This is my first reply to this Scope seminar, so I need to say where I am coming from. I like Nick's metaphor about the edge of research, which describes me as well. I do research mostly for the sake of development. In the last ten years or so, my goal has been supporting networks of small communities in mathematics education, in three directions: other developers (Math Future project and its subgroups like Math Game Developers), authors (Delta Stream Media), and parents/homeschool coops/math circles (Moebius Noodles and Natural Math projects).
I find this list of metaphors hugely useful. I have made several Degrees of Freedom lists (what you call Emergence lists) for my communities, for example:
- Problem-solving - Inquiry - Self-organized learning, a rubric for parents who map activities during Math Circles
- A bunch of math game design lists, such as the spectrum from gamification to intrinsic math, and another one from Takers to Makers
- Intellectual consumerism at the lowest rungs on Bloom's ladder in math, and the producer communities (producer-consumer spectrum, the same as Takers and Makers)
- Learners' influence in computer environments (p.386) - which turned out to be too complex for casual use
In my experience, people love well-organized lists with pictures! Just look at the popularity of sites like Cracked or Buzzfeed. However, nested lists like you have in that document (lists within lists) or other complex, nonlinear data structures need a whole lot of visual support, and require a lot of storytelling. When the time is short, complex data structures are only for specialists.
I will be adapting these Footprint Metaphors for my math ed communities, for sure. The adaptations will include:
- visual mapping of structures, such as branching trees or concept maps
- three concrete examples with every term
- rephrasing some of the terms into lay language
- inserting and naming middle points on the spectra where only two extremes are named
- math pictures! - like fractals to depict complexity and emergence
Thank you very much for your work!!!