In planning for long-duration spaceflight, it will be important to accurately model the exposure of astronauts to heavy ions in the Galactic Cosmic Rays (GCR). As part of an ongoing effort to improve heavy-ion transport codes that will be used in designing future spacecraft and habitats, fragmentation cross sections of 28Si have been measured using beams with extracted energies from 290A MeV to 1200A MeV, spanning most of the peak region of the energy distribution of silicon ions in the GCR. Results were obtained for six elemental targets: hydrogen, carbon, aluminum, copper, tin, and lead. The charge-changing cross sections are found to be energy-independent within the experimental uncertainties, except for those on the hydrogen target. Cross sections for the heaviest fragments are found to decrease slightly with increasing energy for lighter targets, but increase with energy for tin and lead targets. The cross sections are compared to previous measurements at similar energies, and to predictions of the NUCFRG2 model used by NASA to evaluate radiation exposures in flight. For charge-changing cross sections, reasonable agreement is found between the present experiment and those of Webber, et al. and Flesch, et al., and NUCFRG2 agrees with the data to within 3 percent in most cases. Fragment cross sections show less agreement between experiments, and there are substantial differences between NUCFRG2 predictions and the data.