Reconceitualização das categorias de skemp de compreensão relacional e compreensão instrumental como critérios globais

The thesis presents a systematic description about the meaning, as Skemp, relational understanding and understanding instrumental, in the context of mathematics learning, being that we had as a guide his understanding of the schema. Especially, we analyze some academic productions, in the area of Mathematics Education, who used the categories of understanding relational and instrumental understanding how evaluative instrument and we see that in most cases the analysis is punctual. Being so, whereas the inherent understanding relational schema has a network of connected ideas and non-insulated, we investigated if the global analysis, where it is the understanding of the diversity of contributory concepts for formation of the concept to be learned, is more appropriate than the punctual, where does the understanding of concepts so isolated. For this, we apply a teaching module, having as main content the Quaternos Pythagoreans using History of Mathematics and the work of Bahier (1916). With the data we obtained the teaching module to use the global analysis and the punctual analysis, using research methodology the Case Study, and consequently we conduct our inferences about the levels of understanding of the subject which has made it possible for us to investigate the ownership of global analysis at the expense of punctual analysis. On the opportunity, we prove the thesis that we espouse in the course of the study and, in addition, we highlight as a contribution of our research evidence of need for a teaching of mathematics that entices the relational understanding and that evaluation should be global, being necessary to consider the notion of schema and therefore know the schematic diagram of the concept that will be evaluated

Reflexões sobre a construção e evolução de conceitos geométricos nas séries intermediárias do ensino fundamental

This thesis represents a didactic research linked to the Post-graduation Programme in Education of the Universidade Federal do Rio Grande do Norte which aimed to approach the construction of the geometrical concepts of Volume of the Rectangular Parallelepiped, Area and Perimeter of the Rectangle adding a study of the Area of the Circle. The research was developed along with students from the 6th level of the Elementary School, in a public school in Natal/RN. The pedagogical intervention was made up of three moments: application of a diagnostic evaluation, instrument that enabled the creation of the teaching module by showing the level of the geometry knowledge of the students; introduction of a Teaching Module by Activities aiming to propose a reflexive didactic routing directed to the conceptual construction because we believed that such an approach would favor the consolidation of the learning process by becoming significant to the apprentice, and the accomplishment of a Final Evaluation through which we established a comparison of the results obtained before and after the teaching intervention. The data gathered were analyzed qualitatively by means of a study of understanding categories of mathematical concepts, in addition to using descriptive statistics under the quantitative aspect. Based on the theory of Richard Skemp, about categorization of mathematical knowledge, in the levels of Relational and Instrumental Understanding were achieved in contextual situations and varied proportions, thus enabling a contribution in the learning of the geometrical concepts studied along with the students who took part in the research. We believe that this work may contribute with reflections about the learning processes, a concern which remained during all the stages of the research, and also that the technical competence along with the knowledge about the constructivist theory will condition the implementation of a new dynamics to the teaching and learning processes. We hope that the present research work may add some contribution to the teaching practice in the context of the teaching of Mathematics for the intermediate levels of the Elementary School

Um estudo sobre a aprendizagem de números irracionais no ensino médio

The present study describes theoretical practical relationships between development and application of activities in Mathematics education. It s proposed a methodological approach to Mathematics in the first grade of Ensino Médio, supported by an experiment involving Irrational Numbers education by using constructive activities, applied obeying an educational sequence. Constructivism is used as an important theoretical reference in teaching learning process of Mathematics. The methodological intervention was done with two classes of students of the first grade of Ensino Médio, in two public schools, a state one and a federal one, located on the city of Natal, Rio Grande do Norte. The development, application and testing of the activities used on this experiment led us to think more profoundly about the value of constructivism ideas and understand that the use of activities that obey an educational sequence favors the learning. It s also discussed the research results, commented on a way to contribute to the advances of the proposal and it s more constant use. The participation and testing of the students were analyzed and judged using Skemp s Instrumental Understanding and Relational Understanding concepts. The results of the research were considered good, so we believe this methodological intervention can be used more frequently in the classes of Ensino Médio and also be applied to teachers in courses of initial education and continuous formation

Autonomie et reconnaissance

La notion d’autonomie personnelle joue un rôle central dans les théories politiques contemporaines et, plus spécifiquement, dans les théories de la justice. Or, dans le paradigme libéral dominant, elle est définie par une compréhension rationaliste de l’agent individuel. La présente étude défend la nécessité de redéfinir ce concept d’autonomie à la lumière des développements philosophiques et psychologiques qui ont complexifié notre compréhension de la subjectivité. L’emploi du concept d’autonomie relationnelle développé par certains auteurs féministes et par certains théoriciens de la reconnaissance semble pour ce faire prometteur. En passant par une critique du libéralisme politique rawlsien, cette étude cherche à montrer qu’une compréhension relationnelle de l’autonomie est nécessaire pour expliquer la motivation à la coopération sociale et pour redéfinir la justice et l’injustice de façon à ce qu’elles correspondent à l’expérience sociale vécue.

Evidence for unusual spatial location coding in Williams syndrome: an explanation for the local bias in visuo-spatial construction tasks?

Individuals with Williams syndrome (WS) display poor visuo-spatial cognition relative to verbal abilities. Furthermore, whilst perceptual abilities are delayed, visuo-spatial construction abilities are comparatively even weaker, and are characterised by a local bias. We investigated whether his differentiation in visuo-spatial abilities can be explained by a deficit in coding spatial location in WS. This can be measured by assessing participants' understanding of the spatial relations between objects within a visual scene. Coordinate and categorical spatial relations were investigated independently in four participant groups: 21 individuals with WS; 21 typically developing (TD) children matched for non-verbal ability; 20 typically developing controls of a lower non-verbal ability; and 21 adults. A third task measured understanding of visual colour relations. Results indicated first, that the comprehension of categorical and coordinate spatial relations is equally poor in WS. Second, that the comprehension of visual relations is also at an equivalent level to spatial relational understanding in this population. These results can explain the difference in performance on visuo-spatial perception and construction tasks in WS. In addition, both the WS and control groups displayed response biases in the spatial tasks. However, the direction of bias differed across the groups. This finding is explored in relation to current theories of spatial location coding. (c) 2005 Elsevier Inc. All rights reserved.

Um estudo sobre o ensino-aprendizagem das demonstrações matemáticas

Demonstrations are fundamental instruments for Mathematics and, as such, are frequently used by mathematicians, math teachers and students. In fact, demonstrations are part of every Mathematics teaching environment, because Mathematics considers something true when it can be demonstrated. This is in contrast to other fields of knowledge that employ observation and experimentation to validate truth. This dissertation presents a study of the teaching and learning of demonstrations in Mathematics, describing a Teaching Module applied in a course on the Theory of Numbers offered by the Mathematics Department of the Universidade Federal do Rio Grande do Norte for mathematics majors. The objective of the dissertation was to propose and test a Teaching Module that can serve as a model for teaching demonstrations. The Teaching Module consisted of the following five steps: the application of a survey to determine the students‟ profiles and their previous knowledge of mathematical language and techniques of demonstration; the analysis of a series of dialogues containing arguments in everyday language; the investigation and analysis of the structure of some important techniques of demonstration; a written assessment; and, finally, an interview to further verify the principal results of the Teaching Module. The analysis of the data obtained though the classroom activities, written assessments and interviews led to the conclusion that there was a significant amount of assimilation of the issue at the level of relational understanding, (SKEMP, 1980). These instruments verified that the students attained considerable improvement in their use of mathematical language and of the techniques of demonstration presented. Thus, the evidence supports the conclusion that the proposed Teaching Module is an effective means for the teaching/learning of mathematical demonstration and, as such, provides a methodological guide which may lay the foundations for a new approach to this important subject

Algunos indicadores del desarrollo del esquema de derivada de una función

El objetivo de esta investigación es caracterizar algunos indicadores del desarrollo del esquema de derivada en estudiantes de pos-secundaria. Usamos los niveles intra, inter y trans del desarrollo de un esquema propuestos por Piaget y García para caracterizar el uso flexible que los estudiantes hacen de la equivalencia lógica entre diferentes elementos matemáticos cuando resuelven un problema, como un indicador del desarrollo del esquema de derivada. Este indicador ayuda a explicar la transición entre los niveles inter y trans de desarrollo del esquema derivada.

Mothering and ‘insider’ dilemmas:feminist sociologists in the research process

This paper is about care, insider positions and mothering within feminist research. We ask questions about how honest, ethical and caring can we really be in placing the self into the research process as mothers ourselves. Should we leave out aspects of the research that do not fit neatly and how ethical can we claim to be if we do? Moreover, should difficult differences, secrets and silences that emerge from the research process and research stories that might 'out' us as failures be excluded from research outcomes so as to claim legitimate research? We consider the use of a feminist methods as crucial in the reciprocal and relational understanding of personal enquiry. Mothers invest significant emotional capital in their families and we explore the blurring of the interpersonal and intrapersonal when sharing mothering experiences common to both participant and researcher. Indeed participants can identify themselves within the process as 'friends' of the researcher. We both have familiarity within our respective research that has led to mutual understanding of having insider positions. Crucially individuals' realities are a vital component of the qualitative paradigm and that 'insider' research remains a necessary, albeit messy vehicle in social research. As it is we consider a growing body of literature which marks out and endorses a feminist ethics of care. All of which critique established ways of thinking about ethics, morality, security, citizenship and care. It provides alternatives in mapping private and public aspects of social life as it operates at a theoretical level, but importantly for this paper also at the level of practical application.

Leader-member exchange, group- and individual-level procedural justice and reactions to performance appraisals

Previous research has established that relationships with authority figures and procedural justice perceptions are important in terms of the way in which employees react to organizational procedures that affect them. What is less clear are the reasons why exchange quality with authorities is related to perceptions of process fairness and the role of procedural justice climate in this process. Results indicate that individual-level perceptions of procedural justice, but not performance ratings, partially mediate the relationship between exchange quality and reactions to performance appraisals, and that procedural justice climate is positively related to perceptions of procedural justice and appraisal reactions. These results support a more relational than instrumental view of justice perceptions in organizational procedures bound by exchange quality with an authority figure. Our study suggests that it is essential for managers to actively monitor and manage employee perceptions of process fairness at the group and individual levels. © 2015 Wiley Periodicals, Inc.

Participatory ergonomics: Understanding the contributions of reflection groups in a hospital food service

Aim: To identify how the methodology of Reflection Groups (RG) can contribute to approach social-psychological problems, so often observed as obstacles in PE efforts. The objective was also to verify the contributions from RG to the implementation of ergonomics recommendations, which were a starting point and organized group discussions. Method: A concrete case was used as an illustration, and studied in depth: RG with administration and production workers` representatives from the Department of Nutrition and Dietetics of a cardiologic hospital in Sao Paulo, Brazil. RG are temporary thinking groups, taking place outside the workplace and having delegative and consultive participation. They make use of Operative Groups, an adapted form of tripartite group, activity as an instrumental resource, group dynamic techniques and videotaping. In 2007, 31 meetings took place during paid working hours with 7 groups of different composition, ranging from 1.5 h to 3 h. Results: Additionally to the positive effects in communication and psychosocial environment, RG could also contribute to changes in interpersonal relationships, cooperation, personal and work behaviours. By dealing with aspects which could hinder the explicit task: fears, conflicts, and stereotyped beliefs and behaviours; resistance to change could be broken and group members could learn. RG allowed input about new risks; continuous information and feedback about ongoing ergonomics interventions so that immediate corrective action could be taken. The main form of participation was in administrative, organizational, and psychosocial problems which required a better clarification and identification of their real causes, commitment, and elaboration of strategies and negotiation of different stakeholders in their solution. Conclusion: RG takes advantage of homogeneous and heterogeneous groups, in face to face communication. The interactions in the groups are task-oriented (explicit task) but attaining groups` goals depends on a relational interaction (implicit task). Relevance to industry: Reflection groups can bring important contributions to ergonomics and industry because they favour the discussion, disclosure of problems and incorporation of solutions, enabling interventions in working organization, psychosocial environment and relationships in a collective and participatory approach, promoting health and social integration. (C) 2010 Elsevier B.V. All rights reserved.

Understanding the practical sense of health actions: contributions of Philosophical Hermeneutics

Health actions have a powerful tech no-scientific armory invested in their instrumental success. Conversely, they have a fragile conceptual basis for the understanding and transformation of the practical sense of health-disease-care processes that especifically take place nowadays. This essay intends to identify the potential contributions of philosophical hermeneutics to overcome such fragility. With this purpose and through contemporary hermeneutics, the recovery of the aristotelian distinction between theory, technique and praxis and its repercussions is discussed, for a systematic treatment of the practical reason of health actions. Against this backdrop, the following stands out: the dialogic essence of understanding-interpreting human acts; the fusion of horizons as the movement of realization of those processes of understanding; and happiness projects, existential guide to everyday life, as the impulse and the possibility of openness of the reason to the practical sense of health actions.

Earthquakes in western Iberia: improving the understanding of lithospheric deformation in a slowly deforming region

Mainland Portugal, on the southwestern edge of the European continent, is located directly north of the boundary between the Eurasian and Nubian plates. It lies in a region of slow lithospheric deformation (< 5 mm yr(-1)), which has generated some of the largest earthquakes in Europe, both intraplate (mainland) and interplate (offshore). Some offshore earthquakes are nucleated on old and cold lithospheric mantle, at depths down to 60 km. The seismicity of mainland Portugal and its adjacent offshore has been repeatedly classified as diffuse. In this paper, we analyse the instrumental earthquake catalogue for western Iberia, which covers the period between 1961 and 2013. Between 2010 and 2012, the catalogue was enriched with data from dense broad-band deployments. We show that although the plate boundary south of Portugal is diffuse, in that deformation is accommodated along several distributed faults rather than along one long linear plate boundary, the seismicity itself is not diffuse. Rather, when located using high-quality data, earthquakes collapse into well-defined clusters and lineations. We identify and characterize the most outstanding clusters and lineations of epicentres and correlate them with geophysical and tectonic features (historical seismicity, topography, geologically mapped faults, Moho depth, free-air gravity, magnetic anomalies and geotectonic units). Both onshore and offshore, clusters and lineations of earthquakes are aligned preferentially NNE-SSW and WNW-ESE. Cumulative seismic moment and epicentre density decrease from south to north, with increasing distance from the plate boundary. Only few earthquake lineations coincide with geologically mapped faults. Clusters and lineations that do not match geologically mapped faults may correspond to previously unmapped faults (e.g. blind faults), rheological boundaries or distributed fracturing inside blocks that are more brittle and therefore break more easily than neighbour blocks. The seismicity map of western Iberia presented in this article opens important questions concerning the regional seismotectonics. This work shows that the study of low-magnitude earthquakes using dense seismic deployments is a powerful tool to study lithospheric deformation in slowly deforming regions, such as western Iberia, where high-magnitude earthquakes occur with long recurrence intervals.

Helping medical students to acquire a deeper understanding of truth-telling.

PROBLEM: Truth-telling is an important component of respect for patients' self-determination, but in the context of breaking bad news, it is also a distressing and difficult task. INTERVENTION: We investigated the long-term influence of a simulated patient-based teaching intervention, integrating learning objectives in communication skills and ethics into students' attitudes and concerns regarding truth-telling. We followed two cohorts of medical students from the preclinical third year to their clinical rotations (fifth year). Open-ended responses were analysed to explore medical students' reported difficulties in breaking bad news. CONTEXT: This intervention was implemented during the last preclinical year of a problem-based medical curriculum, in collaboration between the doctor-patient communication and ethics programs. OUTCOME: Over time, concerns such as empathy and truthfulness shifted from a personal to a relational focus. Whereas 'truthfulness' was a concern for the content of the message, 'truth-telling' included concerns on how information was communicated and how realistically it was received. Truth-telling required empathy, adaptation to the patient, and appropriate management of emotions, both for the patient's welfare and for a realistic understanding of the situation. LESSONS LEARNED: Our study confirms that an intervention confronting students with a realistic situation succeeds in making them more aware of the real issues of truth-telling. Medical students deepened their reflection over time, acquiring a deeper understanding of the relational dimension of values such as truth-telling, and honing their view of empathy.