Innovation has become an all-purpose tonic, the default prescription for every pain associated with the retrenching American economy. Whatever the problem — slower growth, global competition, fewer well-paying jobs — innovating, we are told, is the solution.

Now a pair of MIT professors has dissected the practice of innovating and found it to be generally misunderstood. In “Innovation: The Missing Dimension,” published by Harvard University Press in October, Richard K. Lester and Michael J. Piore argue that much of the innovation effort in American business goes into solving problems but relatively little into identifying possibilities and opportunities in the marketplace.

“We are in danger of learning the wrong lessons about innovation,” Lester and Piore warn in the book. “As a result, we risk neglecting those capabilities that are the real wellsprings of creativity in the US economy — the capacity to integrate across organizational, intellectual, and cultural boundaries, the capacity to experiment, and the habits of thought that allow us to make sense of radically ambiguous situations and move forward in the face of uncertainty.”

While innovation is typically seen as a single process, Lester and Piore break it into two parts: problem solving and interpretation. Companies focus constantly on the former, which tends to be a rational step-by-step process. If they talk about the latter at all, it is under the guise of “listening to the customer,” a less well-defined discipline.

Much of the book is devoted to case studies of product development in fields ranging from cellphones to medical equipment to bluejeans. Successful innovators ”created spaces where they could have open-ended conversations” about technology and markets, Lester, who directs MIT’s Industrial Performance Center, said in an interview.

One of their chief strengths was the ability to interpret a situation. “We compare the interpretive manager to the host of a cocktail party,” Lester said. “She decides who to invite, she brings people together, she begins conversations, and she tries to keep the conversations going. That’s radically different from what the problem-solving manager does, which is often to get a product out the door.”

A more sophisticated understanding of these conversations, and their role in innovation, could be a boon for Boston, a world center of technology, research, and expertise of all stripes. “When companies come here, they’re locating in an environment that is intellectually rich and full of people who are asking questions,” noted Mitchell Adams, executive director of the Massachusetts Technology Collaborative.

The collaborative runs the Massachusetts Nanotechnology Institute, devoted to bringing together people from science, business, finance, and academia who are interested in the field. “There is no club or bar you can go to to talk about nanotechnology,” Adams said.

In the past, much of the conversation about technologies and their possibilities took place at corporate research centers, such as Bell Labs and Xerox PARC, that pioneered new technology and sparked the innovation that drove the great economic expansion of the 1990s. But corporations increasingly have been reining in their basic research and concentrating on applied research. As a result, more of the responsibility for innovation has shifted to research-oriented universities like Massachusetts Institute of Technology.

Smart companies seek to plug into campus technology dialogues by taking part in collaborative research projects, said Lester, who agrees the Boston area should be able to capitalize on the trend.

“In this area,” he said, “we have institutions that are already some of the most important public spaces in our economy for this interpretive process: the universities, the teaching hospitals. Companies are coming here not because they want to solve problems but because they want to be in on the conversation in these interpretive spaces.”