Math 23 is aiming to go global. Motivated by the chance to create what is likely the first proof-based math class online, lecturer Paul G. Bamberg ’63 organized a meeting last week with Harvard Extension School representatives and students from his course to discuss possibilities for distance-learning. Preliminary tests for an entirely online version of Math 23b will begin in the spring. Efforts to digitize Math 23 are part of an ongoing distance-learning movement in several universities, including Harvard. Distance education aims to provide access to lecture videos so students can take courses regardless of geographic or time constraints, with some courses even being offered for free online.
E-PROOFS?
Distance education had its humble beginnings in the 1800s in the form of correspondence courses that took place via mail. After the advent of radio and television in the early to mid-20th century, some universities tried to create distance-learning courses that could be taken for credit. These endeavors never caught on, however, and were ultimately unsuccessful.
Digital video recording and the Internet have, in recent years, provided yet another avenue for distance education, one that may be more promising than previous experiments. Online courses can be accessed anywhere and at any time, and also allow for the possibility of collaboration with instructors and other students through video-conference technology.
For about 12 years, the Harvard Extension School has been offering an online option for some of its courses so that students geographically distant from Harvard can still enroll in classes. Over 150 of the Harvard Extension School’s approximately 680 courses are currently available online. Math 23 could be the newest addition to the list.
“I had first thought that this would not work for Math 23, since a key feature of the course was presenting proofs to other students,” says Bamberg. He changed his mind a few weeks ago, when he started allowing students to turn in proofs in a video format instead of the traditional PDF. “These videos consist mainly of people writing out equations for proofs on paper or whiteboard while explaining their solution,” says Bamberg.
Terrence B. McKenna ’14 was one of the early adopters of the proof video. He says that proofs are much easier to understand in video form, since the proof presenters must thoroughly explain all the intricacies involved in each step. “In the video you really have to know your stuff,” agrees Irene Y. Chen ’14. “It really demonstrates ability instead of just writing down the proof.”
In the spring, Bamberg hopes to have an Extension School Math 23b section that meets solely through video conference. Students would present proofs in video format and would not need to come to class at all. This system could allow students from around the world to enroll in Math 23 under the Harvard Extension School.
But the class itself depends on collaboration through student study groups, cooperation on problem sets, and “proof parties” accompanied by food and drink. Could this all be replicated online?
“You can’t really have an online proof party, and you especially can’t do it with refreshments,” says Bamberg. Even lecture videos might be insufficient, according to Bamberg, since the general view among faculty is that a video is no substitute for a live lecture. Students seem to agree. “I think you’re more engaged in person,” says Kyle S. Solan ’14, a student in Computer Science 50, which has video lectures. “It’s more immersive than sitting there watching the lecture on your computer.”
Regardless of the difficulties they may face, Bamberg and the Extension School will begin testing the distance-learning delivery of Math 23b in January. “You never really know what’s going to happen,” says Bamberg. “But it’s worth giving a try.”
A PEEK INTO THE IVORY TOWER
Another movement at the Harvard Extension School is the Open Learning Initiative, which currently features just eight classes with topics ranging from Chinese history to abstract algebra.
Several elite universities, including MIT, Stanford, and Yale, feature websites that grant free access to course materials and lecture videos. According to Dr. Henry H. Leitner, the Chief Technology Officer at Harvard’s Division of Continuing Education, many Harvard faculty are interested in getting courses out to the world, but some political decisions from the university administration still need to be made.
Classes that use significant amounts of third-party materials cannot be made available online to the general public since they may violate the doctrine of “fair use” granted by copyright laws. Under the Teach Act, professors can show their in-class students almost any third-party content they like. When those lectures are disseminated to the others, however, the Teach Act no longer applies. Issues such as these, Leitner says, are frustrating but important to deal with.
“It’s a little early to predict where this’ll go,” says Leitner. He is hopeful that more classes will continue being added to the Open Learning Initiative, but its future will likely remain unclear for at least a few more months.
The twin efforts to expand Harvard’s educational opportunities to Extension School students and to the public at large are ongoing and incomplete, but they reveal an important contemporary trend towards more open education in general. So the next time a big lecture class starts getting boring, look around for a video camera—someone across the world might be watching.
