This is a randomized Phase III trial for children less than 36 months old with high-risk medulloblastoma/PNET. It is designed to determine whether the addition of high dose methotrexate to three cycles of the 4 drug induction backbone (Regimen B) will achieve a higher complete response rate versus three cycles of the 4 drug induction regimen itself (Regimen A). Both of these induction regimens will be followed by three tandem stem cell transplants using the maximum tolerated dose of thiotepa of 10mg/kg/day. After completion of 3 cycles of induction therapy, if complete response has not been attained, then a second surgical attempt at gross total resection is strongly encouraged, if feasible. Although radiation therapy is not a part of this clinical trial, guidelines for radiation therapy are included and the use of radiation therapy should be given serious consideration following the completion of resection.