This paper reports on an attempt to involve mathematics teachers, with a limited previous experience in exploring statistical concepts, in the collaborative design of computational tools that can be used for simulating data sets. It explores the constructionist conjecture that the design of such tools will encourage designers as learners to reflect upon the statistical concepts incorporated in the tools under development, since generating data-sets on the basis of different characteristics, such as average, spread, or skewness, necessitates the making explicit of thinking related to these notions and the construction of some sense of random processes. It describes how involvement in the design process involved participants in coming to see distributions as statistical entities, with aggregate properties that indicate how their data is centred and spread.