Variation and Expectation for Six-Year-Olds

Watson (2005) made the claim that contrary to the traditional order of introduction in the school curriculum, where measures associated with expectation (e.g. mean) were introduced years before measures associated with variation (e.g. standard deviation), children began to develop the concept of variation before that of expectation. This study explores the primitive understanding of the two ideas by seven 6-year-olds as they worked through four interview protocols devised for older students. The protocols included drawing ten lollies from a container of 100, 50 of which were red, creating a pictograph from concrete materials to show how many books some children had read; interpreting from a movable bar chart with information on how children travel to school; and explaining maximum daily temperatures for their city. These contexts were then used to ask the students to make predictions, for example related to the number of red lollies out of 10, who would most want a book for Christmas, how a new child would come to school, and the highest maximum temperature for a year. Across the contexts, students were asked to create or manipulate representations of information (data). At no time were the words “variation”, “expectation”, or “data” used with the children. Videos, transcripts, and written artefacts were analysed to document demonstration of understanding of the two concepts in relation to data. Evidence of appreciation of variation occurred much more frequently than evidence of appreciation of expectation.