage children as they make the transition into high school and through puberty. The program is based on a combination of education about the developmental needs of adolescents, skills training to improve communication and problem-solving, plus specific modules to deal with common problems encountered by parents and adolescents that can escalate into major conflict and violence. It is designed to increase the engagement of parents of adolescent and pre-adolescent children by providing them with easy access to evidencebased parenting advice and support. This paper presents data collected as part of a survey of over 1400 students in first year high school at 9 Brisbane schools. The survey instrument was constructed to obtain students' reports about behaviour which is known to be associated with their health and wellbeing, and also on the extent to which their parents promoted or discouraged such behaviour at home, at school, and in their social and recreational activities in the wider community. Selected data from the survey were extracted and presented to parents at a series of parenting seminars held at the schools to promote appropriate parenting of teenagers. The objectives were to provide parents with accurate data about teenagers' behaviour, and about teenagers' reports of how they perceived their parents' behaviour. Normative data on parent and teenager behaviour will be presented from the survey as well as psychometric data relating to the reliability and validity of this new measure. Implications of this strategy for increasing parent engagement in parenting programs that aim to reduce behavioural and emotional problems in adolescents will be discussed.