Question types: STACK

Maintained by Picture of Christopher Sangwin Christopher Sangwin, Tim at Lone Pine Koala Sanctuary Tim Hunt
The STACK question type adds a sophisticated assessment in mathematics and related disciplines, with emphasis on formative assessment underpinned by computer algebra.
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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.

  simplify(student_answer-teacher_answer) = 0
  mark = 1,
  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:
    1. Textual comments for the student.
    2. A numerical mark.
    3. Answer notes from which statistics for the teacher are compiled.

These broadly correspond to formative, summative and evaluative functions of assessment. Which of these outcomes is available to the student, and when, is under the control of the teacher.

  • 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 student's expression.


This plugin is part of set STACK.


Screenshot #0


Picture of Christopher Sangwin
Christopher Sangwin (Lead maintainer)
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  • Picture of Stephen Parry
    Wed, 15 Mar 2017, 5:34 AM
    Thanks for the quick turnaround on #281 and you're welcome on the bug report.

    I teach A level Computer Science and I am hoping to configure / extend STACK to cope with some Computer Science problems e.g. integer, fixed and floating point base 2 and 16 conversions and arithmetic; boolean algebra and anything else I can get it to do. Are you open to some contributions in this area?
  • Picture of Christopher Sangwin
    Wed, 15 Mar 2017, 6:24 AM
    Yes Stephen, very open to contributions. If you are based in the UK, then getting together to talk about this might be possible and productive. I know CS needs some features we haven't added yet. Maxima has good support for *display* of numbers in other bases, but we might need some input and evaluation functions. Someone else in Edinburgh is working on Boolean algebra, but I'm not sure if that will make its way into STACK!

    Please do get involved.
  • Picture of Phan Chon
    Wed, 2 Aug 2017, 10:56 AM
    Hi all,

    Please let me know wich version can work fine with moodle 3.3!

  • Picture of Christopher Sangwin
    Wed, 2 Aug 2017, 4:36 PM
    Thanks for the question Phan Chon,
    I'm in the process of final testing for STACK 3.6 and STACK 4.0 (both will be released within days of each other. STACK 4.0 is an irreversible upgrade). They will both work with Moodle 3.3.

  • Picture of Joël Schmid
    Thu, 14 Sep 2017, 3:09 PM
    Hey guys,
    If someone else has maxima version 5.38.0 on CentOS 7 installed from the EPEL repo, the STACK optimisation doesn't currently work. Rebuilding 5.38.1 from source, seems to solve the problem.
    See for more information.
    Cheers, Joël
  • Picture of Stephen Parry
    Fri, 29 Sep 2017, 1:46 PM
    I ma running STACK 4.0 latest on 3.1 and I've been experimenting with trying to get it to recognise boolean algebra questions. It has some quirks which have me stuck currently:
    1. Is there a way of using an equation editor, other than dragmath (which seems to be dying because of browser based Java dying) for a student to enter the answers?
    2. In the validation panel, when my student types in an answer (long hand), it will convert some operations to the correct symbols, but not others. So if they type in not(A) or not(B) the "not" operators get converted, but not the "or" operator. Is this a bug? any ideas where please?
    3.When it comes to checking the correctness of the answer in preview I can only see the correct or incorrect user type message I have to go the status variable further down in the technical small print. This seems to affect all stack questions currently and the show whether correct option seems to have no effect.
    4. Which answer test would you recommend?
    5. With AlgEquiv and CasEquiv Sometimes the answer gives status:correct, but mostly it gives status:giveup.
    Please help!
  • Picture of Christopher Sangwin
    Fri, 29 Sep 2017, 4:01 PM
    Why don't you email me ( with a couple of question on paper and we can work together to develop some examplars? I'm keen to get this right, and there are lots of options in the interface.

    The short answer to 1 is "not currently". I let Dragmath slide after the Java browser security issues, and a general lack of time. A good Javascript maths editor would be a great project generally.

  • Picture of Stephen Parry
    Fri, 6 Oct 2017, 1:16 PM
    Hi Chris,
    How do I get STACK to allow text entry of a string? We have String, StringSloppy and RegExp tests, but I keep getting unknown function errors because it's trying to interpret the answer as algebra.
  • Picture of Christopher Sangwin
    Fri, 6 Oct 2017, 4:13 PM

    The fundamental design of STACK is that *every* answer should be a Maxima expression.

    The answer tests String, StringSloppy and RegExp are provided so that string matches can be done on the internal Maxima string representation of a mathematical expression. They were not, originally, designed to assess strings as student's answers.

    I recently added the "notes" input. This input is not assessed automatically by STACK, and students can use it to record working, or comments for the teacher. It would be possible to add in a "string" input type, which wraps the student's answer in string quotes to create a valid maxima object.

    Can I ask why you need to do this? Sometimes, the underlying need can be done with another method.

    I'm happy to talk about adding support for strings if there is a genuine need.

  • Picture of Christopher Sangwin
    Fri, 6 Oct 2017, 4:23 PM
    Sorry, I forgot to mention that students can type in a Maxima string e.g. "Hello world". They need to use the quotes to make it a Maxima expression. This, of course, is not really a sensible input mechanism!
  • Picture of Stephen Parry
    Fri, 6 Oct 2017, 5:59 PM
    It so that my student can directly enter base 16 or base 2 without it being incorrectly interpreted. Even for the character entry field, it seems to try and interpret the text as an expression.
  • Picture of Wolfgang Stettler
    Thu, 9 Nov 2017, 4:29 PM
    Some of our lecturers would like to use Stack in their courses. I am not sure whether to put everything on the Moodle server or to set up a separate server for Maxima (with pool). I would like to know how much (additional) load Stack/Maxima create create on a Moodle server. We have a single Moodle server at the moment but are changing to a load-balanced setup in summer 2018.
  • Tim at Lone Pine Koala Sanctuary
    Thu, 9 Nov 2017, 6:18 PM
    It is OK to put evertyhing on the same server. Using a separate pool server gives slighly faster performance, and more security and scalability, but it is another thing to set up.
  • Picture of Stuart Anderson
    Sun, 17 Dec 2017, 7:46 PM
    Chris: The link to is broken (at least today it is). Have Birmingham taken your site down since you left? Should it now be a Newcastle URL?
  • Picture of Christopher Sangwin
    Sun, 17 Dec 2017, 8:18 PM
    Thanks Stuart, I've updated this to
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