Phenomenological perspective on mathematics education

This is a philosophical essay on a phenomenological way to understand and to work out Mathematics Education. Its philosophical grounding is the Husserlian work, focusing on its key word "going to the things themselves" in order to keep us away from the theoretical educational truth, took as the unique one. We assume the attitude of being on the life-world with the students and Mathematics as a field of research and practice that show and express themselves through lived experiences and through language. We assume to be in search of understanding of education, learning and Mathematics, as we take care, consciously, of what we are doing and saying in the same movement of saying and doing it.

Training courses for teachers through the distance learning: practice reports used virtual environment TELEDUC

This paper describes the experiences of long-distance courses, it focused on the continuing education of basic education teachers in all Brazilian territory. Such courses were offered by CECEMCA (Center for Continuing Education in Mathematics Education, Science and Environment), linked to the Universidade Estadual Paulista Julio de Mesquita Filho - Campus de Rio Claro during 15/01/2009 to 30/11/2009. The subjects report to the theme of Education, Geography and Environment, it was organized in four courses: "Introduction to Cartography," Environment and climate change - thinking a new paradigm of sustainable green planet "," Remote Sensing in environmental studies Environment "and" Methodological Alternatives for Inclusive Classroom: Experimenting with visual and hearing impairments". So, we show here, the feasibility and importance of distance learning tools for education, specifically teacher training, based on the results obtained in these courses.

Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses ℳ values of linear functional (integrals over hyperspheres) and is exact for all 2ℳ-harmonic functions, and consequently, for all algebraic polynomials of n variables of degree 4ℳ - 1.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polyno-mial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high. © 2001 American Society of Animal Science. All rights reserved.

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age. © 2004 Elsevier B.V. All rights reserved.

Biomolecular information, brain activity and cognitive functions

Molecular neurobiology has provided an explanation of mechanisms supporting mental functions as learning, memory, emotion and consciousness. However, an explanatory gap remains between two levels of description: molecular mechanisms determining cellular and tissue functions, and cognitive functions. In this paper we review molecular and cellular mechanisms that determine brain activity, and then hypothetize about their relation with cognition and consciousness. The brain is conceived of as a dynamic system that exchanges information with the whole body and the environment. Three explanatory hypotheses are presented, stating that: a) brain tissue function is coordinated by macromolecules controlling ion movements, b) structured (amplitude, frequency and phase-modulated) local field potentials generated by organized ionic movement embody cognitive information patterns, and c) conscious episodes are constructed by a large-scale mechanism that uses oscillatory synchrony to integrate local field patterns. © by São Paulo State University.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Performance of children with learning difficulties in fine motor function and handwriting

This study aimed to compare and characterize the fine, sensory and perceptive function performance and handwriting quality between students with learning difficulties and students with good academic performance. Methods: This study comprised 192 students from 2nd to 4th grades, both genders, whose ages ranged from 7 to 11 years old. The students were distributed into: GI, GII, GIII and GIV, comprising 96 students with learning difficulties, and groups GV, GVI, GVII, GVIII comprising 96 students with good academic performance. The students were submitted to evaluation of fine motor, sensorial and perception functions and handwriting evaluation under dictation. Results: The results showed that the students with learning difficulties, from 1st to 3rd grade, had lower performance on tests of fine motor, sensory and perceptive function, when compared to the students with good academic performance in the same grade; the students from 4th grade, both groups, did not show changes on fine motor, sensory and perceptive function; and only the students of GII showed dysgraphia. Conclusions: the results presented in this study suggest that the qualitative aspects of fine motor, sensory and perceptive skills reflect the integrity and maturity of central nervous system and can probably play an important role in early diagnosis of development disorders and consequently prevent academic disorders such as handwriting performance.

Fundamentos teóricos da atividade de estudo como modelo didático para o ensino das disciplinas científicas

Pós-graduação em Educação para a Ciência - FC

A resolução de problemas no processo ensino-aprendizagem-avaliação de matemática na e além da sala de aula

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O processo de construção de objetos de aprendizagem em cálculo diferencial e integral durante uma atividade de design

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A produção de significados durante e processo de enisno-aprendizagem-avaliação de equações polinomiais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O ensino do conceito de função e conceitos relacionados a partir da resolução de problemas

Pós-graduação em Educação Matemática - IGCE

Aspectos conceituais e instrumentais do conhecimento da prática do professor de cálculo diferencial e integral no contexto das tecnologias digitais

Pós-graduação em Educação Matemática - IGCE

Grupos de estudo como possibilidade de formação de professores de matemática no contexto da geometria dinâmica

Pós-graduação em Educação Matemática - IGCE