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This is an unfinished essay from 2001, found nearly a decade and a half later in a box of odds and ends. The essay foreshadows our ongoing research on peer produced peer learning, and also helps to highlight some of the difficulties associated with this enterprise.


THE POINT. This is an effort at understanding how research skills in the mathematical sciences [but it could be any topic] can be acquired by students.

WHO WE ARE. We are students at a state-funded liberal arts college based in Sarasota, Florida [but it could be anyone]. Our school is called New College. The emphasis of the program at New College is self-directed learning.

SELF-DIRECTED LEARNING. Since people have free will and learn from experience, self-directed learning could be said to take place wherever people engage in any activity. However, this view is unfounded, and the implication is false. Unstructured learning is more accurately undirected. If learning is structured, say by a teacher, this does not imply that it is self-directed, even given the free will of the learner to participate. The choice to participate in learning is not the same as directing the learning. Structure can impose the direction on a (passive) learner. This does not mean that the presence of a teacher or a system to learn implies that the student's learning is not self-directed. The criterion we are looking for is that the student have an active, ongoing and purposive role in deciding the structure of his/her/its [e.g. in the case of computer programs] learning environment. A teacher must be informed by and responsive to the student's feedback, or the learning the student does under that teacher's instruction is not self-directed.

INTEGRATION OF RESEARCH AND EDUCATION. In deciding upon a course of study, it behooves the student, as he/she/it examines a potential activity, to consider questions such as these, with the utmost care:

  • What is the intellectual merit of the proposed activity?

  • Is there sufficient access to resources?

  • How well-conceived and organized is the proposed activity?

  • To what extent does the proposed activity suggest and explore creative and original concepts?

  • To what extent will it enhance possibilities for future work?

  • What are the broader impacts of the proposed activity?

  • What is the product?

If these questions are addressed well, the student will enter upon a focused program and will have already at the beginning devised a coherent plan for its satisfactory completion. Furthermore, the product is likely to be a net benefit to society. The idea of traditional education is that it is the student, with an increased knowledge and skill base, who constitutes the product. His/her/its knowledge and skills (upon exiting the educational program) are valued by society, and he/she/it is willing to put forth during the program a commensurate amount of blood, sweat, and tears (not to mention tuition and time) to extract the valuable knowledge and skills. In scientific fields, one of these skills is supposed to be the ability to do research. The idea that "the best proof of someone's research ability is the research they have done" has played a significant role in the way scientific education, and the scientific enterprise, has been run in recent years. Research experience at the undergraduate level is one of the top criteria considered by graduate programs in science when they decide which candidates to admit. It is not without reason, then, that national programs for undergraduate researchers (most notably, the National Science Foundation's Research Experiences for Undergraduates (REU) summer programs) are highly competitive, taking only the best qualified applicants nationwide. Many technical and land-grant universities have internally- or industry-funded Undergraduate Research Opportunities Programs (UROP) which offer financial awards to undergraduate students, which enable them to collaborate with faculty on specialized research projects in their joint field of interest, or to do original work on their own. These programs make it possible for students to make research a part of their background. In particular, such programs give students a chance to see what it is like to work on open problems (usually the problems devised by the program administrator or principal investigator; occasionally on questions proposed by the student researchers themselves). It goes without saying that such experiences are typically only part of the curriculum. The NSF's vision of integrating research and education is to have individuals concurrently assume responsibilities as researchers, educators, and students, where all engage in joint efforts that infuse education with the excitement of discovery and enrich research through the diversity of learning perspectives. The benefits of such a system are manifold. It is however very difficult to implement in most educational contexts. A place like New College, where the culture already is disposed towards student self-direction, may be unique in its ability to foster an undergraduate scientific curriculum based primarily on research. The questions listed at the beginning of this section are the questions a researcher must answer when initiating a research program for undergraduates. (They were lifted from the NSF's summary of how they review REU proposals.) By pointing out here that the same questions are the natural questions for a student to ask when considering how to invest his/her/its time and energy, we mean to point to the unique possibility afforded the self-directed learner, namely: he/she/it can act as a researcher, an educator, and a student concurrently, and, to a degree that is possible for very few, harmoniously.

RESEARCH AS A WAY OF LIFE (ADDITIONAL REVIEW CRITERIA SPECIFIC TO REU). There are other criteria considered by the NSF, for example, the qualifications of the person who proposes the research project. This isprima facie difficult for undergraduates to fulfil satisfactorily. Further criteria include:

  • The appropriateness and value of the educational experience for the student participants, particularly the appropriateness of the research project(s) for undergraduate involvement and the nature of student participation in these activities.

  • The quality of the research environment, including the record of the mentor(s) with undergraduate research participation, the facilities, and the professional development opportunities.

  • Appropriateness of the student recruitment and selection plan, including plans for involving students from underrepresented groups and from institutions with limited research opportunities.

  • Quality of plans for student preparation and follow-through designed to promote continuation of student interest and involvement in research.

  • For REU sites, effectiveness of institutional commitment and of plans for managing the project and evaluating outcomes.

Some afterthoughts, with the benefit of hindsight (2015)

The idea that an undergraduate student could run an REU program is perhaps not entirely ridiculous, but it is still extremely unlikely to work -- as the essay points out. What is possible is for a student or group of students to set up a website and collaborate informally online. This is what Aaron Krowne did in around 2001, with I joined a few years later, as a graduate student in mathematics. PlanetMath was a little bit like an always-on version of the project outlined in the essay above. The main emphasis was on building a mathematics encyclopedia, but some contributors were doing original research and collaborating with each other. The site administrators and assorted devotees were also doing a lot of meta-level thinking about how the project could improve. In 2005 or thereabouts, I started a wiki called AsteroidMeta to help organize those discussions. By this time, I was no longer in the mathematics graduate programme: I had more or less stopped going to classes a year earlier. My interests had more to do with how computers could change the way people do mathematics than in doing mathematics the way it had always been done. Myself and a few other PlanetMath contributors published research papers on this theme in a symposium on Free Culture and the Digital Library that Aaron helped organize at Emory, where he was then Head of Digital Library Research. Working on informal collaborations like this, and doing related open source software development, I built a CV that helped me get into another postgrad program in 2010. This time, in the United Kingdom, where I was able to largely set my own research agenda from the start. I focused on rebuilding the PlanetMath website (as described in theHandbook chapter on "New Designs for Co-Working and Co-Learning"). Presenting some of this work at Wikimania 2010, I met Charlie Danoff, and when we later met online at P2PU, we decided to sit in on each others first round of courses. As the term progressed, we collaboratively developed a critique of the way things worked at P2PU and suggested some principles that would guide improvement. We called this "paragogy." When Howard Rheingold learned about this work from Charlie, who was taking one of his online classes at RheingoldU, he suggested the more accessible name "peeragogy." To our pleasant surprise Howard then drew on his network of friends and fans to kick off the Peeragogy project. Naturally, I joined, and was able to draw on what we learned in my thesis. Unlike the previous time around, I also had a lot of formal support from my supervisors, as well as a lot of self-organized support from others, and I completed the program successfully. In doing so, I began to accrue the credentials that would be necessary for organizing a formally-funded research project like the one outlined in the essay above. Doing this in the undergraduate research setting would, of course, require interested undergraduates. At the moment, I'm employed as a computer science researcher, exploring the development of peer learning and peer production with the computational "its" mentioned in the essay. The Peeragogy project continues to be a great resource for collaborative research on research and collaboration.