Children creating ways to represent changing situations: On the development of homogeneous spaces

Este artigo investiga criancas criando representacoes para situacoes que mudam com o tempo. Articulamos a distincao entre espacos homogeneos e heterogeneos e refletimos sobre a tendencia que as criancas tem de criar espacos hibridos entre os mesmos. Usando exemplos de sala de aula e de entrevistas, discutimos duas familias de tarefas que parecem facilitar o desenvolvimento de espacos homogeneos: 1) tornar caracteristicas selecionadas diretamente visiveis, ao inves de serem necessarios calculos e passos intermediarios; por exemplo, ser capaz de comparar diretamente diferentes conjuntos de dados combinados em um unico grafico, e 2) explorar componentes imageticos bem definidos, que podem ser usados para tracar graficos, tais como segmentos de reta ou sequenciamento da esquerda para a direita, que sao introduzidos como recurso. Abstract This paper focuses on children creating representations on paper for situations that change over time. We articulate the distinction between homogeneous and heterogeneous spaces and reflect on children’s tendency to create hybrids between them. Through classroom and interview examples we discuss two families of tasks that seem to facilitate children’s development of homogeneous spaces: 1) making selected features directly visible, instead of requiring intermediate steps and calculations; for example, to be able to directly compare different sets of data combined in a single graph, and 2) exploring well-defined figural components that can be used in graphing, such as line segments or sequencing from left to right, that are introduced as a resource. Key-words: Situations; change over time; graph; hybrids; heterogeneous; homogeneous spaces.