The aim of this research is to develop principles for a pedagogy of risk in socio-scientific issues. Risk is challenging to teach because of its contested conceptual basis incorporating epistemic and non-epistemic values, its situated nature and its mathematical basis in probability and statistics. In our project--"Promoting Teachers' Understanding of Risk in Socio-scientific Issues" (TURS)--we have built a set of mature software tools designed through an epistemological analysis of risk and consideration of teaching and learning, as reflected in discussions with teachers. This software provides teachers with tools that enable them to express what they see as the significant issues, giving feedback for them to re-draft their models in the light of the consequences of their decisions. Pairs of science and mathematics teachers have modelled a scenario based on personal decision-making for a surgical intervention. Inductive analysis of teacher dialogue has generated four key findings: teaching risk lends itself to a multi-disciplinary approach; recognition of the multi-dimensional nature of risk can be elicited through engagement with contextualised biological dilemmas; use of executable models promotes discussion of the complexity of risk, and expressive tools can be designed which support coordinated analysis of the multi-dimensional nature of risk. (Contains 2 figures.)