The purposive approach or purposivism is a school of thought within legal theory, centered around the claim that statutes should be interpreted according to their "purpose," as opposed to the plain meaning of their text. Purposivism stands in contrast to textualism, which claims that the "correct" meaning of a statute is based on the plain meaning of the words in the statute book. While textualism is, currently, more culturally "well-known" than purposivism (due to the fact that the late Justice Antonin Scalia was an enthusiastic and vocal proponent of textualism, at least when it suited him), purposivism is probably more widely adopted among practicing judges. However, empirical data would be difficult to generate, because a practicing judge may be a purposivist without actually being aware that there is such a thing as purposivism.
For a concise illustration of the difference between the purposivist and textualism approaches, consider the following hypothetical, attributable to the legal theorist Lon L. Fuller. A city has a park, where many people have complained about cars driving down the pathways, endangering park-goers. In response to this problem, the city enacts an ordinance: "it is unlawful to bring a vehicle into the park." Years later, a group of veterans obtains approval from the city to erect a World War II monument in the park. The monument is a large concrete pillar, atop of which is mounted a World War II tank. The tank has no engine, and is completely fixed to the pillar. So, does the placement of this monument in the park violate the "no vehicles in the park" statute? A hard-line textualist would have to say that it would — the plain language of the statute prohibits any vehicle from being located in the park. A tank is a vehicle, and this tank is inside the park. However, a purposivist would look beyond the statute, to the purpose of the statute — to prevent the endangering of pedestrians walking in the park. Since the tank, affixed to the pedestal, poses no danger to pedestrians, a purposivist would conclude that no statutory violation has taken place.
The debate between textualists and purposivists really is a debate about the political theory underlying separation of powers. Textualists think that when a judge departs from clear and determinate textual language, the judge is "rewriting the law," which violates the principles of Separation of Powers — the legislature, not the judiciary, gets to write the laws. Another common argument that textualists raise is that the "statutory purpose" is something of a legal fiction: for instance, Congress is comprised of hundreds of individual lawmakers, with their own motivations, plans, and agendas. Who's to say that they all had the same "purpose" in mind for a statute when they passed it?
Purposivists tend to counter these arguments by arguing that the lawmakers, when they wrote the law, lacked the time and the foresight necessary to predict every possible situation to which a statute might be applied. Furthermore, applying statutory text in a rigid, unrealistic way can often produce frustrating social outcomes. Moreover, purposivists also tend to view "separation of powers" quite differently than textualists do: whereas textualists tend to conceive of judges more like faithful agents of the lawmakers, purposivists tend to see the role of the judiciary as having more to do with imposing checks and balances on the legislature. Put differently, purposivists acknowledge that sometimes the legislature does a bad job at writing laws, and that such statutes, in order to interact with and regulate the world in a reasonable way, sometimes require a bit of interpretive assistance and "reading between the lines," so to speak.