Surveying methods to visualize, narrate, and interact with theorems in educational math games
In the FrameIT project we build a framework for educational math games such that mathematical content in these games (e.g., theorems, proofs, deduction of conclusions) is outsourced to a full-blown logical inference engine (namely, MMT). This makes it possible to detangle knowledge management from game design in serious games.
MMT allows the formalization of complex mathematical theorems in the style "given these prerequisites, those are the consequences." In the FrameIT project, we call theorems formalized in this style scrolls. During game play, users can apply such theorems interactively. For example, they can first fill, say, the first prerequisite of a given theorem, then wait (and see the interactive response), and finally fill in the second prerequisite. So far, we employ a minimalistic visualization, yet one that is already interactive. See Figures 5 and 6 in our workshop paper "Dynamic User Interfaces via Incremental Knowledge Management" for a figurative overview and read the paper for all details.
A project or thesis could target enhancing this feature:
- Requirements Analysis: we could demand theorems be equippable with text descriptions (already done), math formulae (TeX, MathML?), images (SVGs?). How interactive should these elements be?
- Survey of Possible Implementation Strategies
- How to tackle rendering? Use HTML or SVG rendering engine in Unity?
- How to tackle interactivity?
- Is the interactivity, i.e. data binding, mono- or bidirectional?
- Specification of FrameIT MMT server <-> Unity frontend communication protocol
- Implementation
- Evaluation
A major technical problem may be that rendering of SVG and HTML within Unity is quite limited or only possible via costly plugins.
Related GitHub issues: https://github.com/UFrameIT/UFrameIT/issues/18, https://github.com/UFrameIT/UFrameIT/issues/70.