This is a multi-group research study which plans to evaluate the overall progression-free survival of children with average-risk medulloblastoma treated with craniospinal radiation and local boost radiotherapy plus one of two adjuvant chemotherapy regimens differing in the replacement of CCNU by cyclophosphamide. The long-term neurocognitive, endocrinologic and cardiopulmonary sequelae of radiotherapy with adjuvant chemotherapy will be determined, as well as the feasibility of routine surveillance scans to detect sub-clinical recurrent disease. Another objective of this study will be to evaluate the sensitivity of molecular and biochemical techniques to predict progression-free survival and disease relapse. Following surgery, patients will be randomized to receive Regimen A or B of treatment. Both regimens will include 2340 cGy of craniospinal radiation and 3240 cGy of boost radiation directly to the primary tumor with weekly vincristine doses. Six weeks following the completion of radiotherapy, patients will begin eight cycles of maintenance chemotherapy for Regimen A; CCNU, cisplatin, and vincristine or Regimen B; cyclophosphamide, vincristine and cisplatin.