50 resultados para Complexity of mathematics teaching practices

em Repositório Institucional UNESP - Universidade Estadual Paulista "Julio de Mesquita Filho"


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The aim of this paper is to discuss teachers' perceptions of change in their thought and/or practice over time and their perceptions of what kind of experiences or challenges might have influenced those changes. Two mathematics teaching life histories of Brazilian teachers are examined, considering a context of curriculum development in the state of São Paulo, Brazil. Reflection on teachers' thought and practice and interest in their own development, including interest in their own learning of mathematics, seemed to be the most important internal aspects influencing change and development. Close support seemed to be the most important external aspect. The retrospective analysis put a good face on personal change and development. (C) 2000 Elsevier B.V. Ltd. All rights reserved.

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In the 1960s occurred great changes in the general education and, specially in the mathematical teaching, throughout Brazil. Besides the Law Diretrizes e Bases for Education (law 4024/1961), such changes also was occurred by opposite educational movements. In one side, those ones that valorized the popular education and culture and, for the other side, the international agreements between universities and government organs, like SUDENE and MEC, with United States Agency for International Development (USAID). These agreements purposed the cultural alignment. In this article we will expose some of these agreements and their interference in two courses for teachers' education. These teachers taught mathematics for the elementary school, in Rio Grande do Norte.

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This paper presents some outcomes from research based on classroom experiences. The main themes are the use of mirrors, kaleidoscopes, dynamic geometry software, and manipulative material considering their possibilities for the teaching and learning of Euclidean and non-Euclidean geometries.

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We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study - day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects axe due to the nature of the subjects themselves. Further and better study, teaching and economical conditions axe more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

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Mathematics education in Brazil, if we consider what one may call the scientific phase, is about 30 years old. The papers for this special issue focus mainly on this period. During these years, many trends have emerged in mathematics education to address the complex problems facing Brazilian society. However, most Brazilian mathematics educators feel that the separation of research into trends is a theoretical idealization that does not respond to the dynamics of the problems we face. We raise the conjecture that the complexity of Brazilian society, where pockets of wealth coexist with the most shocking poverty, has contributed to the adoption and generation of different strands in mathematics education, crossing the boundaries between trends. At a more micro level, we also raise the conjecture that Brazilian trends in research are interwoven because of the way that Brazilian mathematics educators have experienced the process of globalization over these 30 years. This tapestry of trends is a predominant characteristic of mathematics education in Brazil. © FIZ Karlsruhe 2009.

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Background: The tectum is a structure localized in the roof of the midbrain in vertebrates, and is taken to be highly conserved in evolution. The present article assessed three hypotheses concerning the evolution of lamination and citoarchitecture of the tectum of nontetrapod animals: 1) There is a significant degree of phylogenetic inertia in both traits studied (number of cellular layers and number of cell classes in tectum); 2) Both traits are positively correlated accross evolution after correction for phylogeny; and 3) Different developmental pathways should generate different patterns of lamination and cytoarchitecture.Methodology/Principal Findings: The hypotheses were tested using analytical-computational tools for phylogenetic hypothesis testing. Both traits presented a considerably large phylogenetic signal and were positively associated. However, no difference was found between two clades classified as per the general developmental pathways of their brains.Conclusions/Significance: The evidence amassed points to more variation in the tectum than would be expected by phylogeny in three species from the taxa analysed; this variation is not better explained by differences in the main course of development, as would be predicted by the developmental clade hypothesis. Those findings shed new light on the evolution of an functionally important structure in nontetrapods, the most basal radiations of vertebrates.

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The aim of this paper is to discuss the teachers' need, as autonomous professionals, to evaluate their own pratice. Considering that Descriptive Functional Analysis (DFA) may be a pedagogical method for analysis, implementation, and change of teachers' mathematics teaching practices, the objective of the present research was to teach repertoires compatible with DFA to two mathematics teachers in elementary schools of São Paulo state. When teachers are responsible for evaluation and self evaluation, they recognize themselves as fundamental agents of transformation in education.

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In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

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

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Maltose and glucose fermentations by industrial brewing and wine yeasts strains were strongly affected by the structural complexity of the nitrogen source. In this study, four Saccharomyces cerevisiae strains, two brewing and two wine yeasts, were grown in a medium containing maltose or glucose supplemented with a nitrogen source varying from a single ammonium salt (ammonium sulfate) to free amino acids (casamino acids) and peptides (peptone). Diauxie was observed at low sugar concentration for brewing and wine strains, independent of nitrogen supplementation, and the type of sugar. At high sugar concentrations altered patterns of sugar fermentation were observed, and biomass accumulation and ethanol production depended on the nature of the nitrogen source and were different for brewing and wine strains. In maltose, high biomass production was observed under peptone and casamino acids for the brewing and wine strains, however efficient maltose utilization and high ethanol production was only observed in the presence of casamino acids for one brewing and one wine strain studied. Conversely, peptone and casamino acids induced higher biomass and ethanol production for the two other brewing and wine strains studied. With glucose, in general, peptone induced higher fermentation performance for all strains, and one brewing and wine strain produced the same amount of ethanol with peptone and casamino acids supplementation. Ammonium salts always induced poor yeast performance. The results described in this paper suggest that the complex nitrogen composition of the cultivation medium may create conditions resembling those responsible for inducing sluggish/stuck fermentation, and indicate that the kind and concentration of sugar, the complexity of nitrogen source and the yeast genetic background influence optimal industrial yeast fermentation performance.

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The structural complexity of the nitrogen sources strongly affects biomass production and secretion of hydrolytic enzymes in filamentous fungi. Fusarium oxysporum and Aspergillus nidulans were grown in media containing glucose or starch, and supplemented with a nitrogen source varying from a single ammonium salt (ammonium sulfate) to free amino acids (casamino acids), peptides (peptone) and protein (gelatin). In glucose, when the initial pH was adjusted to 5.0, for both microorganisms, higher biomass production occurred upon supplementation with a nitrogen source in the peptide form (peptone and gelatin). With a close to neutrality pH, biomass accumulation was lower only in the presence of the ammonium salt. When grown in starch, biomass accumulation and secretion of hydrolytic enzymes (amylolytic and proteolytic) by Fusarium also depended on the nature of the nitrogen supplement and the pH. When the initial pH was adjusted to 5.0, higher growth and higher amylolytic activities were detected in the media supplemented with peptone, gelatin and casamino acids. However, at pH 7.0, higher biomass accumulation and higher amylolytic activities were observed upon supplementation with peptone or gelatin. Ammonium sulfate and casamino acids induced a lower production of biomass, and a different level of amylolytic enzyme secretion: high in ammonium sulfate and low in casamino acids. Secretion of proteolytic activity was always higher in the media supplemented with peptone and gelatin. Aspergillus, when grown in starch, was not as dependent as Fusarium on the nature of nitrogen source or the pH. The results described in this work indicate that the metabolism of fungi is regulated not only by pH, but also by the level of structural complexity of the nitrogen source in correlation to the carbon source.

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Biomass and ethanol production by industrial Saccharomyces cerevisiae strains were strongly affected by the structural complexity of the nitrogen source during fermentation in media containing galactose, and supplemented with a nitrogen source varying from a single ammonium salt (ammonium sulfate) to free amino acids (casamino acids) and peptides (peptone). Diauxie was observed at low galactose concentrations independent of nitrogen supplementation. At high sugar concentrations altered patterns of galactose utilisation were observed. Biomass accumulation and ethanol production depended on the nature of the nitrogen source and were different for baking and brewing ale and lager strains. Baking yeast showed improved galactose fermentation performance in the medium supplemented with casamino acids. High biomass production was observed with peptone and casamino acids for the ale brewing strain, however high ethanol production was observed only in the presence of casamino acids. Conversely, peptone was the nitrogen supplement that induced higher biomass and ethanol production for the lager brewing strain. Ammonium salts always induced poor yeast performance. The results with galactose differed from those obtained with glucose and maltose which indicated that supplementation with a nitrogen source in the peptide form (peptone) was more positive for yeast metabolism, suggesting that sugar catabolite repression has a central role in yeast performance in a medium containing nitrogen sources with differing levels of structural complexity.