Função afim e suas propriedades através da resolução de problemas

Pós-graduação em Matemática em Rede Nacional - IBILCE

Cálculo mental e a produção do conhecimento matemático

This text presents the research developed with students of the 5th year of elementary school at a public school in the city of Taubaté-SP, involved in solving problems involving the Mental Calculation. The read authors show that the Mental Calculation is relevant for the production of mathematical knowledge as it favors the autonomy of students, making it the most critical. Official documents that guide educational practices, such as the Parâmetros Curriculares Nacionais also emphasize that working with mental arithmetic should be encouraged as it has the potential to encourage the production of mathematical knowledge by the student. In this research work Completion of course the tasks proposed to students, who constituted the fieldwork to production data, were designed, developed and analyzed in a phenomenological approach. The intention, the research was to understand the perception of students in the face of situations that encourage them to implement appropriate technical and mental calculation procedures. We analyze how students express and realize the strategies for mental calculation in the search for solution to problem situations

A Resolução de problemas no ensino de matemática

The Troubleshooting is a methodology that stands out in mathematics teaching, it provides a meaningful learning, favoring the intellectual development of the student and the autonomous and critical thinking. In this work an exploratory study on the use of Problem Solving as a teaching strategy. Along it is discussed the importance of problem solving, which is a problem and their differences for years, the types of problems, how to solve a problem and as a teacher should apply problem solving in the classroom choosing problems and exercises adequate and properly questioning the student

Written Solutions of Mathematical Word Problems

In this action research study of my classroom of ten ninth grade algebra students, I investigated how my students expressed written solutions of mathematical word problems. I discovered that my students writing and performance improved as they experienced different strategies to attack problem solving. These experiences helped improve the confidence of my students in their problem solving skills and in their mathematical writing. I also discovered that my teaching style changed, as my students took on more responsibility for their learning. As a result of this research, I plan to implement problem solving activities in all my classrooms next year. I also plan to have my students develop their written communication skills by presenting their solutions to their problem solving activities in writing.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Improving Student Engagement and Verbal Behavior Through Cooperative Learning

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and understanding when compared to individual practice. At the end of the action research, students were questioning each other, and the instructor was answering questions only when the entire group had a question. The third area of data collection focused on what effect heterogeneous cooperative groups had on students’ listening skills when compared to individual practice. In the research I implemented individual quizzes and individual presentations. Both of these had a positive effect on listing in the groups. As a result of this research, I plan to continue implementing the round robin style of in- class practice with heterogeneous grouping and randomly selected individual presentations. For individual accountability I will continue the practice of individual quizzes one to two times a week.

Reasonable or Not? A Study of the Use of Teacher Questioning to Promote Reasonable Mathematical Answers from Sixth Grade Students

In this action research study of my sixth grade mathematics class, I investigated the influence a change in my questioning tactics would have on students’ ability to determine answer reasonability to mathematics problems. During the course of my research, students were asked to explain their problem solving and solutions. Students, amongst themselves, discussed solutions given by their peers and the reasonability of those solutions. They also completed daily questionnaires that inquired about my questioning practices, and 10 students were randomly chosen to be interviewed regarding their problem solving strategies. I discovered that by placing more emphasis on the process rather than the product, students became used to questioning problem solving strategies and explaining their reasoning. I plan to maintain this practice in the future while incorporating more visual and textual explanations to support verbal explanations.

Cálculo mental e a produção do conhecimento matemático

This text presents the research developed with students of the 5th year of elementary school at a public school in the city of Taubaté-SP, involved in solving problems involving the Mental Calculation. The read authors show that the Mental Calculation is relevant for the production of mathematical knowledge as it favors the autonomy of students, making it the most critical. Official documents that guide educational practices, such as the Parâmetros Curriculares Nacionais also emphasize that working with mental arithmetic should be encouraged as it has the potential to encourage the production of mathematical knowledge by the student. In this research work Completion of course the tasks proposed to students, who constituted the fieldwork to production data, were designed, developed and analyzed in a phenomenological approach. The intention, the research was to understand the perception of students in the face of situations that encourage them to implement appropriate technical and mental calculation procedures. We analyze how students express and realize the strategies for mental calculation in the search for solution to problem situations

A Resolução de problemas no ensino de matemática

The Troubleshooting is a methodology that stands out in mathematics teaching, it provides a meaningful learning, favoring the intellectual development of the student and the autonomous and critical thinking. In this work an exploratory study on the use of Problem Solving as a teaching strategy. Along it is discussed the importance of problem solving, which is a problem and their differences for years, the types of problems, how to solve a problem and as a teacher should apply problem solving in the classroom choosing problems and exercises adequate and properly questioning the student

Learning generalization in problem solving by a blue-fronted parrot (Amazona aestiva)

Pepperberg (The Alex studies: cognitive and communicative abilities of gray parrots. Harvard University Press, Cambridge;1999) showed that some of the complex cognitive capabilities found in primates are also present in psittacine birds. Through the replication of an experiment performed with cotton-top tamarins (Saguinus oedipus oedipus) by Hauser et al. (Anim Behav 57:565-582; 1999), we examined a blue-fronted parrot`s (Amazona aestiva) ability to generalize the solution of a particular problem in new but similar cases. Our results show that, at least when it comes to solving this particular problem, our parrot subject exhibited learning generalization capabilities resembling the tamarins`.

Community College Student Participation in Undergraduate Research: An Explanatory Case Study for Faculty and Research Mentors

This study adapted the current model of science undergraduate research experiences (URE's) and applied this novel modification to include community college students. Numerous researchers have examined the efficacy of URE's in improving undergraduate retention and graduation rates, as well as matriculation rates for graduate programs. However, none have detailed the experience for community college students, and few have employed qualitative methodologies to gather relevant descriptive data from URE participants. This study included perspectives elicited from both non-traditional student participants and the established laboratory community. The purpose of this study was to determine the effectiveness of the traditional model for a non-traditional student population. The research effort described here utilized a qualitative design and an explanatory case study methodology. Six non-traditional students from the Maine Community College System participated in this study. Student participants were placed in six academic research laboratories located throughout the state. Student participants were interviewed three times during their ten-week internship and asked to record their personal reflections in electronic format. Participants from the established research community were also interviewed. These included both faculty mentors and other student laboratory personnel. Ongoing comparative analysis of the textual data revealed that laboratory organizational structure and social climate significantly influence acculturation outcomes for non-traditional URE participants. Student participants experienced a range of acculturation outcomes from full integration to marginalization. URE acculturation outcomes influenced development of non-traditional students? professional and academic self-concepts. Positive changes in students? self-concepts resulted in greater commitment to individual professional goals and academic aspirations. The findings from this study suggest that traditional science URE models can be successfully adapted to meet the unique needs of a non-traditional student population – community college students. These interpretations may encourage post-secondary educators, administrators, and policy makers to consider expanded access and support for non-traditional students seeking science URE opportunities.

The utility of rapid participatory appraisal for community assessment, diagnosis, and policy development

The selection of a model to guide the understanding and resolution of community problems is an important issue relating to the foundation of public health practice: assessment, policy development, and assurance. Many assessment models produce a diagnosis of community weaknesses, but fail to promote planning and interventions. Rapid Participatory Appraisal (RPA) is a participatory action research model which regards assessment as the first step in the problem solving process, and claims to achieve assessment and policy development within limited resources of time and money. Literature documenting the fulfillment of these claims, and thereby supporting the utility of the model, is relatively sparse and difficult to obtain. Very few articles discuss the changes resulting from RPA assessments in urban areas, and those that do describe studies conducted outside the U.S.A. ^ This study examines the utility of the RPA model and its underlying theories: systems theory, grounded theory, and principles of participatory change, as illustrated by the case study of a community assessment conducted for the Texas Diabetes Institute (TDI), San Antonio, Texas, and subsequent outcomes. Diabetes has a high prevalence and is a major issue in San Antonio. Faculty and students conducted the assessment by informal collaboration between two nursing and public health assessment courses, providing practical student experiences. The study area was large, and the flexibility of the model tested by its use in contiguous sub-regions, reanalyzing aggregated results for the study area. Official TDI reports, and a mail survey of agency employees, described policy development resulting from community diagnoses revealed by the assessment. ^ The RPA model met the criteria for utility from the perspectives of merit, worth, efficiency, and effectiveness. The RPA model best met the agencies' criteria (merit), met the data needs of TDI in this particular situation (worth), provided valid results within budget, time, and personnel constraints (efficiency), and stimulated policy development by TDI (effectiveness). ^ The RPA model appears to have utility for community assessment, diagnosis, and policy development in circumstances similar to the TDI diabetes study. ^

Analytical study and evaluation results of power optimizers for distributed power conditioning in PV arrays

The use of modular or ‘micro’ maximum power point tracking (MPPT) converters at module level in series association, commercially known as “power optimizers”, allows the individual adaptation of each panel to the load, solving part of the problems related to partial shadows and different tilt and/or orientation angles of the photovoltaic (PV) modules. This is particularly relevant in building integrated PV systems. This paper presents useful behavioural analytical studies of cascade MPPT converters and evaluation test results of a prototype developed under a Spanish national research project. On the one hand, this work focuses on the development of new useful expressions which can be used to identify the behaviour of individual MPPT converters applied to each module and connected in series, in a typical grid-connected PV system. On the other hand, a novel characterization method of MPPT converters is developed, and experimental results of the prototype are obtained: when individual partial shading is applied, and they are connected in a typical grid connected PV array

Competence Monitoring in Project Teams by using Web based portfolio management systems

This paper reports a learning experience related to the acquisition of project management competences. Students from three different universities and backgrounds, cooperate in a common project that drives the learning-teaching process. Previous related works on this initiative have already evaluated the goodness of this multidisciplinary, project-based learning approach in the context of a new educative paradigm. Yet the innovative experience has allowed the authors to define a rubric in order to measure specific competences in project management. The study shows the rubric’s main aspects as well as competence acquisition evaluation alternatives, based in the metrics defined. Key indicators and specific reports obtained from data base fields in the web tool will support this work. As a result, new competences can be assessed, such ones like teamwork, problem solving, communication and leadership. Final goal is to provide an overall competence map to the students at the same time they improve their skills.

The history of technology in education. A comparative study and forecast

Area, launched in 1999 with the Bologna Declaration, has bestowed such a magnitude and unprecedented agility to the transformation process undertaken by European universities. However, the change has been more profound and drastic with regards to the use of new technologies both inside and outside the classroom. This article focuses on the study and analysis of the technology’s history within the university education and its impact on teachers, students and teaching methods. All the elements that have been significant and innovative throughout the history inside the teaching process have been analyzed, from the use of blackboard and chalk during lectures, the use of slide projectors and transparent slides, to the use of electronic whiteboards and Internet nowadays. The study is complemented with two types of surveys that have been performed among teachers and students during the school years 1999 - 2011 in the School of Civil Engineering at the Polytechnic University of Madrid. The pros and cons of each of the techniques and methodologies used in the learning process over the last decades are described, unfolding how they have affected the teacher, who has evolved from writing on a whiteboard to project onto a screen, the student, who has evolved from taking handwritten notes to download information or search the Internet, and the educational process, that has evolved from the lecture to acollaborative learning and project-based learning. It is unknown how the process of learning will evolve in the future, but we do know the consequences that some of the multimedia technologies are having on teachers, students and the learning process. It is our goal as teachers to keep ourselves up to date, in order to offer the student adequate technical content, while providing proper motivation through the use of new technologies. The study provides a forecast in the evolution of multimedia within the classroom and the renewal of the education process, which in our view, will set the basis for future learning process within the context of this new interactive era.