Definition of the Toulmin Method
Thorough analysis requires us to go beyond the kinds of "gut-level" responses we undergo when reading. To respond analytically to an argument is to do much more than state a basic agreement or disagreement with it; it is to determine the basis of our agreement or disagreement. In other words, analysis is a process of discovering how the argumentative strategies an author employs (the how and why levels of an argument) lead us to respond to the content (the what level) of that argument in the way that we do. Sometimes, too, such analysis can cause us to change our minds about our judgment of how effective or ineffective an argument is.
The Toulmin method, in short, is an effective way of getting to the how and why levels of the arguments we read. It is a type of textual "dissection" that allows us to break an argument into its different parts (such as claim, reasons, and evidence) so that we can make judgments on how well the different parts work together.