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Recent curricular reforms increasingly promote the integration of computational thinking into mathematics education through the use of digital technologies. This paper contributes to this debate by examining the role of the program in digital environments for mathematics learning, with particular attention to its varying degrees of visibility. Grounded in a historical and theoretical analysis of computational thinking, the paper conceptualizes a continuum between computers-with-programming-languages and computer-based microworlds, focusing on how mathematical problems are transformed into tasks within specific digital environments. To illustrate the kinds of questions we should ask with regard to the affordances of various programming environments three illustrative vignettes are presented. Their discussion also highlights how they constitute examples of different configurations of program visibility, and argues that while microworlds have broadened access to powerful mathematical explorations, the progressive invisibility of the program risks weakening its mediating role in the development of computational thinking.