What is meant by "dual federalism," and how is it different from "cooperative federalism"?
Federalism is a system of government where the power is distributed across different levels. In the United States, we have a system with two levels, a federal or national government, and underneath that state governments.  Dual federalism is a period between 1819 and 1936 where there was a clear separation of powers between the federal government and the state governments.  During this time the “national government left the states largely to their own devices in major policy areas” which included “education, transportation, and civil rights, among others”.  
During the dual federalism period, two important cases set the stage for the next time period called “cooperative federalism” (1936-present).  The first case was McCulloch v. Maryland which cited the Constitution's  supremacy clause and implied powers of the federal government in a verdict that prohibited the state of Maryland from taxing a federal bank.  The second case was Gibbons v. Ogden which cited the power of the federal government to regulate interstate commerce giving Gibbons a monopoly to ferry people from New Jersey to New York.  These two cases were used by the Federal government during the New Deal as precedent to enable cooperative federalism which is “an intermingling of power, policy, and resources among the national and state governments”. The “government established programs providing federal funding in areas that were traditionally the exclusive domains of the state, such as health, transportation, education, employment, and poverty relief”.  This differs from dual federalism in that we now have a mixing and sharing of powers between the state and national governments.