President Barack Obama and Chinese President Xi Jinping in Rancho Mirage, Calif., in 2013. (Evan Vucci/AP)

James Mann is a fellow at the Johns Hopkins School of International Studies and the author of three books about America and China, including “About Face: A History of America’s Curious Relationship With China.”

This summer, President Obama offered a pithy description of the way that inertia sometimes prevents the United States from discarding old ideas that no longer fit current circumstances.

“Sometimes we allow ourselves to be trapped by a certain way of doing things,” he said. “We don’t have to be imprisoned by the past. When something isn’t working, we can — and will — change.”

The president was talking about Cuba. But he should also apply these words with equal force to U.S. policy toward China.

As Washington prepares for a visit from Chinese President Xi Jinping next week, American thinking about China seems stuck on concepts developed in the 1970s, ’80s and ’90s. Since that time, however, China has evolved in ways that few, if any, in Washington saw coming. It has become more assertive overseas, more repressive at home and more mercantilist in its trade practices than was anticipated two decades ago. Back then, American leaders regularly predicted that trade and prosperity would produce a more open China, one that would ease into the existing international system created under U.S. leadership.

Yet even as China moves in new directions, we use the mindset of the past when we talk about it. We continue to draw on ideas dating to Richard Nixon’s opening — even though it seems likely that Nixon himself, were he alive today, would take a much tougher stance toward China than he did in 1972.

Several intellectual traps stand in the way of developing new approaches.

The first is the notion of “engagement.” This concept dates to the period after the 1989 Tiananmen Square massacre, when President George H.W. Bush resisted proposals to cut off all contact with Chinese leaders. Instead, he laid down a policy of engagement — meaning that his administration would meet with Chinese leaders in hopes of changing them. President Bill Clinton perpetuated the use of “engagement,” and it has become a catchphrase for conciliatory, non-punitive approaches to our differences.

But it was never really clear what “engagement” sought, other than meetings and talk. And now, a quarter century after Tiananmen, when no one suggests cutting off contact, “engagement” has lost whatever slight meaning it once held.

Likewise, those who resist any policy change frequently argue that, beginning with Nixon, eight presidents in a row have come around to roughly the same China policies — and that therefore these policies should not be altered. This idea also has a history. Since the Nixon era, several presidents — most notably Ronald Reagan and Clinton — have campaigned promising to change U.S. policy toward China, only to do an about-face in office.

Yet the history isn’t so simple. Obama, for example, actually did a reverse about-face: He set out to avoid conflict, then toughened his approach after his first year in office. More fundamentally, as Obama’s words on Cuba recognize, what a series of predecessors have done does not answer what the United States should do when circumstances change. Nixon himself inherited a China policy carried out by his four immediate predecessors, but rightly reversed the policy.

Then there are the recurrent calls for a “G-2.” It is sometimes proposed that China and the United States should reach a broad strategic accommodation allowing them, together, to guide the affairs of the world. This idea gained strength during the financial crisis, when China appeared to be the economically strongest partner for the United States. More recently, Xi’s repeated proposal for a “new type of major-power relationship” seems a variant of the old calls for a “Group of 2.”

But such formulations overlook larger realities. They implicitly downgrade the interests of U.S. allies and friends (Japan, India, South Korea and the European Union, for starters) who would naturally feel threatened by the notion of the United States and China teaming up without them. They also ignore fundamental differences in values and political systems. Do advocates expect the United States to stay silent on issues such as China’s severe repression of dissent?

The underlying reality is that the congruence of strategic interests that held the United States and China together in the late Cold War no longer exists. And the desire of the U.S. business community for trade and investment in China, which drove U.S. policy in the 1990s, has also been transformed: These days, U.S. businesses tend to come to the White House not to get help in expanding trade but looking for a tougher line on issues such as intellectual property and cybertheft. In this climate, efforts to perpetuate the old U.S.-China relationship seem increasingly out of touch.

The truth is, the United States’ China policy is already changing at the working levels of government and at the grass-roots level, but our overriding ideas about this relationship have not kept pace. Over the next few years, a new U.S. policy toward China is sure to emerge, but it may do so gradually, from the bottom up.

As it does, some simple concepts could be brought back into play. One is the idea that China should be treated by the same rules as other countries. Another is the notion of reciprocity: When China penalizes U.S. businesses or media, the United States should respond with similar limits on Chinese entities. We should develop a more businesslike approach, forsaking the dream that some personalized diplomacy or dramatic communiqué can bring back the special relationship of the past.

The United States and China are in a new era. It’s time to develop policies and ideas that don’t try fruitlessly to replicate the past.