Tech Reports
Tech Report kmi-10-03 Abstract
Problem solving and mathematical knowledge
Techreport ID: kmi-10-03
Date: 2010
Author(s): Joe Corneli
This report describes the research goals, and intermediate milestones related to an investigation of the relationship between problem solving and mathematical knowledge in an online mathematics community. The proposal is to build a problem-solving layer over the encyclopedia layer that comprises the central feature of the current PlanetMath.org. Research will proceed by examining the activities of people in this space (e.g. connecting, discussing, working, recording, sharing, learning, etc.) and analysis of these activities in context, pursuant to creating useful adaptive recommendations for learners. The investigation will include a qualitative component, based on participant observation of peer learning in this space. We propose to add three core features to the software system that underlies PlanetMath: (1) building blocks of an open platform for testing and evaluating various learning and instruction methods, (2) algorithms for recommendations following the cognitive tutoring approach, and (3) support for end-user participation in developing problem sets and relevant analytics. Outcomes will include a statistical study of how various activity patterns correlate with indicators of learning, and a set of narratives that assemble these key factors into problem-solving and teaching/learning strategies.
Future Internet
KnowledgeManagementMultimedia &
Information SystemsNarrative
HypermediaNew Media SystemsSemantic Web &
Knowledge ServicesSocial Software
Social Software is...
Interacting with other people not only forms the core of human social and psychological experience, but also lies at the centre of what makes the internet such a rich, powerful and exciting collection of knowledge media. We are especially interested in what happens when such interactions take place on a very large scale -- not only because we work regularly with tens of thousands of distance learners at the Open University, but also because it is evident that being part of a crowd in real life possesses a certain 'buzz' of its own, and poses a natural challenge. Different nuances emerge in different user contexts, so we choose to investigate the contexts of work, learning and play to better understand the trade-offs involved in designing effective large-scale social software for multiple purposes.
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