The dominant emphasis in current e-learning practice is instructionist in character. This is surprising when we consider that the benefits of constructionism as a learning paradigm are so widely recognised. Moreover, though the constructionist philosophy can be seen as applying to activities that are not necessarily computer based (such as bricolage and concept mapping), its modern application in educational technology has been closely linked with computer use. In particular, Papert’s work on mathematical education through Logo programming has both informed the original concept of constructionism and been a major influence over subsequent computer-based constructionist developments. This chapter questions whether — despite these precedents — traditional computer programming paradigms are well suited for the constructionist educational agenda. It argues that other approaches to computer model building, such as those based on spreadsheet principles, are in fact much better aligned to the objectives of constructionism. Building on this basis, it proposes that more effective computer support for the constructionist perspective can potentially be offered by Empirical Modelling (EM). Adopting this approach demands a reappraisal of the relationship between the formal and the informal with relevance for education, mathematics, and computing.