The core-collapse supernova (CCSN) mechanism is fundamentally 3D, with instabilities, convection, and turbulence playing crucial roles in aiding neutrino-driven explosions. Simulations of CCNSe including accurate treatments of neutrino transport and sufficient resolution to capture key instabilities remain among the most expensive numerical simulations in astrophysics, prohibiting large parameter studies in 2D and 3D. Studies spanning a large swath of the incredibly varied initial conditions of CCSNe are possible in 1D, though such simulations must be artificially driven to explode. We present a new method for including the most important effects of convection and turbulence in 1D simulations of neutrino-driven CCSNe, called Supernova Turbulence In Reduced-dimensionality, or STIR. Our new approach includes crucial terms resulting from the turbulent and convective motions of the flow. We estimate the strength of convection and turbulence using a modified mixing-length theory approach, introducing a few free parameters to the model that are fit to the results of 3D simulations. For sufficiently large values of the mixing-length parameter, turbulence-aided neutrino-driven explosions are obtained. We compare the results of STIR to high-fidelity 3D simulations and perform a parameter study of CCSN explosion using 200 solar-metallicity progenitor models from 9 to 120 M-circle dot. We find that STIR is a better predictor of which models will explode in multidimensional simulations than other methods of driving explosions in 1D. We also present a preliminary investigation of predicted observable characteristics of the CCSN population from STIR, such as the distributions of explosion energies and remnant masses.