OBJECTIVES: I. Assess whether a cyclophosphamide-containing combination chemotherapy regimen increases progression-free survival compared to a lomustine-containing regimen in children with newly diagnosed, average-risk medulloblastoma. II. Determine progression-free and overall survival of children treated with craniospinal radiotherapy and local boost radiotherapy for a total dose of 5580 cGy followed by adjuvant lomustine/cisplatin/vincristine vs. cyclophosphamide/cisplatin/vincristine. III. Determine the long-term neurocognitive, endocrinologic, and cardiopulmonary sequelae associated with craniospinal radiotherapy, local boost radiotherapy, and adjuvant chemotherapy in these children, and determine whether replacement of lomustine with cyclophosphamide alters the incidence and degree of sequelae. IV. Determine whether cellular and biologic parameters, including tumor molecular genetic analysis, DNA ploidy, mitotic activity markers, and immunohistochemical analysis, are correlated with progression-free survival, overall survival, and patterns of disease relapse in these patients. V. Evaluate the utility of routine magnetic resonance imaging surveillance studies of the head and spine in detecting subclinical recurrent disease.