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

Knowledge
Management Multimedia &
Information Systems Narrative
Hypermedia New Media Systems Semantic Web &
Knowledge Services

Future Internet is...

With over a billion users, today's Internet is arguably the most successful human artifact ever created. The Internet's physical infrastructure, software, and content now play an integral part of the lives of everyone on the planet, whether they interact with it directly or not. Now nearing its fifth decade, the Internet has shown remarkable resilience and flexibility in the face of ever increasing numbers of users, data volume, and changing usage patterns, but faces growing challenges in meetings the needs of our knowledge society. Globally, many major initiatives are underway to address the need for more scientific research, physical infrastructure investment, better education, and better utilisation of the Internet. Within Japan, USA and Europe major new initiatives have begun in the area.

To succeed the Future Internet will need to address a number of cross-cutting challenges including:

Scalability in the face of peer-to-peer traffic, decentralisation, and increased openness

Trust when government, medical, financial, personal data are increasingly trusted to the cloud, and middleware will increasingly use dynamic service selection