The core pedagogic problem considered here is how to effectively teach statistics to physicians who are engaged in a "learning health system" (LHS). This is a special case of a broader issue--namely, how to effectively teach statistics to academic physicians for whom research--and thus statistics--is a requirement for professional advancement. A distinguishing feature of these students is the degree of imbalance between high levels of scientific maturity and relatively low levels of training in mathematics and computer programming. Using a constructivist framework, the curriculum is organized around a set of model cases and an explicit conceptual map of how those cases are related. When teaching LHS physicians, the model cases should be different from those used to teach statisticians: they must be simple, clinically relevant, and developed by example. To create such cases, the discipline of statistics must not only be deconstructed but must also then be reconstructed in a framework that is accessible to its students. This is a principle that should also be generally applicable to teaching statistics to non-statisticians from other disciplines.