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.