Problem solving and mathematical knowledge

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.