Constructionism can be a powerful framework for teaching complex content to novices. At the core of constructionism is the suggestion that by enabling learners to build creative artifacts that require complex content to function, those learners will have opportunities to learn this content in contextualized, personally meaningful ways. In this paper, we investigate the relevance of a set of approaches broadly called "educational data mining" or "learning analytics" (henceforth, EDM) to help provide a basis for quantitative research on constructionist learning which does not abandon the richness seen as essential by many researchers in that paradigm. We suggest that EDM may have the potential to support research that is meaningful and useful both to researchers working actively in the constructionist tradition but also to wider communities. Finally, we explore potential collaborations between researchers in the EDM and constructionist traditions; such collaborations have the potential to enhance the ability of constructionist researchers to make rich inferences about learning and learners, while providing EDM researchers with many interesting new research questions and challenges.