Presenting mathematical formulae is a fundamental part of its communication. Authors, and applications, may choose to encode formulae in their documents using presentation markup, as is done in TeX or MathML-presentation. An alternative practice is to encode formulae by their semantics, using OpenMath or Content-MathML and letting an automated process convert the formulae to presentation code.

This last way supports the many value-added services of semantic mathematical encodings, since it exposes the formulae semantics. We present an approach where the rendering process is configurable by author-defined notations that can be interleaved with user-defined notations. This process can be dynamically enriched by new notations of (new) symbols that were just found since it bases on notations documents which are declarative.

Aside of serving of food for the rendering process, the notations documents appear to provide also the right information that can be presented to authors which shop for their symbol.

Presentation of the EU funded project InterGEO. This project will focus on the use of OpenMath as a tool to express the mathematical objects in a Common File Format for Dynamic Geometry Systems (DGS).

After skirting the question of why one might still want to use TeX, I assume that you nevertheless will, and describe why you might want to use LaTeXML to convert TeX documents to XML, HTML and MathML. A brief, teaser, tutorial is then presented.

This talk concerns the implementation and intended future extension of a computer aided assessment system for mathematics known as STACK, a System for Teaching and Assessment using a Computer algebra Kernel.

Assessment is a fundamental part of the learning cycle and is often the primary driver of students' learning. The outcome of assessments is feedback of various kinds and an item of assessment has a number of potential purposes. Although assessment is a key part of the learning process for the student, for the teacher marking is repetitive, time consuming and difficult.

When undertaking assessment the teacher is required to make many fine judgements rapidly. For the student there is often a delay of some days between completing work and receiving any feedback, during which the focus of attention has moved to something entirely new. It is natural therefore to seek to automate this process.

In mathematics, "the process of assessment" often involves establishing various mathematical properties of a student's work. This could include the teacher asking "has an appropriate method been selected and correctly used?", "is the final answer algebraically equivalent to my answer?", or "is this expression fully
simplified?".

For this process to be automated it is necessary to have software tools with which mathematical expressions can be manipulated and tested against objective criteria. Mainstream computer algebra systems (CAS) are certainly designed specifically to manipulate expressions, but they are not designed with this application in mind. Indeed, the application of CAS to support an online assessment system is quite different from the
roles to which a CAS is traditionally put.

STACK makes use of the computer algebra system Maxima for a variety of tasks, the most important of which is establishing mathematical properties of student's answers. At the current state of development the system is able to manipulate the final answer given by the student. In version 2.0, due for release in September 2007, multi-part questions will
allow some follow-through marking, better partial credit and richer linked questions with sub-parts and riders. Version 2.0 will also be fully integrated into the Moodle Virtual Learning Environment.

Future research is underway to consider how students might interact with a tutorial system to fully explore steps in their working. At this stage it is clear that we are far from a full understanding of the process of interactions which take place during mathematics tutorial. Hence, the talk presents the designs for a feedback model which builds upon STACK.
This model will be used to analyze students' working and responses at different levels of complexity and to provide appropriate feedback.

The feedback model draws on the findings of a cross-disciplinary literature review on error and feedback research. It contains a description of solution steps which allow it to break student responses down into basic mathematical units and provide feedback using this.