"Transferable patterns in learning mathematics"
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Learning can be thought of in several layers: (1) knowledge elements; (2) connections between them; (3) use of the knowledge network; (4) patterns in use. This phase of the project assumes that (1-3) are reasonably well supported, and targets level (4).
- Research Problem
- Say whether we can obtain transferable learning quality between individuals.
- The focus here is on one of the things we expect it would be difficult or expensive for people to do without significant technological support.
- Motivation
- Good advice is currently a scarce resources. The optimistic view of this project is that something resembling good advice will emerge out of repeated use of the resources here. The weak point in this system is that (like most other social artefacts), it requires human use in order to work. In order to ameliorate this, we endeavor to offer people something in return for their attention. We begin with the basic assumption that what we are offering is a profound learning opportunity, in the context of "mathematics by the people, for the people". The study should help us understand what this means.
- Methodology
- There should be various "inference from activities" models around.
- For example, we could look at very simple evolutionary models (e.g. agents mining the web from MIT in the late 90s).
- Implications
- If this works, the implication is that there is a sort of invisible hand of learning, much like the invisible hand of the marketplace. Centralized planning of mathematics curricula may become less important, and educators or "publishers" may instead look for new specialized heuristics to introduce into the recommendation system. The "business model" may shift away from educational institutions per se, towards upskilling in technical fields. It's not that teaching and tutoring is irrelevant (the system relies on such activities) but they may be harder to charge for in a context where the invisible hand has become more visible.
- Future/related work
- This paper certainly doesn't mean "the end of scarcity", even within the PlanetMath ecosystem. In particular, we imagine that development effort will still be somewhat scarce at this point in time. The PlanetComputing effort described in the next section is meant to address that concern!
- References