Like her predecessors, Rousseff has insisted on dealing with the United States on equal footing and will not be bossed around. But she has also signaled clearly that she wants a productive relationship with the leading power in the world and has no taste for ideologically tinged disputes.

Obama’s discussions with Rousseff could change the tenor of the conversation in Washington about Brazil.

Part of the Brazil story is structural. With the axis of global power migrating away from the North Atlantic, engaging Brazil on its own terms will increasingly become a necessity on issues that require deep cooperation, such as financial governance, climate change, nuclear proliferation and food security. Moreover, American interests in Latin America will require growing degrees of consultation and cooperation with the leading regional power, Brazil.

Part of the story is about values. As the world struggles to find a common new conception of global order, Brazil is a valuable asset: It sits firmly in the West but it is well equipped by history to engage “the rest.” It is a multiethnic, vibrant democracy and a market economy. Weaving their own narrative of exceptionalism based on stunning social achievements at home, Brazilians relate to the American Dream in ways both profound and inspiring.

Brazil will turn down any proposals to become a formal ally of Washington. But as a major beneficiary of globalization, it will not seek to overturn the existing rules of the game. Rather it will try to adapt them smoothly to a changing world.

Obama’s visit to Brazil also has the potential to transform talk there about the United States. As it rises, Brazil will confront problems that it has found it possible to ignore before — cocaine and criminal networks from the Andes, labor conflict in Africa, China’s currency manipulation. Brazil will also come under increasing pressure both from the developing world and the stronger powers to show where it stands. In such an environment, Brazil will benefit from an effective channel to Washington. Obama’s visit can create one.

The presidential visit is full of symbolism. Breaking the gender and race barriers in their respective countries, Rousseff and Obama illustrate the powers of democracy. The visit will also be full of pragmatism. With both presidents facing major domestic challenges on job creation, education, infrastructure and overall competitiveness, the conversation might reveal some surprising common ground.