This paper starts by assessing deficiencies in teaching statistics before summarizing research<br>that has focused on pupils' misconceptions of probability. In contrast, in previous research has explored what<br>pupils of age 11-12 years do know and can construct, given access to a carefully designed environment.<br>These pupils judged randomness according to unpredictability, lack of pattern in results, lack of control over<br>outcomes and fairness, as indeed would experts. However, it was only through interaction with a virtual<br>environment, ChanceMaker that the pupils began to express situated meanings for aggregated long-term<br>randomness. That data is then re-analyzed in order to reflect upon the design decisions that shaped the<br>environment itself. Four main design heuristics are identified and elaborated: testing personal conjectures,<br>building on pupil knowledge, linking purpose and utility, fusing control and representation. It is conjectured<br>that these heuristics are of wider relevance to teachers and lecturers, who aspire to shape the experience of<br>young and naïve probabilists through their actions as designers of tasks and pedagogical settings.
