Gilda Guimarães

Conception and alternative conception of mean: a comparative study among teachers and students from basic school

RESUMO O presente estudo analisa concepcoes de estudantes e professores sobre media, tanto aquelas validas quanto as alternativas, com validade para alguns casos. Um teste, em lapis e papel, composto de 3 questoes foi elaborado e aplicado com 287 estudantes e professores brasileiros, dos quais: 54 eram alunos da 4a serie e 47 eram da 5a serie do ensino fundamental, 61 eram estudantes iniciantes e 82 eram estudantes concluintes do curso de pedagogia, e 43 eram professores das series iniciais do ensino fundamental. O teste foi aplicado de forma coletiva, em sala de aula. Excetuando o grupo de professores, todos os grupos tendem a confundir media com adicao dos valores ou com o valor maximo. Os resultados mostram que, apesar da evolucao no entendimento do conceito de media em relacao ao nivel de escolaridade, algumas confusoes ainda sao identificadas entre o grupo de professores.

How Kindergarten and Elementary School Students Understand the Concept of Classification

Teaching statistics has been increasingly valued in recent years. To understand the physical and social world that surrounds us, knowing how to systematize information and/or understand the information matched is fundamental. Thus, knowing how to classify data is a fundamental skill. This article aims to analyse what students between 5 and 9 years old and teachers who teach those grades know and can learn about activities involving classification. To this end, we present the results of three different studies conducted with elementary school children and teachers. The results reveal that children are able to classify from a previously defined criterion and to discover a classification criterion, but experience more difficulties when creating criteria to classify. We believe this may be explained, partially, by the lack of familiarity with this type of activity both in everyday life and at school, as they are generally asked to classify from pre-defined criteria instead of producing their own. However, since kindergarten children are already able to classify in different situations and, most importantly, they are able to learn easily the skills needed to classify, we believe that if they have instruction that leads them to reflect about classification, they learn easily, thereby evidencing the important role of the school.

1, 2: What Did We Do? 3, 4: Let’s Learn Some More! Research on Early Schooling Mathematics Education in Brazil

In this chapter, we describe and analyse studies conducted by Brazilian researchers interested in investigating the processes of teaching and learning mathematics in the early years of schooling. To this end, we discuss the research carried out by Working Group 01, WG01, of the Brazilian Society of Mathematics Education, SBEM, focused on the study of mathematics education in kindergarten and elementary school. We consider the interests of WG01 members in relation to the research themes chosen and the theoretical-methodological approaches adopted to investigate the complex phenomena of mathematical learning. The studies developed by this group, which involve students and teachers, have focused on issues that still receive little attention; on the early-education classes; on content introduced as part of recent curriculum changes in Brazil; and on public policies that aim to improve Brazilian mathematics education. The chapter also highlights the innovations associated with the research conducted by the group, as well as aspects that future research should consider. We hope to contribute to a better understanding on how teaching and learning of mathematics occur, and how it becomes a part of the early years of schooling in Brazil and other parts of the world.

LOS ASPECTOS DIDÁCTICOS BÁSICOS DEL SISTEMA DE NUMERACIÓN DECIMAL EN LOS LIBROS DE TEXTO

This paper is an analysis of the aspects involved in the learning of the decimal numbering system (SND) in the first three years of primary school. The strategies and procedures that constitute the essence of the SND are highlighted, as well as the teaching resources that contribute to this purpose and serve as guidance to teachers when choosing a book for their classrooms. All of them were considered in an instrument that has been applied to the texts of three Spanish publishers and other Brazilian ones that are largely used in both countries. The results show that this item is engaged in more than 72% of the activities, so it provides a quite approximate description of the totality of the texts. A surprising distance from everyday life mathematics and from significant learning was also observed, going against what is universally accepted today.