Recent studies have highlighted the potential importance of informal inferential reasoning (IIR) in supporting learners' general statistical reasoning. This paper presents a framework based on a retrospective analysis of design research in the context of technology-rich statistical professional learning experiences for high school mathematics teachers. The framework was developed to understand elements of the tasks--identified as statistically, contextually, and/or technologically provocative--that appeared to trigger the teachers' engagement and IIR. Characteristics that make a task provocative and how tasks may interact to impact learning are explored and connected to theories including expectation failure and epistemological obstacles. (Contains 1 table and 6 figures.)