We have used a numerical treatment to investigate time-dependent phenomena associated with transient crystal nucleation in a model silicate melt. Our approach is the first to explicitly account for both thermodynamic (surface and bulk free energies) and kinetic (equilibrium and nonequilibrium transport) driving forces in molten silicates. The degree of undercooling, transient nucleation behavior, and structural relaxation effects are included in our model. Our model can simulate a variety of natural processes, ranging from the rapid cooling of fragmenting melt during a volcanic eruption to the slow devitrification of a chilled lava flow. To illustrate the utility and generality of our approach, we present numerical solutions for T--t paths that mimic the conditions of experimental studies on the one-component lithium disilicate system <Davis et al., 1997>. Our numerical simulations suggest that the formation of a finite number of crystalline clusters occurs on quench of starting materials. Nucleation is enhanced initially by preexisting nuclei when quenched glasses are subjected to a nucleation treatment. The simulations further suggest that the effect of preexisting nuclei, cooling rate, and nonequilibrium viscosity becomes negligible for longer nucleation treatments (>1000 min). We also provide simulation results for the geologically relevant physical model of the devitrification of a lava flow following burial by a new flow, including the calculation of the crystal size distribution (CSD). This example exhibits several interesting features, indicating multiple nucleation events, negative nucleation rates, and widely disparate final CSDs depending on the position within the flow.