This research study is for people with a specific type of leukemia called Philadelphia chromosome positive acute lymphoblastic leukemia (the type the patients have). The investigators plan to give you combination of 3 drugs (dasatinib, mitoxantrone, cytarabine) for the first part of the chemotherapy (called Induction). The investigators have previously shown that the combination of mitoxantrone and cytarabine is very effective in your kind of leukemia. The purpose of this study is to establish a safe dose range of dasatinib in combination with this standard induction chemotherapy based on side effects. If possible, the trial will also give us an idea of how well this combination might work in treating your leukemia. Previous studies have shown that dasatinib can produce responses when given alone for your kind of leukemia. By using the dasatinib together with the chemotherapy, the investigators believe that we can kill even more leukemia cells than with either treatment alone. The investigators will initially treat patients with a low dose of dasatinib and monitor for side-effects. If the initial group of patients is able to tolerate this low-dose of dasatinib, then future patients will receive higher doses of dasatinib. Mitoxantrone and cytarabine chemotherapy is the standard therapy at the investigators' institution for the patient's leukemia and it is the combination of dasatinib with this chemotherapy that is new and investigational in this study.