STACK

The STACK question type adds a sophisticated assessment in mathematics and related disciplines, with emphasis on formative assessment underpinned by computer algebra.
The STACK system is a computer aided assessment package for mathematics, which provides a question type for the Moodle quiz. In computer aided assessment (CAA), there are two classes of question types.
Selected response questions
In these questions, a student makes a selection from, or interacts with, potential answers which the teacher has selected. Examples include multiple choice, multiple response and so on.
Student-provided answer question
In these questions the student’s answer contains the content. It is not a selection. Examples of these are numeric questions.
STACK concentrates on student-provided answers which are mathematical expressions. For example, a student might respond to a question with a polynomial or matrix. Essentially STACK asks for mathematical expressions and evaluates these using computer algebra. The prototype test is the following pseudo-code.
if
simplify(student_answer-teacher_answer) = 0
then
mark = 1,
else
mark = 0.
STACK uses a computer algebra system (CAS) to implement these mathematical functions. A CAS provides a library of functions with which to manipulate students’ answers and generate outcomes such as providing feedback. Establishing algebraic equivalence with a correct answer is only one kind of manipulation which is possible.
Using CAS can also help generate random yet structured problems, and corresponding worked solutions.
In STACK a lot of attention has been paid to allowing teachers to author and manage their own questions. The following are the key features.
Question versions are randomly generated within structured templates.
There are many different kinds of inputs. These are, for example, where the student enters a mathematical expression, or makes a true/false selection.
Mathematical properties of students’ answers are established using answer tests within the CAS Maxima.
Feedback is assigned on the basis of these properties using a potential response tree. This feedback includes: