Detecting mathematics learning online

Abstract

The purpose of the paper is to design a rubric for assessment of informal learning in undergraduate level mathematics. Our proposed assessment strategy would support and parallel the mathematics learning environment we are developing at PlanetMath. PlanetMath is currently an open Web 2.0 system that consists of peer-produced encyclopaedia articles and forum discussions: we will add facilities for contributing textbook-style problems and solutions, and detailed activity tracking to model and support learning.

PlanetMath.org was initially developed by Aaron Krowne during the course of his Master's studies at Virgina Tech. PlanetMath is a virtual community and peer-produced repository of mathematical knowledge. Its central feature is a peer-produced mathematics encyclopaedia, which has been written by a group of around 300 volunteers, and now containing nearly 9000 entries defining over 15000 terms. Similarly to Wikipedia, its contents are available under the terms of the Creative Commons By/Share-Alike License, but as a subject-specific encyclopaedia, it tends to have more specialised content (e.g. detailed proofs).
The design we are using to transform PlanetMath from being primarily a reference resource into a new learning environment will include all of the traditional activities associated with building and maintaining PlanetMath's encyclopaedia (e.g., writing and editing articles, forum discussions, corrections and requests), an a new "problem solving layer", which contains problems, solutions, links from the problems into the encyclopaedia (and vice versa), as well as discussions about problems (including evaluation or marking), and course packets that combine problems with expository material.
Viewing PlanetMath as a learning environment encompassing interactions among humans, technology and artefacts such as terms, articles, problems and solutions, our proposed analytical framework aims to examine the process of learning in a social context and to support the cycle of knowledge building in which learner-produced materials have an important role to play.
It appears that the biggest strength of our proposed approach to detecting learning is its three layer framework: we can detect specialised vocabulary use, socio-technical features like "working at the cutting edge", and manage a catch-all category of heuristics which can be used to detect and talk about different ways of thinking. While there is a somewhat domain-specific mathematical flavour to this approach, we feel it poses an interesting model for educators and educational scientists working in other fields to consider adapting to their purposes. Further work will need to be done to establish whether this analytical framework can effectively detect patterns of learning.