To love the beauty of an equation, what do you need to learn? (Some Observations about a Liberal Education, and Three Roles for Technology)

My last post, summarizing a talk by Michael Roth on the values of liberal education, was the first in a series that are part of my own redefined, re-energized sense of the goals of a college or university education. The post that follows was originally written in 2006.

In 1967, when I was a first-year student in engineering, I took physics. To derive a mathematical equation to describe how a pendulum sways back and forth, the professor began with Newton's Laws. Then he wrote line after line of algebra down the blackboard, each line representing a step in the reasoning. The climax at the bottom of the board: a surprisingly short equation which, the professor told us, was called the Equation of Simple Harmonic Motion. T is the time it takes the pendulum to swing, L is the length of the pendulum, and g represents the strength of gravity. One implication: how long it takes a pendulum to swing depends only on how long the pendulum is, not on how hard you push it.

The professor then pointed out that this equation doesn't just describe the swinging of a pendulum. The same equation, he said, also describes the vibration of a weight suspended between two springs. And it also describes the flow of electricity in a simple electrical circuit that consists of a battery and three elementary components (a resistor, a capacitor, and an inductance, as I recall) linked together with wire. Then the professor leaned forward over the lectern and asked passionately, "Isn't that beautiful?" I was in the second row and I wrote it all down, concluding my notes with the word 'beautiful,' just in case "beautiful" turned up on the next quiz.

Several months later I learned the same equation again, this time in a calculus course, and the lecturer said the same thing. And "beautiful!" I wrote once again in my notes. And I heard "beautiful" down a third time, two years later, in an introduction to electrical engineering.

Two years later, I had become a doctoral student in management at that same university. I shared an office with Lew Erwin, a doctoral student in mechanical engineering. We had been undergraduates together and were good friends.

"So why did you leave engineering?" Lew asked me one day. I was already enough of a manager to answer a question with a question, so I retorted, "Why did you stay in engineering?"

He thought for a moment and then responded, "Well, take something like the Equation of Simple Harmonic Motion. It describes the motion of a pendulum, and a mass vibrating between two springs, and electricity flowing through a simple RLC circuit, and I think that's beautiful!" What happened to me at that moment has happened again every time I've told the story. And it's happening as I write these words. My eyes teared up, my jaw dropped, and I said in awe, "My god, it is beautiful."

Almost twenty years later, I was listening to a couple of physicists at the University of Maryland, Joe Redish and Jack Wilson, talk with one another. By this time I was a program officer with responsibilities to find and then support innovative work in higher education. I'm afraid my attention wandered after a while as they talked with one another. One of them said something like, "Yahda yahda yahda equation of simple harmonic motion." And suddenly all of those things that happened in college came up back to me and for the first time I wondered, "Why was it that three excellent instructors worked so hard to teach me something, and failed completely, when a couple years later a simple remark did the trick?"

So I wrote a little paper for myself, comparing two quite different notions about why this might be so.

1. Maybe I'd matured, in the way that William Perry once described college students maturing. Perry's research suggested that younger students tend to see the world in black and white terms, with the professors the sources of truth and knowledge. After a couple of years of development, they can conceive that there might be more than one truth but, at this point, they have only themselves as a point of reference. "Everyone has a right to his own opinion," is a comment that's a hall of this stage. Only later, often not until after graduation, can students use evidence and their own values to choose among several 'truths,' using evidence reason to take a stand and to act.
2. Or perhaps I'd seen the beauty so easily because, by this time, I'd done research myself and had learned how hard it is to describing something complicated and real in a simple, useful way, and how much harder it is to come up with such a simple, useful conceptual description that would 'work' for three different situations that, on the surface, looked completely different. (By that argument, the way to help freshmen see the beauty is to make sure they do this kind of research when in high school).

I finished the paper unsure of which explanation was more persuasive. It seemed a good agenda for future research.

I sent a copy to Lew Erwin, by now a professor himself at our old university. Next time I saw him, I asked "So which of these two theories is right?"

"You're wrong," he laughed. "Both your theories are wrong. You learned about the beauty of the equation from me because it was me who told you. I'm your friend. That's certainly how I learned it. At nights sometimes, I would sit on the roof of our fraternity with my friend Phil Abbot, looking at the stars and talking about things like this."

Lew went on, "I've been teaching for a while now and I've figured out that a teacher may be able to teach what to think. But only a friend can teach you how to feel about it."

I think there's some truth in all three explanations. College does help some students develop through a very complex process of reorganizing the ways they understand the world. And research -- research that encourages students to develop explanations and then test those explanations -- can help. But Lew was right, too. Our relations and conversations with friends, often outside classrooms, can change how we feel about things

Lew died young. It was the most horrible of ironies: late one night, as he lay sleeping with his wife, his wonderful heart just stopped beating. I told this story about him, me, and the equation of simple harmonic motion at his memorial service. Ever since, I've told it to others, to let them know what Lew taught me. Please pass it on.

PS. Want to learn about the Equation of Simple Harmonic Motion? Here's one of many sources on the Web.

PPS. What does all this have to do with educational uses of technology?   We know that technology, whether that technology is a computer or a piece of chalk, doesn't cause learning.  However, technology can serve the cause of learning by enabling people to learn in ways that might otherwise be difficult or impossible. 

1. So, if you believe the Perry explanation, technology can give students more choices in how to learn, choices that stretch but don't go beyond the student's stage of understanding. That's a strategy that Perry scholars have recommended.
2.  If you think that research experience was the key, computers and the Internet have vastly widened the scope of meaningful research open to undergraduates and students in K-12 schools.
3. And if you think that being with friends is key, consider how to use modern technology to increase the ways in which people can bump into one another, and commune. 

To repeat, none of these uses of technology would compel all students to learn the beauty of that equation. But aren't they three interesting ways to water the seeds we plant?

Beyond the University: Why Liberal Education Matters, Michael Roth

• Liberate
• Animate
• Cooperate
• Instigate

Michael Roth, author of Beyond the University: Why Liberal Education Matters and President of Wesleyan University, used those four terms to summarize historical threads that have combined to justify and shape liberal education.  He explained them in a dynamic and sometimes hilarious keynote at American University's annual teaching day conference last month.  Roth's talk begins at the 57:44 mark of this video segment.

Liberate - as Jefferson and others argued, higher education is a process in which, through inquiry, students should learn who they can become, and what they can do.  This ideal is the opposite of the notion that students should first decide what to do, and then to college in order to become an X as quickly as possible. The latter is something between training and indoctrination, Roth argued, not a liberal (liberating) education.

Animate - As Emerson and others asserted, higher education should make elements of the world come alive for for the student while making the student more alive to that world. Things that had seemed dull, stupid or inscrutable can become marvelous, intimate, and awesome to a more educated human. 

Cooperate - American pragmatists argued that freedom is empty without cooperation and interdependence.  William James said that education is overcoming your blindness about how the world looks to others, why those others think as they do and feel as they do.  Education should attack the pathologies of individualism, not reinforce them. another thread: Jane Addams wanted an education that would prepare a student to make a better world, not to paralyze and distract them by only being able to finding the faults in the acts of others. Don't sacrifice compassionate understanding on the alter of critical thinking.

Instigate -John Dewey, Richard Rorty,and Emerson saw a goal of liberal education as helping students learn to think against the grain, to question and change what has been accepted as normal or obvious.

This is just one of the reasons why I've recently come to see more clearly that education for the workplace should not define higher ed:  potential student (a) picks a job, (b) picks a course of study, (c) succeeds in that course of study, and (d) gets that job).  Instead much of the hard work of higher education- that part that can take several years of work - is to developing the kinds of capabilities described above - capabilities essential for a respondible job, for becoming a citizen, and for becoming even more true to your self.

Interesting opening at LaGuardia CC

Bret Eynon and his colleagues at LaGuardia are highly respected for their work on integrative learning and ePortfolios.  Bret asks for help in spreading the word about an exciting new position now open at the College:

"LaGuardia Community College was recently awarded a prestigious $2.9
million US ED "First in the World" grant. “Project COMPLETA:
Comprehensive Support for Student Success” links digital technology
with exciting pedagogical and co-curricular innovations to build success
for more than 25,000 of LaGuardia’s diverse, low-income students.
COMPLETA links a range of High Impact Practices, including the First
Year Experience, into a transformative, college-wide, integrative
design.   We're inviting applications for a Project Coordinator who will
play a critical role in helping to lead this showcase project.

"We're looking for candidates who have experience with higher education
innovation and project management.  COMPLETA links pedagogy, assessment,
professional development, and technology, including ePortfolio and
learning analytics.  We're seeking a smart, energetic innovator who will
be committed to our students, someone who can learn and grow as an
educational leader as they help to advance our nationally-recognized
change initiatives.  Detailed position description and application
information are both available at
https://www.rfcuny.org/hr/pvn/cgi-bin/show_job.asp?pvn=RMP-1141

"Please share this announcement with anyone you know who you might be
interested and appropriate.  The position is open till filled; resume
review will begin on January 27th.  We will circulate this announcement
now and again after the holidays.   Thanks for any assistance you can
provide."

An Incremental Approach to Improving Learning Outcomes (Better than "Flipping")

Arguably the most important facing higher education is that, for a variety of reasons, the ways students aren't mastering higher order skills (ability to use knowledge to analyze, create, innovate, act wisely and ethically, etc.) nearly as much as needed nor as much as they once did.  Arum and Roksa's Academically Adrift is one persuasive source of empirical evidence on that point.  Just one of many important reasons for declining student achievement: full-time students are investing only about half the time in academic work than they did thirty years ago.

Against this backdrop comes a rush of discussion and confusion about 'flipping courses,' a notion that is sometimes justified as a strategy for improving higher order learning.  I think the term 'flipping' is being used to point to some good changes but, as a label, it's more misleading than helpful.

For example, a recipe for improving learning needs to include more than one way to assure that students learn from their assignments, including doing the kind of work, and enough work, to reorganize their minds.

I recently gave a featured address at the International Conference on College Teaching and Learning on this set of questions, entitled "Bit by Bit: An Incremental Approach to Improving Learning."

Briefly, many elements are needed for a successful, sustainable approach to teaching what is actually college-level learning, including:

1. Reconsidering the course (and academic program) in light of what graduates need to be able to do with the content they've learned, in later courses and after graduation ("backward design");
2. Stealing the students' beer time - assignments and other academic work that are so engaging that students will choose to spend more time studying (this is necessary but not sufficient for students to study more);
3. Leveraging face-to-face opportunities for what can be done best face-to-face;
4. At least four kinds of feedback (what Schön and Argyris called 'learning loops'), including:
• Feedback that keeps students going (farther and deeper), helping them see progress, helping them get unstuck;
• Feedback from that student work going to faculty, to help plan the next class session;
• Feedback to faculty that helps them tweak the design of the course;
• Feedback to faculty that helps all this work seem more rewarding, encouraging those faculty to keep on improving their courses.

I called the talk 'Bit by Bit' because these kinds of improvements don't all need to be done simultaneously or only in this order.  In fact there are even smaller chunks of improvement that can be tried (and supported by the institution), one at a time.

The long term goal, however, is cumulative, major changes in how we teach, how students invest in their own learning, and what our graduates are able to do.

I've recorded a version of the address on YouTube, in two installments. The whole talk is about 50 minutes long:

Part 1: http://youtu.be/Z-1fayCy69k

Part 2: http://youtu.be/VgaFTXCYtzc 

Life experience and academic learning: how should they relate?

George Washington University attracts undergraduates who are exceptionally interested in:

1. Internships, 
2. Service learning, 
3. Study abroad 
4. Undergraduate research.  
5. Student organizations 
6. Athletics.

Should such activities be seen as competing with their academic programs? Or as fuel for academic learning?  

To answer that question, let's start with the goals of an undergraduate education, goals that should span all majors.  Below is one way to categorize the essential learning outcomes of a college education, assembled by the Association of American Colleges and Universities (AAC&U)  through work with hundreds of institutions over the last decade.  (By the way, these are all interlocked; you can't teach much about 'inquiry and analysis' without applying it in one field (e.g., study of science; the arts) or another.

I. Knowledge of Human Cultures and the Physical and Natural World

• Through study in the sciences and mathematics, social sciences,

 humanities, histories, languages, and the arts

Focused by engagement with big questions, both contemporary and enduring

II. Intellectual and Practical Skills, including

• Inquiry and analysis

• Critical and creative thinking

• Written and oral communication 

• Quantitative literacy

• Information literacy

• Teamwork and problem solving 

• Ethical reasoning and action

• Foundations and skills for lifelong learning

Practiced extensively, across the curriculum, in the context of 

progressively more challenging problems, projects, and standards for performance

III. Personal and Social Responsibility, including

• Civic knowledge and engagement—local and global 

• Intercultural knowledge and competence

Anchored through active involvement with 

diverse communities and real-world challenges

IV. Integrative and Applied Learning, including

• Synthesis and advanced accomplishment across general and specialized studies

Demonstrated through the application of knowledge, skills, and responsibilities 

to new settings and complex problems 

Couldn't activities such as undergraduate research, service and the like help strengthen 'intellectual and practical skills, personal and social responsibility, and integrative and applied learning?' And perhaps engaging them with some big questions about  human cultures and the world?

Sounds good, but, in reality, there's a huge gap between formal learning and practical applications. 

Example: Imagine you're looking at your reflection in a bathroom mirror. You see your reflection from the waist up.  

Now imagine yourself backing away from the mirror. (It's a big room). 

As you move further away,  do you see more and more of your body in the mirror until you can see your shoes? the same amount of you? or less and less as you back up until, finally, the top of your head disappears?

When I was first asked that question, I answered incorrectly, a rather alarming outcome considering that:

• I've walked by mirrors about 100,000 times in my long life. So that's 100,000 times when I should have noticed what happens to my reflection when I move toward or away from a mirror.
• It worse than that. When I took high school and college physics, I was taught the law that describes how light reflects from a mirror.  If I'd truly understood that law, I'd have known what happens when backing away from a mirror, even if I'd never seen a mirror. 

Moral of the story:  Academic learning and real world experience, separately, can be weak teachers.   Working with people born in other countries while doing an internship or an undergraduate research project with a faculty member, for example, doesn't guarantee that the student will gain valuable academic insights into how teams work, or into other cultures.

This raises two questions for discussion:
1. How is our institution currently helping students harvest academic value from those six kinds of experience? What's working?
2. What more might we do? 

What do you think? (I'll suggest a few answers of my own in a future post)

Why are Employers Dissatisfied With Universities?

Employers want more from recent college graduates than they're getting.  Take a look at this table summarizing abilities where employers think recent US college and university graduates should be better.  (I'd guess they'd say the same of graduates with master's degrees and Ph.D.s.)

Obviously, institutions have general education programs that are supposed to teach students how to use knowledge in order to think in these ways.  So why do these gaps persist?  All universities need bigger budgets and brighter incoming students. But that doesn't mean that we can't do better with our current students and our current budgets. I think three mistaken notions are interfering with our ability to graduate more capable students.

Mistaken Notion #1: In order to learn to solve unfamiliar complex problems, students must spend more than 90% of their class time and homework time studying what experts have accomplished or discovered in the past.  
Reality: Suppose you wanted to become physically stronger.  What fraction of your workout time should you spend watching exercise videos?  It does comfort many students and faculty when students spend most of their time learning from experts. But to become capable, a student must work on a startlingly large number of problems, and get good coaching as they do so.
Pick a degree program in which you teach.  How's the current balance between learning from experts versus personally doing the work of the field? (One of our Teaching Day speakers, Anders Ericcson, will address this point this coming Friday, October 4.)

Mistaken Notion #2: To develop a capability such as writing, the student should take (only) one course on that capability. 
Reality: Suppose you needed to be able to lift a 100 pound weight tomorrow.  Would it have been sufficient preparation to lift weights intensively in 2010, and then lift nothing until you needed that skill in 2013? Neural science research demonstrates that mental capabilities decay with disuse, just as physical strength does.
That's why some academic programs at institutions like Stanford are now using a 'spiral' approach to designing courses of study.  Crucial capabilities are periodically developed, a bit at a time, in course after course. Each time the student returns to a concept or way of thinking, it's developed further, applied in a new context, and at a greater level of sophistication.

Theory #3: To succeed in X after graduation, study only X.  (For example, if you want to become a successful chemist in the world, it's sufficient to take only chemistry courses, plus direct prerequisites such as physics and mathematics.)  
Reality:   Notice how many of those gaps about which employers are grumbling are at least partly outside the fields where faculty in a department do their research and publishing. For example:

• 89% of employers thought that recent college graduates are too weak in written and oral communications.   (To test whether your students are getting enough practice, coaching and instruction in communication, ask some of your employer alumni to judge a random sample of written and oral communications by students who are soon to graduate.  Our Assessment Office can help you with this.  Do your judges see communications capability as a strength of your students?)
• 81% of employers believed that recent college graduates are too weak in critical thinking and analytic reasoning;  79% were dissatisfied with their ability to apply what they've learned to real world problems; 75% asserted that recent graduates are too weak in complex problem-solving. Real world tasks and jobs usually require knowledge from their major used wisely in combination with other kinds of knowledge.  For example, graduates need to be able to organize in teams, and deal with dysfunctional teams.  How many courses in each degree program offer students practice, instruction and coaching in that area? How would a panel of your alumni rate the skills of current graduates in that area?
• 75% of employers wanted more from recent graduates in ethics. How many courses in your program contribute to a student's ability to reason and act ethically? 

The Association of American Colleges and Universities' LEAP program has been collecting examples of programs that take a different approach to developing these essential learning outcomes (capabilities). And accreditors (and perhaps the Feds) seem to be gradually moving toward paying attention to how we teach and judge (assess) students' development in these areas; the Lumina Foundation's Degree Qualification Profile is intended to be a tool for such assessment and perhaps regulation.

I suspect that university graduates, their employers, and accreditors will soon be paying more attention to what universities like GW are doing to help graduates do well in all these dimensions of a liberal education, no matter major or graduate program they're in.

Do you agree? Would the changes advocated by AAC&U and others be a step forward for your program, or a really bad idea?