## STACK Documentation

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# Authoring quick start 5: question tests

This part of the authoring quick start guide deals with using question tests. The following video explains the process:

## Introduction

In the last couple of parts, we have been working with a simple integration question. Before you continue, confirm that your question variables are set up as follows:

a1 : 1+rand(6);
a2 : 1+rand(6);
nn : 2+rand(4);
exp : a1*(x-a2)^(-nn);
ta: int(exp, x)+c;


Testing questions is time consuming and tedious, but important to ensure questions work. To help with this process, STACK enables teachers to define "question tests". The principle is the same as "unit testing" in software engineering.

## Question testing

Scroll to the top of your question in the preview window and click on Question tests & deployed variants. In the last part we used this window to deploy random variants.

Click Add a test case to add a test to your question. A test case takes a student input. You then specify what the expected outcome is for that input, namely the score, penalty and answer note you expect to land on. Recall from the last part that the Answer note is the name for a specific outcome on a potential response tree.

The penalty is a number deducted from the total mark for each incorrect attempt the student has. By default, it is set to 0.1. You can change the penalty in the General section under Penalty. Note that this feature is only used in the question behaviours Interactive with multiple tries and Adaptive mode, as they are the only ones that allow multiple attempts. We will discuss question behaviours in a later part.

Fill in the following information for your first test case:

ans1 = ta
score = 1
penalty = 0


I.e., if the student puts in the model answer they should pass the first node (checks if they have integrated correctly) and pass the second node (tests that their answer is factored) and end up with a score of 1 and no penalty.

Note that the input is evaluated before the test is conducted. Students are not allowed to enter the variable ta because it is a teacher-defined variable, however the evaluated form, fx. -1*(x-1)^(-3)+c, is an allowed input. For each test case, you can see the un-evaluated input under Test input, and the actual input tested under Value entered.

You can run the test on all deployed versions by clicking on Run all tests on all deployed variants .

You can add as many tests as you think is needed, and it is usually a sensible idea to add one for each case you anticipate. Add in another test case for

ans1 = int(exp,x)
score = 0
penalty = 0.1


Here we create a test case without a constant of integration. In this case STACK should fail to give students any marks, indicating the test passes!

You should also use question tests to check that solving every variant requires the competences that you desire. For example, in this question we want students to know (1) increase the power by 1 and (2) divide by the new power. They should not be able to get away with, for example, increasing the power and multiplying by the new power. Let's add a test case to check this.

ans1 = (a1*(-nn+1))*(x-a2)^(-nn+1)+c
score = 0
penalty = 0.1


We are that if we multiply by $$-nn+1$$ instead of dividing, we should be given a score of 0. If students are required this knowledge for all variants, then all variants should pass this test. Click Run all tests on all deployed variants to check this.

You will see that not all deployed versions pass all tests, and if you click on a variant that failed a test, you will see why! Essentially, when $$nn=2$$, $$-nn+1=-1$$ multiplication and division are equivalent. Essentially, these random variants are "easier" than the others. This illustrates another key use of question tests - ensuring that all variants are the same difficulty and test the knowledge they are supposed to. In light of this, you may want to change nn again to 3+rand(4) . Now all variants should pass all question tests.

Quality control is essential, and more information is given in the page on testing.

## Aside: forbidden words

STACK allows students to use standard mathematical functions, such as sin, cos, etc. Perhaps surprisingly, it also allows students to use int. So in theory, students could input int(...)+c, and the system would mark it correct!

To stop this, go to input:ans1 and under forbidden words, enter int. Forbidden words will render words that are normally allowed invalid.

This example nicely illustrates the way validity can be used to help students. An answer int(p,x)+c is a correct response to the question, but it is invalid. In this example we want them to perform integration, not have the CAS do it!

# Next step

You should now be able to use question tests in STACK.

##### The next part of the authoring quick start guide looks at multipart questions.

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