STACK stands for System for Teaching and Assessment using a Computer algebra Kernel.
Overview
STACK is an open-source system for computer-aided assessment in Mathematics and related disciplines, with emphasis on formative assessment. This documentation is for version 3 of STACK, which provides a question type for the LMS quiz. More about what we are trying to achieve can be found under the philosophy of STACK.
Details
The STACK system is a computer-aided assessment package for mathematics, which provides a question type for the LMS quiz. In computer-aided assessment (CAA), there are two classes of question types.
- Selected response questions
- In these questions, a user makes a selection from or interacts with, potential answers which the instructor has selected. Examples include multiple choice, multiple response and so on.
- User-provided answer question
- In these questions, the user’s answer contains the content. It is not a selection. Examples of these are numeric questions.
STACK concentrates on user-provided answers which are mathematical expressions. For example, a user 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 users’ 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 instructors 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 user enters a mathematical expression or makes a true/false selection.
- Mathematical properties of users’ 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:
- Textual comments for the user.
- A numerical mark.
- Answer notes from which statistics for the instructor are compiled.
These broadly correspond to formative, summative and evaluative functions of assessment. Which of these outcomes is available to the user, and when, is under the control of the instructor.
- Multi-part mathematical questions are possible: each question may have any number of inputs and any number of potential response trees. There need not be a one-to-one correspondence between these.
- Partial credit is possible when an expression only satisfies some of the required properties.
- Plots can be dynamically generated and included within any part of the question, including feedback in the form of a plot of the user’s expression.