⇧   "Peer Supported Problem Solving & Mathematical Knowledge"

Ph. D. thesis, The Open University, due end of 2012. Supervisors: Dr Alexander Mikroyannidis and Dr Peter Scott

The thesis is about adding support for problems and solutions to planetmath.org to build an online, peer-produced, mathematics learning environment. By linking problems into the extant peer-produced mathematics encyclopedia, we provide a rich "knowledge layer" that isn't present in other online learning environments. Conversely, the presence of problems and problem-solving interactions will provide an important quality and completeness check on the encyclopedia. The ability to deliver learning interactions online in a peer-produced context would represent an important innovation for mathematics education. The methods we use will have implications for other technical fields.

• Historical Background
  • The PlanetMath Encyclopedia (wiki) (pdf)
• Theoretical Background
  • Crowdsourcing Education: A Role-Based Analysis (abstract) (book)
  • Paragogy (presented at OKCon'11) & Paragogical Praxis (preprint)
  • Personalised and Peer-Supported Learning: The Peer-to-Peer Learning Environment (P2PLE)
• Literature Review
  • Tag Cloud 1 (image), Tag Cloud 2 (image), Tag Cloud 3 (image)
  • Bibliography (Zotero)
• Implementation
  • Work is ongoing. ⇒
  • Cf. The Planetary System: Web 3.0 & Active Documents for STEM
  • Bluenote: Summary of the PlanetMath port effort after Summer 2011
  [Drupal porting (alpha and beta phases, maintenance), Linked Data, Concept Forest, Recommender system]
• Methodology
  • At each phase, we're trying to detect evidence of learning. ⇒
  • Detecting mathematics learning online (preprint, to appear at NLC 2012)
    [In order to continue this, here I would most likely want to work with someone who knows more statistics than I do, and would want to build on / feed into one or more of the planned studies, below.]
• Studies
  • Bluenote: Planned research studies for Joe's thesis
  • PlanetMath Redux: Web 2.0 infrastructure for mathematical problem solving

  • Once we have a Web 2.0 problem-solving infrastructure, we can see how people use it. ⇒

    [This is the "basic layer" of my proposed Ph. D. work. As implementation is ongoing, I can try to specify what I mean by "Web 2.0 problem-solving infrastructure". It should be possible to gather some requirements from potential users as well.]

    Once we can detect similar/related problems, etc., we can see how that's useful. ⇒

    ["Give me an easier related problem" is the classic Polya heuristic. Detecting similar problems (or similar texts in general) would use textual analysis (Concept Forest) and hypertextual analysis (closest path). We also want to be able to detect the various kinds of indicators of learning that were identified in the Methodology section. Ideally this would be built using a nicely-functioning Linked Data stack, so we can quickly analyse paths and relationships.]

    Make recommendations based on what's been successful for others in similar situations. ⇒

    [Recommendations would tend to come from analyses of quality that come out of applying the proposed methodology in the environment described above. The main question here is whether and how these recommendations improve learning results.]
• Future Work
  • Feature development
  • Bluenote: feature building for the Planetary system
  • Notes on "an open maths marketplace" (2 page PDF)
  • PlanetComputing ⇒
  • Notes on a "Free Technology Guild" (public wiki)
  [Help students and practitioners learn programming and computer science concepts following a similar model.]
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• Research statement
  • Overview of my research question and approach, and the main things I have learned about doing research.
  • Research statement (2 page PDF)