Inclusion Criteria:

* Newly diagnosed, previously untreated: (1) M0 medulloblastoma with > 1.5 cm\^2 residual; (2) M+ medulloblastoma; patients with diffusely anaplastic medulloblastoma are eligible regardless of M-stage or residual tumor

* As of amendment # 2, enrollment of patients with supratentorial PNET has been discontinued
* All patients with M4 disease are not eligible
* A pre-operative magnetic resonance imaging (MRI) scan of the brain with and without contrast is required; NOTE: computed tomography (CT) scans are NOT sufficient for study eligibility

* Post-operative head MRI scan with and without contrast (preferably within 72 hours post-surgery); for patients who undergo stereotactic biopsy only, either a pre or post-operative MRI is sufficient; for patients with M2 and M3 disease, a post-op MRI is strongly encouraged, but not mandatory
* Spinal MRI imaging with and without gadolinium is required within 10 days of surgery if done pre-operatively or within 28 days of surgery if done post-operatively; for posterior fossa tumors, pre-operative MRI scans are preferred
* Lumbar cerebrospinal fluid (CSF) cytology examination must be obtained pre-operatively or within 31 days following surgery; the optimal time for obtaining CSF is prior to surgery or 1-3 weeks following surgery; ventricular CSF (either pre- or post-op) may be used only if a post-operative spinal tap is contraindicated; if a spinal tap is contraindicated and there is no ventricular CSF available, then CSF cytology can be waived for patients with supratentorial tumors or if there is documentation of spinal subarachnoid metastases (M3); patients who are categorized as M1 must have either an intra-operative positive CSF (via lumbar puncture at the end of the procedure) or a positive lumbar CSF obtained > 7 days post-operatively
* Patients must have a Karnofsky performance level of >= 30 for patients > 16 years of age or a Lansky performance scale of >= 30 for patients =< 16 years of age and life expectancy > 8 weeks
* No previous chemotherapy or radiation therapy
* Corticosteroids should not be used during chemotherapy administration as an antiemetic
* Selected strong inhibitors of cytochrome P450, family 3, subfamily A, polypeptide 4 (cytochrome P450 3A4) include azole antifungals, such as fluconazole, voriconazole, itraconazole, ketoconazole, and strong inducers include drugs such as rifampin, phenytoin, phenobarbitol, carbamazepine, and St. John's wort; the use of these drugs should be avoided with vincristine (vincristine sulfate)
* CYP450 3A4 stimulators or inhibitors should be avoided or used with great caution when taking cyclophosphamide; aprepitant should also be used with caution with etoposide or vincristine chemotherapy
* Cisplatin should be used with caution with nephrotoxic drug; aminoglycoside should be avoided or used with caution during or shortly after cisplatin administration and concomitant use with amphotericin B should probably also be avoided; patients receiving cisplatin and other potentially ototoxic drugs such as aminoglycoside or loop diuretics concomitantly should be closely monitored for signs of ototoxicity

* Plasma levels of anticonvulsant agents should be monitored and doses adjusted during therapy with cisplatin
* No other experimental therapy is permitted while on study
* 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:

* 0.8 mg/dL (2 to < 6 years of age)
* 1.0 mg/dL (6 to < 10 years of age)
* 1.2 mg/dL (10 to < 13 years of age)
* 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to < 16 years of age)
* 1.7 mg/dL (male) or 1.4 mg/dL (female) (>= 16 years of age)
* 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; for patients on anti-seizure medications, SGOT (AST) or SGPT (ALT) must be < 5 x ULN
* Absolute neutrophil count (ANC) >= 1,000/uL
* Platelets >= 100,000/uL (untransfused)
* Hemoglobin >= 8 g/dl (may be transfused)
* Female patients who are post-menarchal must have a negative pregnancy test; lactating female patients must agree not to breast-feed while on this trial; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method
* All patients and/or their parents or legal guardians must sign a written informed consent
* All institutional, Food and Drug Administration (FDA), and National Cancer Institute (NCI) requirements for human studies must be met