Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Atividades experimentais no ensino de biologia em escolas públicas do estado do Rio Grande do Norte, Brasil: caracterização geral e concepção de professores

Recent research has revealed that the majority of Biology teachers believe the practice of experimental activities as a didactical means would be the solution for the improvement of the Biology teaching-learning process. There are, however, studies which signal the lack of efficiency in such practice lessons as far as building scientific knowledge is concerned. It is also said that despite the enthusiasm on the teachers‟ part, such classes are rarely taught in high school. Several studies point pedagogical difficulties as well as nonexistence of a minimal infrastructure needed in laboratories as cause of low frequency in experimental activities. The poor teacher performance in terms of planning and development of classes; the large number of students per class; lack of financial stimulus for teachers are other reasons to be taken into account among others, in which can also be included difficulties of epistemological nature. That means an unfavorable eye of the teacher towards experimental activities. Our study aimed to clarify if such scenario is generalized in high schools throughout the state of Rio Grande do Norte Brazil. During our investigation a sample of twenty teaching institutions were used. They were divided in two groups: in the first group, five IFRN- Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Norte schools. Two of those in Natal, and the other three from the country side. The second group is represented by fifteen state schools belonging to the Natal metropolitan area. The objectives of the research were to label schools concerning laboratory facilities; to identify difficulties pointed by teachers when performing experiment classes, and to become familiar with the conceptions of the teachers in regarding biology experiment classes. To perform such task, a questionnaire was used as instrument of data collecting. It contained multiple choice, essay questions and a semi-structured interview with the assistance of a voice recorder. The data analysis and the in loco observation allowed the conclusion that the federal schools do present better facilities for the practice of experimental activities when compared to state schools. Another aspect pointed is the fact that teachers of federal schools have more time available for planning the experiments; they are also better paid and are given access a career development, which leads to better salaries. All those advantages however, do not show a significantly higher frequency regarding the development of experiments when compared to state school teachers. Both teachers of federal and state schools pointed infra-structure problems such as the availability of reactants, equipments and consumption supplies as main obstacle to the practice of experiments in biology classes. Such fact leads us to conclude that maybe there are other problems not covered by the questionnaire such as poor ability to plan and execute experimental activities. As far as conceptions about experimental activities, it was verified in the majority of the interviewees a inductive-empiric point of view of science possibly inherited during their academic formation and such point of view reflected on the way they plan and execute experiments with students

Influence of visual information on optimal obstacle crossing

Human motion seems to be guided by some optimal principles. In general, it is assumed that human walking is generated with minimal energy consumption. However, in the presence of disturbances during gait, there is a trade-off between stability (avoiding a fall) and energy-consumption. This work analyses the obstacle-crossing with the leading foot. It was hypothesized that energy-saving mechanisms during obstacle-crossing are modulated by the requirement to avoid a fall using the available sensory information, particularly, by vision. A total of fourteen subjects, seven with no visual impairment and seven blind, walked along a 5 meter flat pathway with an obstacle of 0.26 m height located at 3 m from the starting point. The seven subjects with normal vision crossed the obstacle successfully 30 times in two conditions: blindfolded and with normal vision. The seven blind subjects did the same 30 times. The motion of the leading limb was recorded by video at 60 Hz. There were markers placed on the subject's hip, knee, ankle, rear foot, and forefoot. The motion data were filtered with a fourth order Butterworth filter with a cut-off frequency of 4 Hz. The following variables were calculated: horizontal distance between the leading foot and the obstacle at toe-off prior to (DHPO) and after (DHOP) crossing, minimal vertical height from the foot to the obstacle (DVPO), average step velocity (VELOm). The segmental energies were also calculated and the work consumed by the leading limb during the crossing obstacle was computed for each trial. A statistical analysis repeated-measures ANOVA was conducted on these dependent variables revealing significant differences between the vision and non-vision conditions in healthy subjects. In addition, there were no significant differences between the blind and people with vision blindfolded. These results indicate that vision is crucial to determine the optimal trade-off between energy consumption and avoiding a trip during obstacle crossing.

OBSTACLE STEPPING and BODY SCALE MODULATING PARAMETERS

The purpose of this study was to investigate gait spatial parameters at the point of departure, with obstacle heights adjusted to individual body scale. Undergraduate student volunteers (M age=22.4 yr., SD=2.1; 6 women, 1 man) were asked to step once, then cross over an obstacle and stop. This behavior was video recorded to extract kinematic data. The obstacle heights corresponded to high (knee-height) and low obstacles (half the knee-height). Points of departure corresponded to far (length of the lower limb) and close (half the length of the lower limb). The close point of departure influenced the trailing foot's placement ahead of the obstacle as well as step length. The high obstacle influenced the trailing foot's toe clearance. An interaction between factors was observed for leading foot toe clearance. Results indicate that body scale affected the participants' locomotor behavior during the obstacle-avoidance task.

Effects of obstacle height on obstacle crossing in mild Parkinson's disease

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Adaptive Locomotion for Crossing a Moving Obstacle

Crossing moving obstacles requires different space-time adjustments compared with stationary obstacles. Our aim was to investigate gait spatial and temporal parameters in the approach and crossing phases of a moving obstacle. We hypothesized that obstacle speed affects gait parameters, which allow us to distinguish locomotor strategies. Ten young adults walked and stepped over an obstacle that crossed their way perpendicularly, under three obstacle conditions: control-stationary obstacle, slow (1.07 m/s) and fast speed (1.71 m/s) moving obstacles. Gait parameters were different between obstacle conditions, especially on the slow speed. In the fast condition, the participants adopted predictive strategies during the approach and crossing phases. In the slow condition, they used an anticipatory strategy in both phases. We conclude that obstacle speed affects the locomotor behavior and strategies were distinct in the obstacle avoidance phases.

Optic Flow Contribution to Locomotion Adjustments in Obstacle Avoidance

Locomotion generates a visual movement pattern characterized as optic flow. To explore how the locomotor adjustments are affected by this pattern, an experimental paradigm was developed to eliminate optic flow during obstacle avoidance. The aim was to investigate the contribution of optic flow in obstacle avoidance by using a stroboscopic lamp. Ten young adults walked on an 8m pathway and stepped over obstacles at two heights. Visual sampling was determined by a stroboscopic lamp (static and dynamic visual sampling). Three-dimensional kinematics data showed that the visual information about self-motion provided by the optic flow was crucial for estimating the distance from and the height of the obstacle. Participants presented conservative behavior for obstacle avoidance under experimental visual sampling conditions, which suggests that optic flow favors the coupling of vision to adaptive behavior for obstacle avoidance.

Sustainable development: epistemological challenges to science and technology. Report of the workshop Sustainable Development: Epistemological Challenges to Science and Technology""

Includes bibliography

Restricciones al desarrollo sostenido en América Latina y el Caribe y requisitos para su superación = Restrictions on sustained development in Latin America and the Caribbean and the requisites for overcoming them = Contraintes faisant obstacle au développement soutenu de l'Amérique latine et des Caraïbes et conditions requises pour y faire face

Incluye Bibliografía

Influence of visual feedback sampling on obstacle crossing behavior in people with Parkinson's disease

The purpose of the current study was to investigate the role of visual information on gait control in people with Parkinson's disease as they crossed over obstacles. Twelve healthy individuals, and 12 patients with mild to moderate Parkinson's disease, walked at their preferred speeds along a walkway and stepped over obstacles of varying heights (ankle height or half-knee height), under three visual sampling conditions: dynamic (normal lighting), static (static visual samples, similar to stroboscopic lighting), and voluntary visual sampling. Subjects wore liquid crystal glasses for visual manipulation. In the static visual sampling condition only, the patients with Parkinson's disease made contact with the obstacle more often than did the control subjects. In the successful trials, the patients increased their crossing step width in the static visual sampling condition as compared to the dynamic and voluntary visual sampling conditions; the control group maintained the same step width for all visual sampling conditions. The patients showed lower horizontal mean velocity values during obstacle crossing than did the controls. The patients with Parkinson's disease were more dependent on optic flow information for successful task and postural stability than were the control subjects. Bradykinesia influenced obstacle crossing in the patients with Parkinson's disease. © 2013 Elsevier B.V.

Erros e obstáculos: os conteúdos matemáticos do ensino fundamental no processo de avaliação

A presente pesquisa apresenta um sucinto levantamento histórico sobre ‘avaliação’, ‘obstáculos’ - epistemológicos e didáticos - e ‘erros’, com o objetivo de fazer um estudo analítico do desempenho dos estudantes de 5ª a 8ª séries em Matemática, utilizando as respostas dadas em avaliações feitas por quatro grupos de estudantes de uma escola pública de Ensino Fundamental em testes específicos de matemática. A investigação foi desenvolvida em várias fases: na primeira, as respostas foram agrupadas em categorias de questões (a) sem respostas, (b) incompletas, além de (c) certas e (d) erradas, como sugere o tema. Na segunda fase, o objetivo foi (e) tentar desvendar as relações entre conceitos contidos nos erros expressos pelos estudantes. Os resultados da pesquisa apontam para um grande percentual de ‘erros’ relativos aos conceitos presentes em assuntos estudados em séries anteriores, mais acentuados do que os assuntos previstos para a série em que se encontrava o aluno, evidenciando que um conteúdo que não tenha sido bem assimilado pode se constituir em um ‘obstáculo didático’ de caráter coletivo e que se propaga pelas séries posteriores. Deste resultado, é possível afirmar que um ‘obstáculo didático coletivo’, uma vez estabelecido, dificilmente será superado pelos discentes sem uma intervenção docente sistemática que considere tal obstáculo e sua possível superação. Isso faz com que pese sobre os professores de matemática a responsabilidade de assumirem e verem com um olhar diferenciado os erros dos estudantes como aprendizes, com a finalidade de discernir entre o ‘erro eventual’ e o ‘obstáculo didático’ (individual ou coletivo), favorecendo a superação das dificuldades advindas dos “conteúdos passados burocraticamente” que obstaculizam a aprendizagem dos assuntos e temas matemáticos que são objeto de estudo nas séries do ensino fundamental.

O cientificismo como obstáculo à compreensão ético-política da Psicologia

In separating the phenomena of their social, human, and ecological contexts, and by not taking into account intentional and valorative categories, natural-scientific methodologies impede the comprehension of some human activities which include values, chiefly ethical and political. In this context, scientism is the dogmatic and non-thematized acceptance of natural-scientific methods. From this point on, in the context of psychology, the aim of this paper is to demonstrate how scientism can function as an epistemological and methodological obstacle to an ethical and political understanding of psychology. Thus, at first, through reflections based on problems encountered in the literature on the subject, scientism's dogmas and some counterpoints are presented; some of its consequences are addressed, by taking up two examples from current literature - the labeling and the racial interpretations, and, finally, a program of research which deals with these problems is presented as an alternative: critical psychology.