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."

How regional teaching institutions can compete more successfully

Tom Carey has just written a provocative blog post in Inside Higher Ed, describing how regional four-year institutions and two-year institutions might reshape and market themselves as teaching institutions of distinctive value in their area.  I'd summarize the message as 1) identify learning outcomes of distinctive value in your region (to some degree, the less universal the better) and that can be linked to some teaching/learning strength in which you're particularly strong (preparing for work in a certain type of job, after preparation by a co-op program with numerous, fascinating placements in that same field, for example). His strategy is much more detailed than this, but it's still a quick read.  Once you've read it, let us know what you think!

What does "Learning Outcome" mean? No, really....

"Confusors" are terms such as "teaching," "assessment," and "interactive,"  each of which has  several widely-held, conflicting definitions. When clashing definitions remain hidden, bad things can happen, needlessly.

For example, imagine a group of faculty hotly arguing the consequences of 'technology in classrooms.'  Perhaps some have a lecture hall in mind, others a seminar room, and still others are thinking about the library because, for them, "classroom" is a synonym for course. Meanwhile some are assuming 'technology' only means computers, a problem if some of the others are imagining cell phones or laboratory demonstration equipment.

Similarly it's dangerous to draw many conclusions from an article about what's wrong with MOOCs if the author didn't explicitly select one of the many accepted, conflicting definitions of "MOOC".

"Learning outcome" is also a confusor, I now realize. Earlier today I read this sentence in a report addressed to provosts and other senior administrators about the value of a new teaching strategy, " ...72% of institutions showed improved student learning outcomes."

Nowhere in this report is the term 'learning outcome' defined. That made me more conscious that most of the time when I hear "learning outcome" used in conversation, it's left undefined.  Set aside the question of whether that 72% improvement was measured in a single course, or across many degree programs.  There are at least three widely-used definitions of 'learning outcomes':

1. Good test results or grades at the end of a unit or a semester. Often good marks can be achieved through memorization or applying routine problem solving skills in a routine way.  Teaching to the test is one way to improve this kind of learning outcome. Cramming for exams is another.  "Here today, gone tomorrow," is what many faculty and educational researchers agree happens to much of this kind of learning.
2. Reduction in failure and dropout rates from a course.  This definition overlaps #1, but sometimes a student might drop a class for reasons unrelated to learning. 
3. Learning that lasts. In this definition, achieving a learning outcome means that students developed a capability and then showed they could use it in a later course, for example.  This definition implies that, if a student has achieved a learning outcome during college, they can use it in graduate school or a job the next year.

So the report I was reading asserted that " ...72% of institutions showed improved student learning outcomes"  What does the author mean? From here on, "learning outcome" joins my list of hot buttons - confusors that can cause real trouble.

PS. This web site describes many more confusors. Do you have a favorite?

I'm starting a new role

I've spent the last few months thinking hard about exactly what I wanted to do next.  A vision of the kinds of improvement that were possible in the long term for university teaching, and a path for getting there began to take shape. (An earlier version of some of those ideas was tested in this blog, in entries like this one.

Once I realized that working with those ideas was my goal, the next challenge was to find a place to put these notions to the test (somewhere near Silver Spring, MD where Leslie and I have long lived) and to find a good team to work with. 

The great news is that there was such a place and they were looking for someone with ideas and a track record like mine. 

So I'm happy to announce that I've just accepted the position of Assoc. Director for Research and Evaluation at the University System of Maryland's Center for Academic Innovation, working with MJ Bishop. The System has a delightful range of distinctive institutions as members, which should provide a good fire in which to cook my half-baked ideas.  And it gives me a chance to give back to the state where we've lived for 35 years.  I'll be starting in my new role on Sept. 22.

Limits to Interactive MOOCS (?)

In a recent Wired article, "The MOOC Completion Conundrum: Can 'Born Digital' Fix Online Education,", Dror Ben-Naim points to the potential of more interactive MOOCs to provide a more individualized, interactive educational experience.

Experience with interactive tutorials over the last half century suggests at least two questions to ask about any new strategy of this type:

1) How many person hours does it take to create, and debug, an hour's worth of student experience?  Historically that figure has been "hundreds to thousands," and the time requirement has changed less than one might guess over the decades. That's partly because the standards for the user experience have increased as the technologies have improved. But an even bigger factor has been the need for human judgment to assess how satisfactory each branch will be for various kinds of learners (learners with different preconceptions, learners with different reading skills, etc. etc.)

2) How many person hours does it take for a faculty member to decide whether this package offers good experience for all students?  Textbooks are generally comparatively easy to judge because tables of contents and thumbing through the book make triage easy. Instructional videos generally take much more time because faculty may feel the need to watch virtually the whole video, or video sequence, before their students see it. Interactive software can take even more time when instructors, unfamiliar with the package, want to see how it reacts to students with varied preparation, misconceptions, etc.  It's that same problem of judging the branching that makes development so expensive.

3) How soon might changes in underlying technology make the user interface seem old-fashioned, or interfere with the operation of the software itself? In that event, where will the money and effort come from to update the software? 

Interactive tutorials have often demonstrated impressive educational results, compared with less interactive ways of teaching the same content or skills.  However most such packages have died without ever progressing to Version 2.0 because there was no satisfactory answer to at least one of those three questions.

So, if you hear about a new technology for creating highly interactive and individualized instruction, it's wise before you leap to ask those three questions.

Impact of Online Teaching Upon Campus Teaching

Some months ago, with help from Camille Funk and Patty Dinneen of the Teaching & Learning Collaborative, I surveyed faculty from George Washington University who had worked with instructional designers to develop and teach online courses during the summer over the last 15 years. Our research question: had this experience influenced their subsequent teaching on campus. In a word: it did.

Faculty who had been through the program once were influenced in many dimensions of their teaching.  For example these kinds of changes in campus teaching were reported by at least half of the respondents:

My syllabus, instructions and directions for students are more clear and complete.

Development tools I learned about for summer I now sometimes use for my campus course materials.

I've re-used or adapted materials from my online course.

I use images, animations or video.

I've started designing a campus course or assignment by first figuring out what students should be able to do as a result.

I assign online discussion among my students.

Faculty who had participated two or more times were influenced much more.

I've heard anecdotal reports of such influence for years but we got a 53% response rate. Of those respondents, 85% reported influence on their campus teaching in at least one dimension.

Here's my full report and the survey that was sent to faculty.  Feel free to use or adapt the survey; if you're doing so, I'd appreciate it if you'd let me know (ehrmannsteve at gmail.com)

Note: One reason this program of developing summer courses has lasted 15 years, attracting both faculty participation and GW resources to support them, was that teaching online summer courses made money for both the university and for the participating faculty. As faculty interest in developing summer courses increased, GW had the incentive to hire more instructional designers to help them.  In effect, improving teaching on campus was being rewarded (via the intervening step of improving teaching, and increasing revenue, online).  That fact suggests a policy I'll describe in my next post.

Propagating Teaching Improvement by making it More Rewarding for Faculty and the Institution

For teaching techniques that are needed institution-wide, seek opportunities where those techniques can be incorporated in programs that can earn the institution, the department and the individual faculty some extra money (e.g., summer courses, new degree programs)  (Sharing revenue with faculty isn't automatic, but, to provide incentives for widespread teaching improvement, it's essential.)

For example, at almost every university and college, it's important to find ways to encourage students to invest more time and effort in assignments outside class.  Today's full-time students spend only about half the amount of time on assignments they did thirty years ago, and about half the time that faculty think students need to spend, according to Arum and Roska in Academically Adrift.

One of several mutually reinforcing ways to do that is by quizzing students online in ways that require them to reason about what they've been assigned to learn. These online quizzes and assignments can both (a) provide instructors with advance notice about students' readiness for class, (b) enable instructors to prompt students about what else they need to do to prepare for class, (c) enable instructors to call on students by name when they get to class, and (d) encourage students to be (even) more ready for the next class meeting.  If there is faculty-staff agreement about the power and flexibility of this use of online preparation of students (and instructors) for upcoming classes, then it makes sense to strongly encourage any new revenue-generating courses and degree programs to include that practice. Once faculty try out the technique in that new degree program or summer course, they may well begin using the approach in their other courses as well.  As these pioneering faculty use the technique, other faculty may follow suit. And the more often students see it in classes, the more likely they will be to accept it as a normal feature of studying.

Make sense? or not?

Example of a flipped course

Mike Moore, Prof. of Economics and International Affairs at George Washington University, has problems with asthma. So this past semester he taught two courses to GW students (mostly) from Santa Fe, New Mexico.  He did it by prerecording his lectures, posting them on YouTube, conducting live online office hours using Blackboard Collaborate, and visiting GW monthly for 90 minute face-to-face sessions with his students.

Mike didn't jump from traditional teaching to this strategy in one huge leap.

Some years ago, he taped some lectures on background material so that students could study and review them as often as they liked.  A few years after that, he tried GW LectureCapture - a system for automatically recording all class sessions and making recordings available only to students in that class. He'd worried that students wouldn't come to class if recordings were available but (as with every other faculty member I've found who's used a system like this), his worries were unfounded.  Attendance was unaffected.

Recently, he realized it would be better for him to spend some time in New Mexico and got permission from Mike Brown, his Dean, to teach a hybrid course - a mix of online and face-to-face instruction.

Early on he decided to use YouTube so that anyone could see his lectures.  He then took a look at examples of classes on YouTube. Some had pretty poor audio or picture quality; he knew he wanted to do better.

To create the lectures with HD quality, he pointed the camera of an iPad at a whiteboard.  He was no longer limited to the normal time constraints of a campus class. So he created about 75 small lectures, averaging 15 minutes in length. Some was material that would normally have been given in class but he also added additional material.  This was the big investment.  "I hope I can do this again because creating those videos took maybe 400 hours of work," he commented: if he teaches the course again, he can reuse some or all of those videos. He likes this approach to creating chunks of video because he can edit them if he likes. That removes the pressure to do each one perfectly the first time.

Even though the material is abstruse, the videos are popular. His videos had already been viewed over 65,000 times and over 60% of those views were requested from outside the United States.

Mike also created some interactive homework online, using Blackboard: multiple choice questions that provide hints to students if their initial answer is incorrect. There are also four online quizzes each semester: multiple choice and only a small fraction of the class grade.

For his live online office with Blackboard Collaborate, Mike uses a tablet so that he can draw. Those sessions are recorded so students can take part live and/or review them later.

Monthly Mike comes to GW for live, 90-minute sessions with students, a mix of lecture and discussion  The midterm and final are administered during these sessions as well. After the midterm he polled students and about 2/3 responded. "They love it, the structure, the delivery.  The most telling set of comments is that they loved being able to listen to the lecture whenever they want, pause, replay to get the details."  One student could take the course despite the fact that he had to spend a month in Malawi during the semester.  I interviewed Mike before the final was administered but he was already pleased with the quality of the students' work. I've heard since that his end-of-course student feedback scores were among the best he's ever received.  

I take particular note on that last point.  Student feedback is not proof of superior learning. But, if the learning itself could be assessed, it would not be surprising to find that this design could be both more accessible to both faculty and students (they don't need to all be in the same place, and there's less need to coordinate schedules) and also produce superior learning outcomes.  There's a long history in education of using technology in ways that can produce gains in quality and access simultaneously, going back to printed books as a way of both increasing an author's audience and enable readers to study the author's words more closely than would be possible in an auditorium.

if you'd like to learn more, Mike's email is mom@gwu.edu.