If you have a research bent, by this point, you may be asking yourself questions like these: How can we understand peer learning better? How can we do research “the peeragogical way”? How do we combine research and peer learning? You may also be asking more technical methodological and instrumentation-level questions: Do we have a good way to measure learning? Which activities and interventions have the biggest payoff?
This chapter summarizes qualitative research I did on PlanetMath.org, using the pattern catalog, as part of my work for my PhD. In the course of the study, I developed 3 new patterns.
The first point to make is that although this research was informal, it is nevertheless (at least in my view) highly rigorous. This is because the pattern catalog is a relatively stable, socially agreed upon object, though it is not fixed for all time. We can use it to help identify “known” patterns, but we can also extend it with new patterns — assuming that we can make an argument to explain why the new patterns are needed. The notion of pattern-finding as a process related to, but distinct from abstraction is described by Richard Gabriel, who emphasizes that the “patterns and the social process for applying them are designed to produce organic order through piecemeal growth” (, p. 31).
We can use the rigorous-but-informal notion of an expanding pattern catalog to help address the high-level questions about peeragogical research mentioned above. The three new patterns I present here are: Frontend and Backend, Spanning Set, and Minimum Viable Project. These patterns are both an “outcome” of research in a real peer learning context — and also a reflection on peeragogical research methods. Like the other peeragogy patterns, they are tools you can use in your own work.
The study was based on interviews with users of a new software system that we deployed on PlanetMath.org. In the interviews, we covered a wide range issues, ranging from basic issues of usability all the way to “deep” issues about how people think about mathematics.
In this project, I was interested not only in how people collaborate to solve mathematical problems, but how they think about “system level” issues. The design I had in mind is depicted in the figures below. The key idea is that patterns emerge as “paths in the grass”, or “desire lines”. The idea that learning design has emergent features is not itself new; see e.g. . What’s new here is a characterization of the key patterns for doing emergent design in a peer learning context.
Map of a virtual campus
Peeragogy patterns as loci for “paths in the grass”
Initial thematic analysis
Before describing the new patterns, I will briefly summarize the themes I identified in the interviews. This can serve as an overview of the current features and shortcomings of PlanetMath system for people who are not familiar with it.
- “Necessary but not sufficient”. Users identified a range of essential features, like a critical mass of other users to talk to.
- “Nice to have”. It was also easy to identify a bunch of cool new “dream” features.
- Challenges with writing mathematics. PlanetMath uses LaTeX, which isn’t entirely easy to learn (however, we could adapt the software to help new users get started).
- Progressive problem solving. The new PlanetMath contains problems and solutions, but no easy way to talk about conjectures. Users would like a better way to share and discuss work-in-progress.
- Personal history, social constructivism. Better features for tracking and, where appropriate, sharing, personal history would help users make sense of what’s happening in the site.
- Regulating learning in a social/mediated context. Different users would look for different things to keep them on track (e.g. expert guidance, or a due “sense of urgency” in feedback from peers).
- Comparison with roles in other contexts. Many users expect a “service delivery” style that is not entirely consistent with the “open” production model used in a free/open, volunteer-driven project. We need to work more on responsiveness in every aspect of the project (keeping in mind that most participants are volunteers).
- Concreteness as a criterion of quality. “Knowing what you can do,” both with the software and with the content, is important. On the content level, pictures help.
- Personalization and localization. The system has a practically unlimited potential for personalization, although many basic personalized interaction modes have not been built yet.
At the next level of analysis, the themes extracted above were further analysed in relationship to the peeragogy pattern catalog.
Frontend and Backend
Definition: In order to design a collaborative system, you want to bring in enough messiness to let new and unexpected features emerge, and you want to facilitate meaningful engagement at every level — but you also need to be aware of the user’s experience, including requirements related to simplicity. As an analogy, imagine a butcher shop. There are reasons for leaving the butchery work to the pros. There’s a similar phenomenon, even with open source systems. The part of the system users experience is often connected to a “backend” that they don’t interact with, at least not as much. The process of working with a system’s frontend is often relatively formal (following specific straightforward rules) whereas the process of working with the backend may be very informal.
Problem: The idea of Frontend and Backend is related to the “Newcomer” pattern: typically one will not expect the user of a system to know how to, or to be motivated to, work with any of the backend features of a system until they have mastered at many of the frontend features. “Users” tend to expect a level of service provision. New users often require some hand-holding.
Solution: As with the example of a butcher shop, the pattern of frontend and backend lends itself to standard service provision and transactional models of exchange. However, it can also be part of more peer-driven activity. For example, sophisticated and committed users of a community website can focus energy on supporting individual newcomers, by helping them develop a high-quality sub-site on their topic of interest. This helps newcomers stay within their comfort zone: having supportive human involvement as part of their frontend experience makes things go more smoothly. At the same time, through a process of reflection on the part of the oldtimers, this effort can simultaneously inform the development of backend features. In addition, the new content can help to raise the profile of the site as a whole. The pattern is in this way associated with Focusing on a Specific Project (in this case, following the interests of the newcomers) and with the Roles pattern, since it requires a committed and knowledgeable mentor who can translate between the user experience in the frontend and the system features in the backend.
Example: David Cavallo wrote about an “engine culture” in rural Thailand, in which structurally open systems made some of the “backend” features of internal combustion engines a part of daily life. Cavallo felt that people who were familiar with tinkering with engines tended to be able to learn how to tinker with software, suggesting that there are some common underlying informal reasoning skills.
Challenges: Mentoring newcomers while also working on system features to support them better constitutes a major commitment. If this work can be spread out among several volunteers — or possibly paid staff — this could have some advantages. On the other hand, depending on the nature of the process, providing a single point of contact for the user may still be the most straightforward.
What’s Next: At PlanetMath, we have an “open engine”, but not necessarily an “open engine culture”. In addition to directly running the pattern described here by focusing on individual users, we want to build pathways for more user involvement in working with the software system. This may involve its own significant outreach and teaching efforts.
Definition: With a well-constructed information access system, you may be able to get what you need without digging. If you do need to dig, it is very good to get some indication about which direction to dig in. At the level of content, this may be achieved by using high-level “topic articles” as narrative map to the content. In general, the Spanning Set may include people as well as less dynamic media objects. In a standard course model, there is one central node, the teacher, who is responsible for all teaching and course communication. In large courses, this model is sometimes scaled up:
Anonymous study participant: [E]veryone’s allocated a course tutor, who might take on just a half-dozen students – so, they’re not the overall person in charge of the course, by any means.
In general, a spanning set is comprised of a set of fundamental actions and fundamental relationships between resources.
Problem: People need to know what can be done with a given resource, and this isn’t always obvious. Relying on a single knowledgeable guru figure isn’t always possible.
Solution: A spanning set of a system’s features, categories, and relations can be comprised of many different kinds of components: for example, a “start menu” or pop-up window showing keyboard shortcuts that shows what can be done with a given tool; a schedule of office hours so that people know how to find help; and topic-level narrative guides to content.
Examples: One social version of a Spanning Set is the classical master/apprentice system, in which every apprentice is supervised by a certified master. In the typical online Q&A context, these roles are made distributed, and are better modeled by power laws than by formal gradations. A “spanning set” of peer tutors could help shift the exponent attached to the power law in massive courses. For instance, we can imagine a given discussion group of 100 persons that is divided according to the so-called 90/9/1 rule, so that 90 lurk, 9 contribute a little, and 1 creates the content. This is what one might observe, for example, in a classroom with a lecture format. We could potentially shift this pcentage by breaking the group up into smaller groups, so that each of the 9 contributors leads a discussion section of 10 persons, at which point, chances are decent that at least some of the former lurkers would be converted into contributors.
Challenges: In practice, principles — like the paragogy principles or like the rules of tennis — are not entirely sufficient for understanding what to do or how things work. Principles and features may be visible as part of a system’s “frontend” — but the actual spanning set of relevant behaviors is emergent.
What’s Next: As a project with an encyclopedic component, PlanetMath can be used to span and organize a significantly larger body of existing material. We have come up with a high-level design for a “cross-index” to the mathematics literature. We’re working on a prototype for Calculus.
Minimum Viable Project
Definition: The Minimum Viable Product approach to software development is about putting something out there to see if the customer bites . Another approach, building on the notion of a Spanning Set, is to make it clear what people can do with what’s there, and see how they engage. A Minimum Viable Project is something someone can and will engage with.
Problem: In general, it is an open question to know what will make a given project engaging. We can point to some likely common features, based on the features of viable systems in general  — but typically, the proof is in the pudding, so we need a methodology for trying things out.
Solution: This “solution” is largely theoretical — taking a project-oriented view on everything, proposing to understand actions and artifacts as being embedded within projects, modeling projects in terms of informal user experience and formal system features (see Frontend and Backend). Where possible, project updates can be modeled with a language of fundamental actions (see Spanning Set). We make the philosophical claim that projects themselves model their outcomes to some degree of fidelity — and that they are made viable by features that connect to the motivations and ambitions of potential participants. The practical side of the proposed solution is to build systems that can express all of these aspects of projects, and study what works.
Challenges: It’s not clear if a unified view of this sort will be broadly useful. The features that make a project in one domain viable (e.g. basketball) may have little to do with the features that make another project in another domain viable.
What’s Next: As we mentioned in the Frontend and Backend pattern, one way to strengthen the PlanetMath project as a whole would be to focus on support for individual projects. The front page of the website could be redesigned so that the top-level view of the site is project focused. Thus, instead of collecting all of the posts from across the site – or even all of the threads from across the site – the front page could collect succinct summary information on recently active projects, and list the number of active posts in each, after the model of Slashdot stories or StackExchange questions. For instance, each Mathematics Subject Classification could be designated as a “sub-project”, but there could be many other cross-cutting or smaller-scale projects.
This chapter has used the approach suggested by Figure 2 to expand the peeragogy pattern language. It shows that the peeragogy pattern language provides a “meta-model” that can be used to develop emergent order relative to given boundary conditions. As new structure forms, this becomes part of the boundary conditions for future iterations. This method is a suitable form for a theory of peer learning and peer production in project-based and cross-project collaborations – a tool for conviviality in the sense of Ivan Illich. In other words, we’re all in the same boat. The things that peer learners need in order to learn stuff in a peer produced setting are exactly the same things that designers and system builders need, too. And one concrete way to assess our collective learning is in terms of the growth and refinement of our pattern catalog.
Frontend and Backend
Principles and features
Minimum Viable Project
A Specific Project, Roadmap, Heartbeat, Divide, Use or Make
Paths in the grass
Peeragogical emergent design: a tool for conviviality
- Gabriel, R. (1996). Patterns of Software. Oxford University Press New York.
- Luckin, R. (2010). Re-designing learning contexts: technology-rich, learner-centred ecologies. Routledge.
- Zimmerman, B. J. & Campillo, M. (2003). Motivating self-regulated problem solvers. In J. Davidson & R. Sternberg (Eds.), The psychology of problem solving (pp. 233-262). Cambridge University Press New York, NY.
- Cavallo, D. P. (2000). Technological Fluency and the Art of Motorcycle Maintenance: Emergent design of learning environments (Doctoral dissertation, Massachusetts Institute of Technology).
- Ries, E. (2011). The Lean Startup: How today’s entrepreneurs use continuous innovation to create radically successful businesses. Crown Pub.
- Stafford Beer (1981). Brain of the firm: the managerial cybernetics of organization. J. Wiley
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