## Question types: STACK

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:
- Textual comments for the student.
- A numerical mark.
- 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.

'''

Units Fail 18*kJ 18000.0*J 2 1 1 ATUnits_compatible_units: (kg*m^2)/s^2. [NOTE expected: ATUnits_compatible_units: kg*m^2/s^2.]

Units Fail 18.1*kJ 18000.0*J 2 0 0

Your answer contains the wrong number of significant digits.

ATUnitsSigFigs_WrongDigits. ATUnits_compatible_units: (kg*m^2)/s^2. [NOTE expected: ATUnitsSigFigs_WrongDigits. ATUnits_compatible_units: kg*m^2/s^2.]

'''

It seems there were unexpected parenths in the units. Is this a bug and if so in Maxima or in Stack please? Thanks.

Anyway, there is an open github issue about this: https://github.com/maths/moodle-qtype_stack/issues/278. Not sure when it will get fixed.

These unit tests fails are very specific. They won't stop your questions from working.

Thanks for pointing this out. It is a *change* in Maxima behaviour. There have been quite a few over the years and I have to adapt STACK to them while maintaining the past behaviour. This is on my radar and I'll certainly look at it. It is a very subtle change in associtativity and the rules which govern order of precedence. Basically it is a change from (a*b)/c to a*(b/c). Does this matter? In this case not really at a mathematical level. In some very elementary mathematics it does. It isn't really a bug, more a change in designed behaviour...

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?

Please do get involved.

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

Thanks!

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.

Chris

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 https://moodle.org/mod/forum/discuss.php?d=357750 for more information.

Cheers, Joël

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!

Why don't you email me (C.J.Sangwin@ed.ac.uk) 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.

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.

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.

Chris

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!

Chris