Inclusion Criteria:

* Patients must be newly diagnosed and have a confirmed histologic diagnosis of nodular desmoplastic (ND) medulloblastoma or medulloblastoma with extensive nodularity (MBEN) from rapid central pathology screening review; please note: patients with Gorlin syndrome are eligible
* Patient must have negative lumbar cerebrospinal fluid (CSF) cytology (lumbar CSF must be obtained unless medically contraindicated); CSF cytology for staging should be performed preferably no sooner than 14 days post operatively to avoid false positive CSF, ideally, CSF should be obtained between day 14 and day 21 to allow for final staging status before enrollment onto the study; Note: patients with positive CSF cytology obtained prior to 14 days after surgery may have cytology repeated to determine eligibility and final CSF status
* Patients must have:

* Pre-operative cranial magnetic resonance imaging (MRI) (recommended with gadolinium) or pre-operative computed tomography (CT) (recommended with contrast)
* Post-operative cranial MRI with and without gadolinium within 72 hours of surgery
* Spinal MRI pre-op with and without gadolinium or post-op with and without gadolinium preferably within 72 hours of surgery
* Patients must be enrolled on study within 31 days of definitive surgical resection at which time tissue is acquired to determine a diagnosis; patients must be enrolled before treatment begins; the date protocol therapy is projected to start must be no later than five (5) calendar days after the date of study enrollment; patients who are started on protocol therapy on a Phase II study prior to study enrollment will be considered ineligible
* Patients must have a performance status corresponding to Eastern Cooperative Oncology Group (ECOG) scores of 0, 1 or 2; use Lansky for patients =< 16 years of age
* Patients must have a life expectancy of >= 8 weeks
* Patients who are receiving dexamethasone must be on a stable dose for at least 1 week prior to study entry
* Peripheral absolute neutrophil count (ANC) >= 1000/uL
* Platelet count >= 100,000/uL (transfusion independent)
* Hemoglobin >= 10.0 g/dL (may receive red blood cell \[RBC\] transfusions)
* Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70 mL/min/1.73 m\^2 or a serum creatinine based on age/gender as follows:

* 1 month to < 6 months: 0.4 mg/dL
* 6 months to < 1 year: 0.5 mg/dL
* 1 to < 2 years: 0.6 mg/dL
* 2 to < 6 years: 0.8 mg/dL
* Total bilirubin =< 1.5 x upper limit of normal (ULN) for age
* Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) or serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) < 2.5 x upper limit of normal (ULN) for age
* Central nervous system function defined as:

* Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled
* Patients must not be in status, coma or assisted ventilation prior to study enrollment

Exclusion Criteria:

* Patients with metastatic disease by either MRI evaluation (brain and spine) or lumbar CSF cytology are not eligible
* Patients must not have received any prior tumor-directed therapy other than surgical intervention and corticosteroids