Polymer–nanoparticle composites play a vital role in ongoing materials development. The behavior of the glass transition of these materials is important for their processing and applications, and also represents a problem of fundamental physical interest. Changes of the polymer glass transition temperature T_g due to nanoparticles have been fairly well catalogued, but the breadth of the transition and how rapidly transport properties vary with temperature T – termed the fragility m of glass-formation – is comparatively poorly understood. In the present work, we calculate both T_g and m of a model polymer nanocomposite by molecular dynamics simulations. We systematically consider how T_g and m vary both for the material as a whole, as well as locally, for a range of nanoparticle (NP) concentrations and for representative attractive and repulsive polymer–NP interactions. We find large positive and negative changes in T_g and m that can be interpreted in terms of the Adam–Gibbs model of glass-formation, where the scale of the cooperative motion is identified with the scale of string-like cooperative motion. These results provide a molecular perspective of fragility changes due to the addition of NPs and for the physical origin of fragility more generally. We also contrast the behavior along isobaric and isochoric approaches to T_g, since these differing paths can be important to compare with experiments (isobaric) and simulations (very often isochoric). Our findings have practical implications for understanding the properties of nanocomposites and have fundamental significance for understanding the properties glass-forming materials more broadly.