The dynamic heterogeneities of glass-forming materials are elucidated for a simple model glass, for which we choose a generalized version of the well-known facilitated kinetic Ising model, originally proposed by Fredrickson and Andersen. The fluctuations within the heterogeneous distribution of reorientation rates are quantified in terms of a rate memory parameter by comparing appropriately chosen two-time and four-time correlation functions. Qualitatively, this parameter expresses after how many relaxation processes a typical relaxator has forgotten its dynamic history. In agreement with most experimental observations the rate memory parameter is close to its minimum value, indicating that the fluctuations within the heterogeneous distribution are on the same time scale as the relaxation processes itself. Upon increasing the ''cooperativity parameter'' in the glass model the rate memory parameter decreases. The same tendency is observed for decreasing temperature. The apparent dependence of the rate memory parameter on cooperativity is rationalized. Furthermore the results are compared with previous simulations of the facilitated kinetic Ising model. (C) 1997 American Institute of Physics.