Linking probability and statistics in young students' reasoning with chance

This article reports on a study in which third-grade students (8–9 years) were given a degree of agency in conducting chance experiments and representing the outcomes. Students chose their own samples of 12 coloured counters, ensuring all colours were represented. They predicted the outcomes of item selection, tested their predictions, explained the outcomes, quantified their chances of colour selections, and created two representations displaying the probabilities. Children displayed awareness of randomness and variation, together with proportional reasoning, as evident in their identification of one or more colours as having a greater chance of being selected, or equal chances when proportions of colours were equal. Evidence of children’s metarepresentational competence appeared in their creation of two representations to display their probabilistic outcomes, with bar and circle graphs, as well as stacked bars, created. The inclusion of their own forms of inscription revealed a range of probability and statistics understandings. In selecting and justifying their preferred representations for conveying their outcomes, students favoured both bar and circle graphs, with a focus on how accurately, effectively, and efficiently their representation displayed the data, with the importance of the inscriptions highlighted.