Utilizando processos geométricos da história da matemática para o ensino de equações do 2º grau

The present work had as principal objective to analyze the, 9th grade students understanding about the solutions of an equation of the 2° degree, using geometric processes of the History of the Mathematics. To do so, the research had as base the elaboration and application of a group of teaching activities, based on Jean Piaget's construtivism. The research consisted of a methodological intervention, that has as subjects the students of a group of 9th grade of the State School José Martins de Vasconcelos, located in the municipal district of Mossoró, Rio Grande do Norte. The intervention was divided in three stages: application of an initial evaluation; development of activities‟ module with emphasis in constructive teaching; and the application of the final evaluation. The data presented in the initial evaluation revealed a low level of the students' understanding with relationship to the calculation of areas of rectangles, resolution of equations of the 1st and 2nd degrees, and they were to subsidize the elaboration of the teaching module. The data collected in the initial evaluation were commented and presented under descriptive statistics form. The results of the final evaluation were analyzed under the qualitative point of view, based on Richard Skemp's theory on the understanding of mathematical concepts. The general results showed a qualitative increase with relationship to the students' understanding on the mathematical concepts approached in the intervention. Such results indicate that a methodology using the previous student‟s knowledge and the development of teaching activities, learning in the construtivist theory, make possible an understanding on the part of the students concerning the thematic proposal

Física para geografia: desafios de uma proposta pedagógica interdisciplinar

This study has as its aim the elaboration, presentation and application of a proposal which makes possible an inter-disciplinary relationship between knowledge of physics and geography in the graduation course for forming geography teachers in the Dom Aureliano Matos Faculty of Philosophy in the city of Limoeiro do Norte in the State of Ceára. Initially, we observe in pertinent literature and opinions of specialists what capacities and abilities are suggested for a future teacher of geography. Following that, we select subject matter which broaches upon physic concepts and may be contextualized within topics present in the daily fare of a geography teacher, such as natural phenomena related principally to natural environment and climate, envolving astronomic features, using didactic materials and resources in easily understood language and without the excessive presence of mathematical formulas. An evaluation of the experience allows us to affirm that inter-disciplinary treatment, as an important alternative for curriculam organization, when applied in the classroom shows that there is better learning, a reduction in class evasion and a significant fall in failures when compared with traditional proposals for the teaching of physics in relation to geography. On the other hand, it is notable that to maintain and augment such measures it is a challenge to be met, with the purpose that students of other courses may perceive that physic concepts have much to do with their reality, and that understanding them is relevant for their professional and personal formation

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

Linguagem matemática: uma proposta de ensino e avaliação da compreensão leitora dos objetos da matemática

This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

Princípio da Indução Matemática no Ensino Médio

We developed this dissertation aiming its in the process of teaching and learning of the Principle of Mathematical Induction and we set our efforts so that the students of the first year of the high school can assimilate the content having the knowledge seen in the basic education as foreknowledge. With this, we seek to awake in the student the interest on proofs, showing how much it s needed in examples that involve contents that he is already seen

Knowledge and attitudes of health care workers from intensive care units regarding nosocomial transmission of influenza: a study on the immediate pre-pandemic period

The transmission of influenza in health care settings is a major threat to patients, especially those with severe diseases. The attitude of health care workers (HCWs) may influence the transmission of countless infections. The current study aimed to quantify knowledge and identify attitudes of HCWs involved in intensive care units (ICUs) regarding the risk of nosocomial influenza transmission. A questionnaire was applied through interviews to HCWs who worked in one of the five ICUs from a teaching hospital. Questions about influenza were deliberately dispersed among others that assessed several infectious agents. Forty-two HCWs were interviewed: nine physicians, ten nurses and 23 nursing technicians or auxiliaries. Among the 42 HCWs, 98% were aware of the potential transmission of influenza virus in the ICUs, but only 31% would indicate droplet precautions for patients with suspected infection. Moreover, only 31% of them had been vaccinated against influenza in the last campaign (2008). Nursing technicians or auxiliaries were more likely to have been vaccinated, both by univariate and multivariable analysis. When asked about absenteeism, only 10% of the study subjects stated that they would not go to work if they had an influenza-like illness. Those findings suggest that, in non-pandemic periods, influenza control in hospitals requires strategies that combine continuous education with changes in organizational culture.

Comparing the Teaching-Learning Process With and Without the Use of Computerized Technological Resources

Computerized technological resources have become essential in education, particularly for teaching topics that require the performance of specific tasks. These resources can effectively help the execution of such tasks and the teaching-learning process itself. After the development of a Web site on the topic of nursing staff scheduling, this study aimed at comparing the development of students involved in the teaching-learning process of the previously mentioned topic, with and without the use of computer technology. Two random groups of undergraduate nursing students from a public university in São Paulo state, Brazil, were organized: a case group (used the Web site) and a control group (did not use the Web site). Data were collected from 2003 to 2005 after approval by the Research Ethics Committee. Results showed no significant difference in motivation or knowledge acquisition. A similar performance for the two groups was also verified. Other aspects observed were difficulty in doing the nursing staff scheduling exercise and the students' acknowledgment of the topic's importance for their training and professional lives; easy access was considered to be a positive aspect for maintaining the Web site.

Teaching the Rational Use of Medicines to medical students: a qualitative research

Background: Prescribing is a complex and challenging task that must be part of a logical deductive process based on accurate and objective information and not an automated action, without critical thinking or a response to commercial pressure. The objectives of this study were 1) develop and implement a discipline based on the WHO's Guide to Good Prescribing; 2) evaluate the course acceptance by students; 3) assess the impact that the Rational Use of Medicines (RUM) knowledge had on the students habits of prescribing medication in the University Hospital.Methods: In 2003, the RUM principal, based in the WHO's Guide to Good Prescribing, was included in the official curriculum of the Botucatu School of Medicine, Brazil, to be taught over a total of 24 hours to students in the 4th year. We analyzed the students' feedback forms about content and teaching methodology filled out immediately after the end of the discipline from 2003 to 2010. In 2010, the use of RUM by past students in their medical practice was assessed through a qualitative approach by a questionnaire with closed-ended rank scaling questions distributed at random and a single semistructured interview for content analysis.Results: The discipline teaches future prescribers to use a logical deductive process, based on accurate and objective information, to adopt strict criteria (efficacy, safety, convenience and cost) on selecting drugs and to write a complete prescription. At the end of it, most students considered the discipline very good due to the opportunity to reflect on different actions involved in the prescribing process and liked the teaching methodology. However, former students report that although they are aware of the RUM concepts they cannot regularly use this knowledge in their daily practice because they are not stimulated or even allowed to do so by neither older residents nor senior medical staff.Conclusions: This discipline is useful to teach RUM to medical students who become aware of the importance of this subject, but the assimilation of the RUM principles in the institution seems to be a long-term process which requires the involvement of a greater number of the academic members.

Nothing too much: reflecting about the role of contextualization in science teaching

The contextualization and discussion about the science role in the social and economical development are unquestionably important for the science teaching process. It doesn't mean, however, that the scientific-theoretic knowledge and the strategies involved in its construction and application might be neglected. In this way, a dangerous situation is created when the contextualization is assumed as a unique and primordial target in science education. This paper presents a research carried out with 15 future chemistry teachers and the results show a worrying "supervalorization", of the contextualization beside other equally important aspects of the chemical knowledge.

Interface entre história da matemática e ensino: uma atividade desenvolvida com base num documento do século XVI

Este artigo propõe a construção de uma interface entre história e ensino de matemática a partir de um diálogo entre historiadores e educadores da matemática. Para tanto, consideramos aspectos epistemológicos e metodológicos ligados à história da matemática, pautada em tendências historiográficas atuais, juntamente com a metodologia baseada no movimento lógico-histórico. A interface contemplou o movimento do pensamento na formação dos conceitos e o contexto no qual tais conceitos foram desenvolvidos, de modo a conduzir à reflexão sobre o processo histórico da construção do conhecimento para a elaboração de atividade didática. Esta atividade teve por base um documento do século XVI dedicado à construção e uso de instrumentos matemáticos, e sua elaboração levou em consideração uma intencionalidade e um plano de ação que viabilizaram o seu desenvolvimento. A organização do ensino articulou as conexões internas e externas trazidas pela análise do documento e a forma do pensamento do desenvolvimento do conceito.

As diferentes “personalidades” do número racional trabalhadas através da resolução de problemas

We address the different "personalities" of the rational number and the concept of proportionality, analyzing the possibilities for using the Mathematics Teaching and Learning through Problem-solving Method. This method is based on the principle that knowledge can be constructed through the use of problems that generate new concepts and new contents. The different meanings of rational number - rational point, quotient, fraction, ratio, and operator - are constructs that depend on mathematical theories in which they are imbedded and the situations that evoke them in problem-solving. Some data will be presented from continuing education courses for teachers, aiming to contribute to understanding regarding the different "personalities" of the rational number. In general, these "personalities" are not easily identified by teachers and students, which is the reason for the many difficulties encountered during problem-solving involving rational numbers. One of these "personalities", the ratio, provides the basis for the concept of proportionality, which is relevant because it is a unifying idea in mathematics.

Survey on tuberculosis teaching in Brazilian nursing schools, 2004

OBJECTIVE: To characterise tuberculosis (TB) teaching in Brazilian nursing schools by state and region and its theoretical and practical contents. METHODOLOGY: In an educational research survey in 2004, 347 nursing schools were identified. Questionnaires were posted to faculties providing training in TB. Data were compiled in a database with a view to descriptive result analysis. Replies to the questionnaire were received by 32% of the nursing schools contacted. RESULTS: Undergraduate TB teaching is heterogeneous. For training in theory, the principle teaching method is through classes in 102 (91.9%) nursing schools. Practical TB teaching is carried out at the primary care level (89.2%). Teachers update their knowledge through events and internet; little reference is made to manuals. The time devoted to practical TB teaching ranges from 10 to 20 hours, although this is not always included in student training. CONCLUSION: Teaching in TB should go beyond the traditional model that focuses only on biological aspects. It should introduce tools that lead to permanent behavioural change, such as a more human approach and social and psychological aspects, such as living conditions, habits and customs. It should involve new partners, such as families, communities and other health professionals, and identify obstacles within the university. © 2006 The Union.

Planning nursing teaching: Educational purposes and clinical competence

Thinking about nursing education implies articulating this issue with the expressions of theoretical frameworks, from the perspective of a pedagogical aspect that includes both constructivism and competencies. The objective was to characterize, from a longitudinal view, the construction of care competencies that exist in the teaching plans of nursing undergraduate programs. This exploratory-descriptive study used a qualitative approach. Documentary analysis was performed on the nine teaching plans of undergraduate care subjects. The ethical-legal aspects were guaranteed, so that data was collected only after the study had been approved by the Research Ethics Committee. The data evidenced a curriculum organization centered on subjects, maintaining internal rationales that seem to resist summative organizations. Signs emerge of hardly substantial links between any previous knowledge and the strengthening of critical judgment and clinical reasoning. As proposed, the study contributed with reconsiderations for the teachinglearning process and showed the influence of constructivism on the proposal of clinical competencies.

Mathematical decomposition technique applied to the probabilistic power flow problem

In this paper a framework based on the decomposition of the first-order optimality conditions is described and applied to solve the Probabilistic Power Flow (PPF) problem in a coordinated but decentralized way in the context of multi-area power systems. The purpose of the decomposition framework is to solve the problem through a process of solving smaller subproblems, associated with each area of the power system, iteratively. This strategy allows the probabilistic analysis of the variables of interest, in a particular area, without explicit knowledge of network data of the other interconnected areas, being only necessary to exchange border information related to the tie-lines between areas. An efficient method for probabilistic analysis, considering uncertainty in n system loads, is applied. The proposal is to use a particular case of the point estimate method, known as Two-Point Estimate Method (TPM), rather than the traditional approach based on Monte Carlo simulation. The main feature of the TPM is that it only requires resolve 2n power flows for to obtain the behavior of any random variable. An iterative coordination algorithm between areas is also presented. This algorithm solves the Multi-Area PPF problem in a decentralized way, ensures the independent operation of each area and integrates the decomposition framework and the TPM appropriately. The IEEE RTS-96 system is used in order to show the operation and effectiveness of the proposed approach and the Monte Carlo simulations are used to validation of the results. © 2011 IEEE.

Saberes profissionais do professor de matemática: focalizando o professor e a álgebra no ensino fundamental

Pós-graduação em Educação - FCT