the next flavor of quantitative reasoning?

Until recently I worked at the CSU system office. Like other states, California is wondering about math – who needs it, how much of it, and for what. My own background in the humanities sometimes let me claim an outsider’s objectivity, but most who know me know I happen to like quantitative reasoning.

When you ask which quantitative skills are useful for all college graduates, you get strange answers, that change over time. I find it a helpful trajectory to keep in mind, as we try to guess what’s next.

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Some of our earliest recorded uses of math relate to counting, taxation, and calendars – things that were useful for the emerging technologies of settlement, agriculture, and sharing resources with strangers. These yielded some of our biggest initial breakthroughs, and legacies like separating circles into a number of degrees approximating the number of days in a year.

As astronomy outgrew human eyesight, we measured moving objects with more precision than counting alone could accurately model. We developed calculus surprisingly soon after the telescope’s wide adoption in the 17th century. That knack for representing rates of change that themselves change over time went on to liberate several centuries of engineering.

If there’s a shift in our own era, then people in many public universities and state systems are trying hard to recognize it. Insistence on calculus as the pinnacle of quantitative reasoning – and the particular algebraic skills required to ascend it – has come under recent fire. It turns out that such algebra is beyond the reach of many students, or maybe just of their grade schools’ powers of preparation.

Yet these days more and more people need college, relatively few of whom go on to launch rockets. Weeding them all out over calculus feels like shortchanging both the students and the broader society, which regularly tells the state universities it would like us to produce more graduates.

Which has us wondering whether there are other kinds of quantitative reasoning that might do instead.

If there’s a front-runner in these sweepstakes then it’s statistics. Just as the telescope made fluency in calculus useful, the technological breakthroughs of virtually connected databases – big data – suddenly make ordinary people want to understand and work confidently with large pools of numeric information: how within those oceans to recognize patterns, to roil a record set, to surface significance.

This is no longer just a skill for government economists, the stats counterpart to algebra’s rocket scientist: these days we all need it. For most of us these vast record sets are as close as the phones in our pockets, and we’re expected as citizens and employees to respond intelligently to what they tell us.

agsi-bhi-asset-heatmap-2262449This way of life is becoming a given so quickly that it’s hard to picture today’s college students using the phrase “big data” into mid-career, any more than my generation is likely to say “color TV.” It all is.

So then are we already too late? Should higher ed be peering around the corner past statistics, and bracing ourselves for other kinds of quantitative reasoning? At this moment of transition we have an opportunity to embrace diverse kinds of quantitative reasoning, before we simply replace one hegemony with another.

Lately I’ve started to wonder. One of the detours relatively late along the road to calculus is a branch of math called “optimization,” which seems increasingly indispensable in a world with too many people and a finite store of food, water, and carbon sinks.

We won’t all need this the way we all need statistical fluency, but it is growing, and spilling out of work and into citizenship, a sure sign that it’s positioned for a GE requirement. Your first exposure to it and mine, if we live another decade or two, is likely to come with your first purchase of a drone or self-driving car.

For a couple of centuries this branch of mathematics has been fiddling with the Traveling Salesman Problem, which seeks to calculate the shortest round-trip route comprising a number of destinations. It is surprisingly hard to solve, and above a threshold number of cities may be literally unsolveable. (For a lucid account see the 2013 story in Wired.) This is relevant to more than Fuller brush salesmen: shortest-route calculations could improve the design of computer chips, for example, or of chemically synthesized DNA.

Meanwhile, in an unrelated development, we seem to be crossing an exciting milestone in the reduction of pilot and driver error, which is the reduction of pilots and drivers. Self-flying drones and self-driving cars have raised the prospect – with Detroit automakers at least – of a new kind of vehicle ownership, moving off the one-driver-one-car paradigm and getting to something closer to sharing and swapping, driverless cars going empty down a stretch of road, summoned by the next temporary user.

Think about that for a moment, all those GPS-enabled devices rolled up onto serverfuls of big data, mapped to an infinite combination of nodes on a round trip that never ends, not just calculating that elusive optimization problem but living it. It’s not hard to think of a machine-learning solution to a problem unassisted humans have called unsolvable.

Whether it comes to pass or not, that kind of discipline-crossing quantitative reasoning, dipping into just enough algebraic reasoning, arithmetic, and sheer number sense to support other kinds of math, seems worth building into college for everyone.

Image source:  “Greek Astronomy” at ibiblio.org

 

Alexandria

In antiquity Alexandria was second only to Rome. The north African port was home to a famous library and one of the seven wonders of the world, the lighthouse Pharos. Both are long gone, but you can see some remains of the physical library.

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Visible remnants of the library at Alexendria, Egypt.

That was about all I thought of it until reading Stephen Greenblatt’s Pulitzer prize-winning The Swerve, which recounts the discovery in 1417 of a poem by Lucretius believed lost. This can sound like dry stuff but the story is vividly, almost luridly told, Greenblatt arguing that this is a moment to which the modern world can trace its origin.

the-swerve

His passage on Alexandria fits into a larger discussion of how all that ancient learning got lost in the first place – fire and intolerance directed at the books themselves, but also sheer time, random periods of social unrest, excessive scrolling and unscrolling, and bookworms.

In the center of the city, at a lavish site known as the Museum, most of the intellectual inheritance of Greek, Latin, Babylonian, Egyptian, and Jewish cultures had been assembled at enormous cost and carefully archived for research. Starting as early as 300 BCE, the Ptolomaic kings who ruled Alexandria had the inspired idea of luring leading scholars, scientists, and poets to their city by offering them life appointments at the Museum, with handsome salaries, tax exemptions, free food and lodging, and the almost limitless resources of the library.

Maybe it’s just because I work in one, but this sounds to me a lot like a university, down to the institution of tenure – but a good dozen centuries before the medieval European institutions we usually cite as our beginnings.

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The library at Alexandria as it may have looked.

And these weren’t merely repositories of knowledge: like our own, they were also expected to generate it:

The recipients of this largesse established remarkably high intellectual standards. Euclid developed his geometry in Alexandria; Archimedes discovered pi and laid the foundation for calculus; Eratosthenes posited that the Earth was round and calculated its circumference to within 1 percent; Galen revolutionized medicine. Alexandrian astronomers postulated a heliocentric universe; geometers deduced that the length of a year was 364 1/4 days and proposed adding a “leap day” every fourth year . . .

. . . The Alexandrian library was not associated with a particular doctrine or philosophical school; its scope was the entire range of intellectual inquiry. It represented a global cosmopolitanism, a determination to assemble the accumulated knowledge of the whole world and to perfect and add to this knowledge.

Who knew? Probably many who read this blog, but I found it a surprising and reassuring sign of something old and essentially human.

However bleak things get, or overrun with fire, unrest, and digital bookworms, we apparently feel driven to systematically and cooperatively keep track of what we know, and add to it.

Image credits: pegnsean.net, thelivingmoon.com

news from Bowling Green, KY

wku-campus

Western Kentucky University has a lot in common with the California State Universities that have employed me for around ten years. It’s an access-oriented, regional comprehensive university, it’s proud of its continuing academic quality in the face of unpredictable challenges, and it would like to improve its graduation rates.

To that end, the university leaders are looking at educational practices that engage their students personally in their learning, making them less likely to drop out.

On Friday I paid WKU a visit to learn more, and share what we’re doing in California. Our discussions focused on high-impact practices, and making them work for a greater share of WKU students by identifying a handful that can be offered consistently, equitably, and campus-wide.

For example, like some CSU campuses, WKU may decide to focus on service learning, undergraduate research, and internships in particular. Those few would then be systematically offered, coded into student records, and regularly assessed for impact.

The links in this sentence will take you to my slides from the morning presentation and the afternoon workshop.

For my part, these are points I want to remember from Friday’s meetings:

  1. Everyone is an educator. Although faculty are authors of WKU’s educational programs, I was struck that our meetings were attended in equal parts by advisers, staff, student leaders, administrators – pretty much everyone who interacts with students. I think one value of high-impact practices is that they take advantage of all the ways humans learn; to that end, this full-spectrum participation seems especially important.
  2. Intentional work requires ongoing professional development. WKU’s efforts in this area are led by Jerry Daday, Executive Director of its Center for Faculty Development. His involvement will be crucial: during a closing discussion of the resources needed for scale-up, people said they needed dedicated training for staff and faculty even more than they needed money.
  3. Colleges will want a role. This was the biggest surprise of my visit, that deans and associate deans need to see themselves in the emerging approach, and will be unhappy if they can’t. Because high-impact practices are often connected to the student’s choice of major, departments won’t feel their identities threatened. And at the large scale of the whole university, picking a handful of signature high-impact practices for everyone will strengthen the institution’s identity. But what about the layer in between the campus and its departments – say, the College of Arts and Letters, or the College of Nursing?

I’m not sure what to do about that. A good answer may lie in integrated approaches to curriculum, like the AAC&U GEMs project, or in “meta-majors,” broad clusters of related subjects that students pursue before they know exactly what to major in. Such integrated pathways may reside in a single college, and lend themselves to a distinct set of high-impact practices.

(References to meta-majors are getting more common, but the field doesn’t have a single authority I can link you to. One example I like is from Complete College America, which describes meta-majors in its “Guided Pathways to Success” toolkit. See the PowerPoint here, and especially slide 22.)

Or maybe, as some in the meetings believed, bringing along the colleges just isn’t a problem: we need those administrative units behind the scenes, and not because our students should know where they are on the org chart.

I get it, but I’m not so sure. We may find that more should be done at the college level with high-impact practices, and how they bring students in, and support their decision to stay.

team science part two

This follows an earlier post on team science, which considered the growing share of research problems that don’t seem solvable by lone researchers.

For universities this is unfortunate because our inherited structures of higher education, things like the nested hierarchies of colleges and departments, and rules for faculty promotion and tenure, assume that people’s research, scholarship, and creative activity is compartmentalized and easy to attribute to individuals.

As the frontiers of knowledge get more complicated and interdisciplinary, new research looks less and less like the model we’re set up for.

This week a joint UC-CSU project called CREDITS met at Lake Arrowhead to consider team science. Participants were half faculty and half administrators, and heard from experts in the ways research groups form, function, and sometimes unravel.

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Such retreats are a privilege of jobs like mine, of course – the idea that you leave your daily routines to meet and hash out alternate approaches to the whole machinery is almost dizzyingly rarefied.

But my own purpose was very down to earth: as academic administrators we regularly need to evaluate the work of people in disciplines we don’t know much about, and traditionally we’ve done that by deferring to the opinions of other experts in the same field. So if an entomologist is up for some kind of recognition or promotion, you ask other entomologists if the candidate’s work appears in reputable bug journals.

Such expedients fail in a world of team science, where a breakthrough may be celebrated outside of the faculty member’s home discipline, and result from an effort with dozens, or sometimes thousands, of teammates. How do you know what’s worthwhile, if the seminal understanding in “ant routing” was appreciated less by other ant scientists but more by UPS dispatchers, management theorists, and environmentalists?

This question of appropriate attribution goes beyond trophies and certificates: in tenure cases it’s literally someone’s job at stake.

credits-1So that’s what I was watching for.

On the administrator track I saw presentations from Kyle Lewis, Dan Stokols, Maritza Salazar, and Renee Rottner, whose own work is itself interdisciplinary, serving as examples as well as guidance. They draw from sociology, psychology, mathematics, counseling, and management, among other fields. But what struck me about their research wasn’t just its varied source materials, but also the numerous ways it’s been applied.

That is, each has consulted to private businesses, philanthropy, and multiple branches of the military – pretty much anyone trying to organize collective action. Recognizing their work appropriately isn’t just a matter of checking for citations among other team-science thinkers, or bylines in the Quarterly Journal of Cooperation-ology. On the contrary, their contributions are important precisely because they transcend the boundaries of expertise, and are applied by people in other fields.

I think there are implications in that for higher ed, and that our tenure committees – or for that matter our graduate programs and department curriculum committees – might do a better job of recognizing significant contributions if they included people from other departments, or even from outside of colleges and universities altogether.

We include some external evaluators already, in things like tenure review and grant applications. So what I’m calling for isn’t a difference of paradigm so much as of emphasis. The cases I’ve participated in consider expertise the real litmus test, and use outside triangulation as a kind of corroboration after the fact.

Maybe it’s time we reverse that.