Carboplatin and Bevacizumab for Recurrent Ependymoma

INCLUSION CRITERIA: * Histologically proven intra-cranial or spinal ependymoma or anaplastic ependymoma. There must be pathologic or imaging confirmation of tumor progression or regrowth. * The patient must have at least 1 block of tissue or 15 unstained slides at a minimum available for central pathology review and molecular profiling of the tissue sample. * All patients must sign an informed consent indicating that they are aware of the investigational nature of this study. Patients must have signed an authorization for the release of their protected health information. * Patients must be greater than or equal to 18 years old. * Patients must have a Karnofsky performance status of \> 60. * Patients must have adequate bone marrow function (white blood cell (WBC) greater than or equal to 3,000/microliter, absolute neutrophil count (ANC) greater than or equal to 1,500/mm\^3, platelet count of greater than to equal to 100,000/mm\^3, and hemoglobin greater than or equal to 10 gm/dl), adequate liver function (Serum glutamic oxaloacetic transaminase (SGOT) \[aspartate aminotransferase (AST) \<92.5 Units/L\] and bilirubin less than or equal to 1.5 mg/dL), and adequate renal function (creatinine \< 1.5 mg/dL and calculated creatinine clearance greater than or equal to 60 cc/min) before starting therapy. Eligibility level for hemoglobin may be reached by transfusion. * Patients must have shown unequivocal radiographic evidence for tumor progression by magnetic resonance imaging (MRI) or computed tomography (CT) scan. * At the time of registration: Patients must have recovered from the toxic effects of prior therapy: greater than or equal to 28 days from any investigational agent, greater than or equal to 28 days from prior cytotoxic therapy, greater than or equal to 14 days from vincristine, greater than or equal to 42 days from nitrosoureas, greater than or equal to 21 days from procarbazine administration, and greater than or equal to 7 days for non-cytotoxic agents, e.g., interferon, tamoxifen, thalidomide, cis-retinoic acid, etc. (radiosensitizer does not count). Any questions related to the definition of non-cytotoxic agents should be directed to the Principal Investigator. * Patients having undergone recent resection of recurrent or progressive tumor will be eligible as long as all of the following conditions apply: * They have recovered from the effects of surgery. * A minimum of 28 days have elapsed from the day of surgery to the day of registration Step 2. * For core or needle biopsy, a minimum of 7 days must have elapsed prior to registration Step 2. * Residual disease following resection of recurrent ependymoma is not mandated for eligibility into the study. To best assess the extent of residual disease post-operatively, a CT/ MRI should be done no later than 96 hours in the immediate post-operative period or at least 4 weeks post-operatively, within 14 days prior to consent. If the within 96-hour after surgery scan is more than 14 days before consent the scan needs to be repeated. If the steroid dose is increased between the date of imaging and consent, a new baseline MRI/CT is required on a stable steroid dosage for at least 5 days. * Patients must have failed prior radiation therapy\* and must have an interval of greater than or equal to 42 days from the completion of radiation therapy to study entry. Note: Patients with an indication for craniospinal radiotherapy (i.e., extensive leptomeningeal disease) but have refused palliative craniospinal radiotherapy are eligible. * Patients with prior therapy that included interstitial brachytherapy or stereotactic radiosurgery must have confirmation of true progressive disease rather than radiation necrosis based upon either positron emission tomography (PET) or Thallium scanning, MR spectroscopy, or surgical/pathological documentation of disease. * Women of childbearing potential must have a negative B (Beta)-human chorionic gonadotropin (HCG) pregnancy test documented within 14 days prior to registration. * Women of childbearing potential and male participants agree to practice adequate contraception. EXCLUSION CRITERIA: * Patients with any significant medical illnesses that in the investigators opinion cannot be adequately controlled with appropriate therapy or would compromise the patients ability to tolerate this therapy. * Patients with a history of any other cancer (except non-melanoma skin cancer or carcinoma insitu of the cervix), unless in complete remission and off of all therapy for that disease for a minimum of 3 years are ineligible. * Patients with an active infection or serious intercurrent medical illness. * Patients found to be pregnant/breast feeding. Patients must not be pregnant because animal studies show that carboplatin and bevacizumab are teratogenic * Patients with any disease that will obscure toxicity or dangerously alter drug metabolism. * Patients who have received prior therapy with bevacizumab, or related drugs (previous therapy with carboplatin is allowed). * Inadequately controlled hypertension (defined as systolic blood pressure \>150 millimeters of mercury (mmHg) and/or diastolic blood pressure \> 100 mmHg) despite antihypertensive medication. * New York Heart Association (NYHA) Grade II or greater congestive heart failure. * History of myocardial infarction or unstable angina within 12 months prior to Day 1. * History of stroke or transient ischemic attack. * Significant vascular disease (e.g., aortic aneurysm requiring surgical repair or recent peripheral arterial thrombosis) within 6 months prior to Day 1. * History of hemoptysis (greater than or equal to 1/2 teaspoon of bright red blood per episode) within 1 month prior to Day 1. * Evidence of bleeding diathesis or significant coagulopathy (in the absence of therapeutic anticoagulation). (To be eligible, Prothrombin time/international normalized ratio (prothrombin time (PT) international normalized ratio (INR)) should be \< 1.4 for patients not on warfarin.) * Patients receiving full-dose anticoagulants therapy (e.g., warfarin or Low-molecular-weigh (LMW) heparin) and does not meet both of the following criteria: * No active bleeding or pathological condition that carries a high risk of bleeding (e.g., tumor involving major vessels or known varices). * In-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or on a stable dose of low molecular weight heparin. * Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to Day 1 of treatment or anticipation of need for major surgical procedure during the course of the study. * Core biopsy or other minor surgical procedure, excluding placement of a vascular access device, within 7 days prior to Day 1. * History of abdominal fistula or gastrointestinal perforation within 6 months prior to Day 1. * Serious, non-healing wound, active ulcer, or untreated bone fracture. * Proteinuria as demonstrated by a urine protein:creatinine (UPC) ratio greater than or equal to 1.0 at screening, or Urine dipstick for proteinuria greater than or equal to 2+ (patients discovered to have greater than or equal to 2+ proteinuria on dipstick urinalysis at baseline should undergo a 24 hour urine collection and must demonstrate less than or equal to 1g of protein in 24 hours to be eligible). * Known hypersensitivity to any component of bevacizumab. * Patients has current active hepatic or biliary disease (with exception of patients with Gilbert's syndrome, asymptomatic gallstones, or stable chronic liver disease per investigator assessment).