A new method, response history Monte Carlo (RHMC), has been developed for solving electron transport problems through homogeneous material, and it is more accurate than the conventional method for energies below a few hundred kilo-electron-volts. Since electrons can suffer thousands of collisions and lose only a fraction of their incident energy, analog Monte Carlo (single scatter) is extremely time-consuming. The conventional electron transport method avoids simulating single scattering events by modeling the effect of multiple collisions. This condensed history method requires assumptions that are invalid at lower energies to analytically determine probability distribution functions (pdfs) representing the electron state after multiple collisions. Like the condensed history method, the RHMC method uses an approximate random walk where each step represents the cumulative effect of many collisions. However, the RHMC method is more accurate than the condensed history method since the multiscattered electron state is sampled from pdfs predetermined by analog Monte Carlo calculations instead of approximate analytic solutions.