President Obama's State of the Union speech this week was -- among other things -- a call to action for strengthening innovation in America. "The first step in winning the future," he said, "is encouraging American innovation.... We need to out-innovate, out-educate, and out-build the rest of the world." And then, "if we want innovation to produce jobs in America and not overseas -- then we also have to win the race to educate our kids."

Without question, there is a link between education and innovation. But the link that typically gets made after that by people speaking about education and innovation -- which President Obama made, as well -- is that in order to get more innovation, we need to focus more on math and science education.

To be clear: Math and science education are important. But the assumptions underlying the focus on math and science, in relation to innovation, are: that innovation is a technical process, or at least takes place most importantly in technical fields; and, that the first step (math and science education) will automatically lead to the second (innovation). Neither of which is necessarily true.

First of all, while scientific and technical innovation is certainly important -- inventing a better solar cell, cancer drug, or information-sorting software -- many of the problems facing the world go beyond the technical sphere. The innovations that led to Seoul being named the "Design Capital of the World" in 2010 had more to do making the city far more "livable," from creating better traffic flow, signage, and even the kind of automatic phone "tree" answering systems citizens encountered when they called city agencies, than it did about any technological innovation. And while a better solar cell would be a huge asset in our search for an alternative to fossil fuels, the problems behind the health-care system mess in the U.S. aren't going to be solved by math or science. Like many of the "sticky problems" in the world, it's a complex, system problem requiring a broader kind of innovative thinking.

Which is, in a way, the point. Innovation experts and consultants stress repeatedly that innovation isn't a matter of subject knowledge. It's about thinking in flexible, integrative, and multidisciplinary ways, across many fields and types of knowledge. It's about being able to synthesize and integrate different perspectives and models; of understanding and taking into account different human, cultural and economic needs, desires, values, and factors and, from all that, glimpsing a new way forward that nobody else managed to see.

And while it's absolutely true that core knowledge in various disciplines is an important piece of that process, a number of educators are beginning to realize that the problem isn't a need for greater focus on math and science. It's a need for better integration among all subject areas, and a need to foster the kind of "integrative" thinking required to make good use of all that knowledge.

Randy Swearer, the current Provost of Philadelphia University, and the former Dean of the Parsons School of Design at The New School in New York, put the challenge this way, in a recent email:

Part of the problem, as I see it, is that you can't teach innovation effectively in the silo structure that is pervasive in academia. The departmental system, process of tenure and promotion, and even physical organization of campuses have traditionally been about specialization in both research and teaching. The liberal arts have been viewed as the 'anti-venom' for this specialization. But this approach compartmentalizes both disciplinary and professional specializations on the one hand, and the liberal arts, on the other. It has also erected a kind of conceptual firewall between these kinds of knowledge. In my view, the dichotomy between specialized studies and general studies is anachronistic, lazy, and intellectually bankrupt. It might have had some basis in an industrial economy, but certainly not now.

Innovation fuses these two modes of knowing and learning. True innovators are adept at taking very specific areas of knowledge (technologies, scientific discoveries, social phenomena, etc.) and constantly reframing them in broader social, cultural, or political contexts. Innovation thinkers also know that in order to find opportunities to act, to make a difference in the world, they must collaborate--and be damn good at it. Higher education has failed miserably at teaching students to deeply and effectively collaborate in order to innovate. Obama's call for innovation, at least in the realm of higher education, implies that the world I work in must radically change--fast.

This point -- that it's the specialization of subject matter, from English and History to math and Engineering, that impedes innovation, more than a lack in any particular subject area -- is made in even greater and stronger detail in an article by William M. Sullivan, a former senior scholar at the Carnegie Foundation for the Advancement of Teaching.

Another advocate of the need for teaching "integrative" thinking in order to foster innovation is Roger Martin, dean of the Rotman School of Management at the University of Toronto. The main web page of the school now touts Rotman as "redesigning business education for the 21st century with a curriculum built around Integrative Thinking." (For a better idea of what "Integrative Thinking" is, at least as Martin describes it, see this short interview he gave on the subject in 2008.)

Fostering innovation, in other words, isn't just a matter of improving the quantity or quality of math and science education. It's a matter of restructuring how we approach and teach all our subjects, from the liberal arts to math, science and engineering. And it means focusing as much on teaching how to combine those fields of knowledge and think in flexible, integrative, and creative ways, as we do on the subject matter itself.

That focus flies in the face of subject-knowledge test scores as a gauge of educational excellence, of course. But that is the Sputnik-level challenge we face, if we really want our talent for innovation to match the increasingly complex, "sticky" problems we need to solve in the century to come.

This post originally appeared in James Fallows's blog.