Programação no ensino de matemática utilizando Processing 2: Um estudo das relações formalizadas por alunos do ensino fundamental com baixo rendimento em matemática

Pós-graduação em Educação para a Ciência - FC

Discourse and Cooperative Learning in the Math Classroom

In this action research study of my 6th grade math classroom I investigated the effects of increased student discourse and cooperative learning on the students’ ability to explain and understand math concepts and problem solving, as well as its effects on their use of vocabulary and written explanations. I also investigated how it affected students’ attitudes. I discovered that increased student discourse and cooperative learning resulted in positive changes in students’ attitudes about their ability to explain and understand math, as well as their actual ability to explain and understand math concepts. Evidence in regard to use of vocabulary and written explanations generally showed little change, but this may have been related to insufficient data. As a result of this research, I plan to continue to use cooperative learning groups and increased student discourse as a teaching practice in all of my math classes. I also plan to include training on cooperative learning strategies as well as more emphasis on vocabulary and writing in my math classroom.

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.

Calculators in the Classroom: Help or Hindrance?

In a world where technology is ever present and ever changing, is too much technology at too young of an age detrimental to a child’s educational success? The purpose of this paper is to share the results of a four-month study that focused on the use of calculators in grade eight. This study was conducted in an eighth grade class, in a small kindergarten through twelfth grade school. This paper will share the findings of a study of a classroom in which calculator use was limited and mental computation was emphasized. The main focus of this study was whether or not there would be any improvement in the computation skills of my students and how, or if, their problem solving would be affected. As a result of this research project, I plan to permanently limit calculator use in grades seven and eight, as well as to implement a computational review that will be conducted yearly with all of my classes.

Homework: Is There More To It Than Answers?

In this action research study of my two high school geometry classrooms, I investigated the use of homework. By changing the focus on homework away from the answers to the process involved in getting the answers, I found that students felt more confident, utilized their class time better, and placed more effort on complex problems. Their questions also became more specific and more effective for finding gaps in their understanding. As a result of this research, I plan to change my strategy in the practice of homework. I will give students the answers on multi-step problems to allow them the opportunity to utilize problem solving and critical thinking skills to gain practice in autonomous learning.

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.

All the World's a Stage: Reaching English Language Learners through Drama

The use of drama with language instruction has long been considered a legitimate practice. A recent survey of the literature shows that English Language Learners (ELLs) may have even more to benefit from the use of drama in the classroom. Studies showed an increase in language and problem-solving ability, as well as student self-efficacy that was transferrable across activities. Following an analysis of the literature is a proposed curriculum based on the findings of the researchers cited. This unit is centered on dramatic activities that make use of all four language domains and includes the examination of plays in writing, on the stage, and as a playwright. In the end, students will be asked to combine all of their skills to put on a completely student-created production. An analysis of the factors surrounding the implementation of such a unit follows the unit itself.

Parental Ethnotheories of Child Development: Looking Beyond Independence and Individualism in American Belief Systems

Over the past several decades, the topic of child development in a cultural context has received a great deal of theoretical and empirical investigation. Investigators from the fields of indigenous and cultural psychology have argued that childhood is socially and historically constructed, rather than a universal process with a standard sequence of developmental stages or descriptions. As a result, many psychologists have become doubtful that any stage theory of cognitive or socialemotional development can be found to be valid for all times and places. In placing more theoretical emphasis on contextual processes, they define culture as a complex system of common symbolic action patterns (or scripts) built up through everyday human social interaction by means of which individuals create common meanings and in terms of which they organize experience. Researchers understand culture to be organized and coherent, but not homogenous or static, and realize that the complex dynamic system of culture constantly undergoes transformation as participants (adults and children) negotiate and re-negotiate meanings through social interaction. These negotiations and transactions give rise to unceasing heterogeneity and variability in how different individuals and groups of individuals interpret values and meanings. However, while many psychologists—both inside and outside the fields of indigenous and cultural psychology–are now willing to give up the idea of a universal path of child development and a universal story of parenting, they have not necessarily foreclosed on the possibility of discovering and describing some universal processes that underlie socialization and development-in-context. The roots of such universalities would lie in the biological aspects of child development, in the evolutionary processes of adaptation, and in the unique symbolic and problem-solving capacities of the human organism as a culture-bearing species. For instance, according to functionalist psychological anthropologists, shared (cultural) processes surround the developing child and promote in the long view the survival of families and groups if they are to demonstrate continuity in the face of ecological change and resource competition, (e.g. Edwards & Whiting, 2004; Gallimore, Goldenberg, & Weisner, 1993; LeVine, Dixon, LeVine, Richman, Leiderman, Keefer, & Brazelton, 1994; LeVine, Miller, & West, 1988; Weisner, 1996, 2002; Whiting & Edwards, 1988; Whiting & Whiting, 1980). As LeVine and colleagues (1994) state: A population tends to share an environment, symbol systems for encoding it, and organizations and codes of conduct for adapting to it (emphasis added). It is through the enactment of these population-specific codes of conduct in locally organized practices that human adaptation occurs. Human adaptation, in other words, is largely attributable to the operation of specific social organizations (e.g. families, communities, empires) following culturally prescribed scripts (normative models) in subsistence, reproduction, and other domains [communication and social regulation]. (p. 12) It follows, then, that in seeking to understand child development in a cultural context, psychologists need to support collaborative and interdisciplinary developmental science that crosses international borders. Such research can advance cross-cultural psychology, cultural psychology, and indigenous psychology, understood as three sub-disciplines composed of scientists who frequently communicate and debate with one another and mutually inform one another’s research programs. For example, to turn to parental belief systems, the particular topic of this chapter, it is clear that collaborative international studies are needed to support the goal of crosscultural psychologists for findings that go beyond simply describing cultural differences in parental beliefs. Comparative researchers need to shed light on whether parental beliefs are (or are not) systematically related to differences in child outcomes; and they need meta-analyses and reviews to explore between- and within-culture variations in parental beliefs, with a focus on issues of social change (Saraswathi, 2000). Likewise, collaborative research programs can foster the goals of indigenous psychology and cultural psychology and lay out valid descriptions of individual development in their particular cultural contexts and the processes, principles, and critical concepts needed for defining, analyzing, and predicting outcomes of child development-in-context. The project described in this chapter is based on an approach that integrates elements of comparative methodology to serve the aim of describing particular scenarios of child development in unique contexts. The research team of cultural insiders and outsiders allows for a look at American belief systems based on a dialogue of multiple perspectives.

OPENING REMARKS - THIRD VERTEBRATE PEST CONFERENCE

To open this Third Vertebrate Pest Conference is a real privilege. It is a pleasure to welcome all of you in attendance, and I know there are others who would like to be meeting with us, but, for one reason or another cannot be. However, we can serve them by taking back the results of discussion and by making available the printed transactions of what is said here. It has been the interest and demand for the proceedings of the two previous conferen- ces which, along with personal contacts many of you have with the sponsoring committee, have gauged the need for continuing these meetings. The National Pest Control Association officers who printed the 1962 proceedings still are supplying copies of that conference. Two reprintings of the 1964 conference have been necessary and repeat orders from several universities indicate that those proceedings have become textbooks for special classes. When Dr. Howard mentioned in opening the first Conference in 1962 that publication of those papers would make a valuable handbook of animal control, he was prophetic, indeed. We are pleased that this has happened, but not surprised, since to many of us in this specialized field, the conferences have provided a unique opportunity to meet colleagues with similar interests, to exchange information on control techniques and to be informed by research workers of problem solving investigations as well as to hear of promising basic research. The development of research is a two-way street and we think these conferences also identify areas of inadequate knowledge, thereby stimulating needed research. We have represented here a number of types of specialists—animal ecologists, public health and transmissible disease experts, control methods specialists, public agency administration and enforcement staffs, agricultural extension people, manufacturing and sale industry representatives, commercial pest control operators, and others—and in addition to improving communications among these professional groups an equally important purpose of these conferences is to improve understanding between them and the general public. Within the term general public are many individuals and also organizations dedicated to appreciation and protection of certain animal forms or animal life in general. Proper concepts of vertebrate pest control do not conflict with such views. It is worth repeating for the record the definition of "vertebrate pest" which has been stated at our previous conferences. "A vertebrate pest is any native or introduced, wild or feral, non-human spe- cies of vertebrate animal that is currently troublesome locally or over a wide area to one or more persons either by being a general nuisance, a health hazard or by destroying food or natural resources. In other words, vertebrate pest status is not an inherent quality or fixed classification but is a circumstantial relationship to man's interests." I believe progress has been made in reducing the misunderstanding and emotion with which vertebrate pest control was formerly treated whenever a necessity for control was stated. If this is true, I likewise believe it is deserved, because control methods and programs have progressed. Control no longer refers only to population reductions by lethal means. We have learned something of alternate control approaches and the necessity for studying the total environment; where reduction of pest animal numbers is the required solution to a problem situation we have a wider choice of more selective, safe and efficient materials. Although increased attention has been given to control methods, research when we take a close look at the severity of animal damage to so many facets of our economy, particularly to agricultural production and public health, we realize it still is pitifully small and slow. The tremendous acceleration of the world's food and health requirements seems to demand expediting vertebrate pest control to effectively neutralize the enormous impact of animal damage to vital resources. The efforts we are making here at problem delineation, idea communication and exchange of methodology could well serve as both nucleus and rough model for a broader application elsewhere. I know we all hope this Third Conference will advance these general objectives, and I think there is no doubt of its value in increasing our own scope of information.

AGRICULTURAL BIRD PROBLEMS IN THE SOUTHEAST

Our chairman has wisely asked that we not spend all of our time here telling each other about our bird problems. In the Southeast, our difficulties with blackbirds are based upon the same bird habits that cause trouble elsewhere: they flock, they roost and they eat, generally taking advantage of the readily available handouts that today's agricul¬tural practices provide. Those of us on the receiving end of these de¬predations of course think that damage in our own particular area must be far the worst, anywhere. Because of the location of our meeting place today, perhaps it is worthwhile to point out that a report prepared by our Bureau's Washington office this year outlined the problem of blackbird damage to corn in the Middle Atlantic States, the Great Lakes Region and in Florida, and then followed with this statement--"An equally serious problem occurs in rice and grain sorghum fields of Arkansas, Mississippi, Texas and Louisiana." The report also men¬tions that the largest winter concentrations of blackbirds are found in the lower Mississippi Valley. Our 1963-64 blackbird-starling survey showed 43 principal roosts totaling approximately 100 million of these birds in Virginia, the Carolinas, Georgia, Alabama, Tennessee and Kentucky. We have our own birds during the summer plus the "tourist" birds from up here and elsewhere during the winter, and all of these birds must eat, so suffice it to say that we, too, have some bird problems in the Southeast. I'm sure you're more interested in what we're doing about them. To keep this in perspective also, please bear in mind that against the magnitude of these problems, our blackbird control research staff at Gainesville consists of 3 biologists, 1 biochemist and one technician. And unfortunately, none of us happens to be a miracle worker. I think, though, we have made great progress toward solving the bird problems in the Southeast for the man-hours that have been expended in this re¬search. My only suggestion to those who are impatient about not having more answers is that they examine the budget that has been set up for this work. Only then could we intelligently discuss what might be expected as a reasonable rate of research progress. When I think about what we have accomplished in a short span of time, with very small expenditure, I can assure you that I am very proud of our small research crew at Gainesville--and I say this quite sincerely. At the Gainesville station, we work under two general research approaches to the bird damage problem. These projects have been assigned to us. The first is research on management of birds, particularly blackbirds and starlings destructive to crops or in feedlots, and, secondly, the development and the adaptation of those chemical compounds found to be toxic to birds but relatively safe to mammals. These approaches both require laboratory and field work that is further subdivided into several specific research projects. Without describing the details of these now, I want to mention some of our recent results. From the results, I'm sure you will gather the general objectives and some of the procedures used.

Alternative Tasks for the Teaching and the Learning of functions: analysis of an intervention in the High School

In this paper we focus on the application of two mathematical alternative tasks to the teaching and learning of functions with high school students. The tasks were elaborated according to the following methodological approach: (i) Problem Solving and/or mathematics investigation and (ii) a pedagogical proposal, which defends that mathematical knowledge is developed by means of a balance between logic and intuition. We employed a qualitative research approach (characterized as a case study) aimed at analyzing the didactic pedagogical potential of this type of methodology in high school. We found that tasks such as those presented and discussed in this paper provide a more significant learning for the students, allowing a better conceptual understanding, becoming still more powerful when one considers the social-cultural context of the students.

Modelling Mathematical Reasoning in Physics Education

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.