Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students' learning while also building on students' contributions. In this article we propose a framework that aims to deepen understanding about the role of instructional engineering in helping reduce the uncertainties of ambitious teaching, particularly with regard to the design and implementation of task sequences that target academically important but difficult-to-achieve learning goals. To illustrate the framework, we consider how instructional engineering helped reduce the uncertainties in enacting ambitious teaching to advance university and secondary students' understanding of what counts as "proof" in mathematics.