Reasoning and proof in classroom (9th grade)

This paper is research oriented and pretends to contribute toward giving empirical evidence about how students develop their reasoning and how they achieved to a proof construction in school context. Its main theme is epistemology. It describes the way in which four students in 9th Grade explored a task related with the discovery of symmetry axes in various geometric figures. The proof constructed by students had essentially an explaining function and it was related with the symmetry axes of regular polygons. The teacher’s role in meaning negotiation of the proof and its need is described through illustrative episodes. The paper presents part of a study which purpose is to analyse the nature of mathematical proof in classroom, its role and the nature of the relationship between the construction of a proof and the social interactions. Assuming a social perspective, attention is focussed on the social construction of knowledge and on the structuring resources that shape mathematical experience. The study’s methodology has an interpretative nature. One outcome of the study discussed here is that students develop first a practical understanding with no awareness of the reasons founding mathematical statements and after a theoretical one leading them to a proof elaboration.

Um Estudo de pavimentação do plano utilizando caleidoscópios e o software Cabri Géomètre II

Pós-graduação em Educação Matemática - IGCE

Ensino-aprendizagem de geometria: uma proposta fazendo uso de caleidoscópios, sólidos geométricos e softwares educacionais

Pós-graduação em Educação Matemática - IGCE

Álgebra motivada pela geometria

Pós-graduação em Matemática Universitária - IGCE

Teorema de Pitágoras: algumas extensões/generalizações e atividades com o Software GeoGebra

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Construções euclidianas e o desfecho de problemas famosos da geometria

Construction techniques with ruler and the compasses, fundamental on Euclidean geometry, have been related to modern algebraic theories such as solving equations and extension of bodies from the works by Paolo Ruffini (1765-1822), Niels Henrik Abel (1802-1829) and Evariste Galois (1811-1832). This relation could provide an answer to some famous problems, from ancient Greece, such as doubling the cube, the trisection Angle, the Quadrature of the Circle and the construction of regular polygons, which remained unsolved for over two thousand years. Also important for our purposes are the notions of algebraic numbers, transcendental and the criteria for constructability, of those numbers. The objective of this study is to reconstruct relevant steps of geometric constructions with ruler (unmarked) and the compasses, from the elementary to the outcome buildings, in the nineteenth century, considering those mentioned problems.

The relationship between physical aspects of quality of life and extreme levels of regular physical activity in adults

This study aimed to check for any significant differences in perceived quality of life, specifically aspects of a physical nature, among volunteers who are more physically active and those less physically active in a university community. The sample consisted of 1,966 volunteers in a university community in Brazil. To assess physical activity levels, volunteers responded to the International Physical Activity Questionnaire (IPAQ), and to analyse the perception of quality of life they responded to WHOQOL-bref, which is classified into three groups according to level of physical activity, taking into account the metabolic equivalent index (MET) over a full week. For comparison, consideration was given to the first and third tertiles, respectively, namely groups of more and less active students. The results indicated that individuals who engaged in more physical activity had a more positive perception of quality of life compared to those who were less active in physical aspects related to the ability to work, energy for day-to-day activities and locomotion.

O aluno portador de visão subnormal na escola regular: desafio para o professor?

Purpose:1) To check self-knowledge and needs for orientation among regular class teachers working with low vision students; 2) To gather information to assist the training on visual deficiency of regular class teachers. Methods: A survey was conducted for the academic year of 1999 among those teachers working in public schools, Campinas/SP/Brazil, of which 11 were municipal and 9 state schools, respectively 79.0% and 90.0% of these schools. A self-administered questionnaire was used as data collection instrument. Results: The sample was composed of 50 teachers with a regular class experience averaging 20 years. Most of them, 94.0%, said that they had no specific preparation in the area of low vision. Only 18 teachers declared to have received some kind of information/orientation in order to work with their low vision students and of those only 15 teachers mentioned the kind of orientation received. The whole group of 50 declared interest in receiving information. From the information/orientation requested 66.0% mentioned extended working class materials, 50.0% visual performance and eye disease of their students and 46.0% visual acuity/visual field. Conclusion: It was detected that teachers of regular classes received none or little information about their low vision students but demonstrated interest in its obtention. It was also shown that those teachers are not prepared to work with visually impaired children.

A inclusão da criança com Síndrome de Down na rede regular de ensino: desafios e possibilidades

O estudo teve como objetivo buscar evidências na literatura acerca da inclusão de crianças com Síndrome de Down na rede regular de ensino. Elaboraram-se revisão da literatura e busca dos artigos nas bases de dados PubMed e PsycINFO, utilizando as palavras-chave Down syndrome, schools, mainstreaming (education), education, infant, newborn, adolescent, child e preschool, no período de 1994 a 2007. Selecionaram-se oito artigos e sua análise permitiu a identificação do tema: experiências e recomendações para a inclusão. Os dados desta revisão, em sua maioria provenientes de relatos de experiências, indicaram que os fatores que colaboraram ou dificultaram o processo de inclusão da criança com síndrome de Down na rede regular de ensino relacionaram-se à escola, aos pais e ao professor. Os resultados deste estudo oferecem possibilidades para melhorar o processo de inclusão, apresentam os desafios e ainda apontam a necessidade do desenvolvimento de novas pesquisas, cujos resultados possam ser aplicados na prática.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Using sentinels to detect intersections of convex and nonconvex polygons

We describe finite sets of points, called sentinels, which allow us to decide if isometric copies of polygons, convex or not, intersect. As an example of the applicability of the concept of sentinel, we explain how they can be used to formulate an algorithm based on the optimization of differentiable models to pack polygons in convex sets. Mathematical subject classification: 90C53, 65K05.

EVOLUTION OF DISPARITY BETWEEN THE REGULAR AND VARIANT PHLOEM IN BIGNONIEAE (BIGNONIACEAE)

Premise of the study: The phloem is a plant tissue with a critical role in plant nutrition and signaling. However, little is still known about the evolution of this tissue. In lianas of the Bignoniaceae, two distinct types of phloem coexist: a regular and a variant phloem. The cells associated with these two phloem types are known to be anatomically different; however, it is still unclear what steps were involved in the evolution of such differences. Methods: Here we studied the anatomical development of the regular and variant phloem in representatives of all 21 genera of Bignonieae and used a phylogenetic framework to investigate the timing of changes associated with the evolution of each phloem type. Key results: We found that the variant phloem always appears in a determinate location, between the leaf orthostichies. Furthermore, the variant phloem was mostly occupied by very wide sieve tubes and generally included a higher concentration of fibers, indicating an increase in conduction and mechanical support. On the other hand, the regular phloem included much more parenchyma, more and wider rays, and tiny sieve tubes that resembled terminal sieve tubes from plants with seasonal formation of vascular tissues; these findings suggest reduced conduction and higher storage capacity in the regular phloem. Conclusions: Overall, differences between the regular and variant phloem increased over time, leading to further specialization in conduction in the variant phloem and an increase in storage specialization in the regular phloem.

Treatment of vitamin D deficiency increases lower limb muscle strength in institutionalized older people independently of regular physical activity: a randomized double-blind controlled trial

Aims: To investigate the effects of a 6-month supplementation with calcium and cholecalciferol on biochemical parameters and muscle strength of institutionalized elderly. Methods: This prospective, double-blind, placebo-controlled, randomized trial included Brazilian institutionalized people 6 60 years of age receiving a 6-month supplementation ( December to May) of daily calcium plus monthly placebo (calcium/placebo group) or daily calcium plus oral cholecalciferol (150,000 IU once a month during the first 2 months, followed by 90,000 IU once a month for the last 4 months; calcium/vitamin D group). Fasting blood samples for 25-(OH) D, PTH and calcium determination were collected (n = 56) and muscle tests were performed ( n = 46) to measure the strength of hip flexors (SHF) and knee extensors (SKE) before ( baseline) and after the 6-month intervention ( 6 months). Results: Due to seasonal variations, serum 25( OH) D significantly enhanced in both groups after treatment, but the calcium/vitamin D group had significantly higher 25-(OH) D levels than the calcium/placebo group (84 vs. 33%, respectively; p < 0.0001). No cases of hypercalcemia were observed. While the calcium/placebo group showed no improvement in SHF and SKE at 6 months (p = 0.93 and p = 0.61, respectively), SHF was increased in the calcium/vitamin D group by 16.4% (p = 0.0001) and SKE by 24.6% (p = 0.0007). Conclusions: The suggested cholecalciferol supplementation was safe and efficient in enhancing 25(OH)D levels and lower limb muscle strength in the elderly, in the absence of any regular physical exercise practice. Copyright (C) 2009 S. Karger AG, Basel

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda`s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance. (C) 2010 Elsevier Inc. All rights reserved.