The quality of presentation of mathematical formulae in learning is of fundamental importance and is a challenge for browser based representation. Formulae in ActiveMath use a semantic format called OpenMath. This format is converted to presentation languages, and learners' mathematical input is converted to this format. This section describes the mathematical notations used in ActiveMath for these input and output processes.
The presentation system uses XSLT stylesheets for the first conversion from OMDoc to one of the presentation formats: HTML (+CSS and Unicode), XHMTL+MathML, or LaTeX. The presentation notations produce an XSLT file that is part of these stylesheets; this file contains all mathematical notations patterns and their translations to the presentation language.
The presentation notation elements are pairs made of an OpenMath prototype (a typical notation) and its rendering in MathML. There are often several notations for a given symbol which depend on the complex expression used (think of the the sum over an integer interval or over an arbitrary set) or on the context of use (for example usage of the ∧ "wee" sign or the word "and" to denote conjunction, which depends on the educational level).
From these elements, the (generated) stylesheets render each formula depending on the language and the media. Other contextual information, such as the author of the item containing the formula, is used at the later stage of personalization.
The presentation notations also feed into the Wiris input editor's domain files which define the methods to input within the graphical formula editor used in the search tool and in the exercises. The latter also allows formula input in plain text using an input syntax resembling that of computer algebra system (by default, Maple).
Because the presentation process is from a rich semantic source, extra interactivity can be offered in this presentation. This includes:
- tooltips indicating the name of the symbol under the mouse or click to see definitions of this symbol
- copy-and-paste of each terms of a formula into an input editor
- many other functions that can be done on a term...
Challenges and Originality
The principle of requesting semantic math from authors is a challenge in itself, and the wealth of mathematical notational language and its abuses may give a hard time to author in content notations. Only a few other projects do so, e.g. Connexions or CellML. The resulting advantages do, we believe, outweight this difficulty, e.g. long-term preservation (agnostic to browser changes) and consistent notations for a learner and the added-value-presentation provided by the features.
Conversion from semantic mathematics to presentation has been done many
times (the ORCCA notations selection tool,
From Notation to Semantics: There and
Back Again (Padovani, Zacchirolli), ...).