The modern math movement(s): an essay on how elementary school teachers in Brazil gave meaning to it

The main goal of this paper is to discuss the production of meaning of the Modern Math Movement. The main sources were data available in school archives and interviews with former teachers that we use in order to focus on the diversity of perspectives -that complement it or oppose it-, which comes up when teachers refer to the Movement. Using this process of signification, teachers whether accept it, invalidate it or adapt it to guidelines imposed to them in their teaching activities. We establish a methodology by following the premises of Oral History to gather oral testimonies. The theoretical foundations in which this article is written are the guidelines of Paul Ricoeur's Hermeneutics, John Thompson's Depth Hermeneutics and Bolivar's narrative analysis.

Pure Spinors in AdS and Lie Algebra Cohomology

We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS(5) x S (5) can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described in this language. We also give some algebraic description of the ghost number 2 vertices, which appears to be new. We use this algebraic description to clarify the structure of the zero mode sector of the ghost number two states in flat space, and initiate the study of the vertices of the higher ghost number.

VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The perspective of the teaching of arts projected by H. Gardner and the National Syllabus Parameters - (arts) of elementary school

In a concise way, the article reports part of the Master of Arts dissertation in Music entitled The meaning of the teaching of Arts in H. Gardner's perspective, presented in the IAUNESP [Arts Institute-State of Sao Paulo University] in 2008. Some considerations on the Statutory Law n. 11.769/08 were added to the original text. The produced research had an exploratory nature and a theoretical mark. Some texts by Howard Gardner, by the psychologist Eliane Leao, as well as the text of the National Syllabus Parameters-Art, from the Department of Elementary Education, served as a foundation for this article. The intended aim was to demonstrate to what extent the pedagogical proposition of the Arts Education projected by H. Gardner is similar to the one proposed by the National Syllabus Parameters, and which would the benefits be in this age group of an artistic sensitizing work for the development of the individual's personality.

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

A legislação escolar brasileira e a organização da álgebra no Ensino Fundamental

This work aims to investigate the presence of algebra in Brazilian school legislation, from 1980 to the present day. The research was developed through qualitative research, with phenomenological approach, using hermeneutic procedures for the analyzes of legal texts. Survey data were obtained through a survey about the educational legislation, specifically referring to the elementary school, guided by the question how is the presence of algebra in brazilian school legislation that organizes the elementary school?. In possession of the data, the analyzes were carried out considering the historical, social and political environment in which the laws were introduced, focusing the educational landscape of the time, as well as the movements that influenced the teaching of mathematics in the country. The analysis of each text -law were arranged in a row explanatory tables of a meta understanding about the observed. The meta understanding of the documents was drawn up on the basis of the convergence of analyzes that resulted in nuclear ideas of the law texts. At the end a comprehensive synthesis is presented, outlining the movement in which algebra is inserted in schools, through the educational legislation

Spectrum generating algebra for the pure spinor superstring

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

Comments on two-loop Kac-Moody algebras

It is shown that the two-loop Kac-Moody algebra is equivalent to a two-variable-loop algebra and a decoupled β-γ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity of versions of the corresponding ordinary models and decoupled abelian fields.

A new deformation of W-infinity and applications to the two-loop WZNW and conformal affine Toda models

We construct a centerless W-infinity type of algebra in terms of a generator of a centerless Virasoro algebra and an abelian spin 1 current. This algebra conventionally emerges in the study of pseudo-differential operators on a circle or alternatively within KP hierarchy with Watanabe's bracket. Construction used here is based on a spherical deformation of the algebra W ∞ of area preserving diffeomorphisms of a 2-manifold. We show that this deformation technique applies to the two-loop WZNW and conformal affine Toda models, establishing henceforth W ∞ invariance of these models.

Dynamical algebra of quasi-exactly-solvable potentials

We show that by using second-order differential operators as a realization of the so(2,1) Lie algebra, we can extend the class of quasi-exactly-solvable potentials with dynamical symmetries. As an example, we dynamically generate a potential of tenth power, which has been treated in the literature using other approaches, and discuss its relation with other potentials of lowest orders. The question of solvability is also studied. © 1991 The American Physical Society.

Higher algebras and mesonic spectrum in two-dimensional QCD

We construct composite operators in two-dimensional bosonized QCD, which obey a W∞ algebra, and discuss their relation to analogous objects recently obtained in the fermionic language. A complex algebraic structure is unravelled, supporting the idea that the model is integrable. For singlets we find a mass spectrum obeying the Regge behavior.

Introdução a álgebra no ensino fundamental: o “X” da questão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Levels of phonological awareness, working memory, and lexical knowledge in elementary school children

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)