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Error carried forward: How to use the function sw_answer

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In this article, we will demonstrate how to work with forward-carried errors in tests. As an example, we will make a set of two exercises. In the first exercise, we will ask a student to determine a formula for a line through two points. In the second part, we will ask to give the coordinates of the intersection with the x-axis. We will make sure that the student will still be awarded points for the second question if they carry the error forward.

What is an error carried forward?

Suppose a student is making a test with a question A and a question B. Sometimes the answer to question B is dependent on the answer to question A. If a student makes a mistake in question A, they will most likely also answer question B wrong, even if they make the correct calculations just because they use their wrong answer in A. In a situation like this, we say that the student “carried the error forward”. Ideally, we want to award points for question B if this happens.

The sw_answer function

We have a set of exercises containing A and B. To retrieve the student's answer to exercise A, we use sw_answer(1, 1, ‘%null’). Let’s go over what this does.

The first argument is 1 because we want to access the first answer field of the question. The second argument is 1 because we want to access the answers in the first exercise of the set. The last argument is the default value ’%null’, this is the fallback value in case the student didn’t provide any answer to the specified field. It's not necessary to provide this last argument. For more details, you can always visit the technical menu.

Suppose we have the following question in the test:

The correct answer is y = 7x - 6. But suppose the student writes y = 7x - 7 instead. The follow-up question is:

They will give the wrong answer: [1, 0]. To make sure this answer is also accepted in a test we make a new variable. In this example, we give it a descriptive name, but this is optional.

Next, we go to question B and add a solution. We choose the evaluation type eval statement. Read more about the evaluation type eval statement here.

Now we have to use the student answer from A and the answer in B to see if they carried the error forward. We will write a short Maxima program that returns true if they carried the error and false otherwise. In this case, they carried the error if the y-coordinate is 0 and if the equation holds when we substitute the values of their answer to B in the equation of their answer to A. Below is an example of how we can do this.

block(
ans_a: $student_ans_a,
ans_b: answer,
 
if ans_b[2] = 0 and subst(x = ans_b[1], ans_a) = 0 
then return(true)
else return(false)
)

And that’s it. Now if a student makes a test and carries an error they can still be automatically awarded points.

Why don't we use "Error carried forward" in practice mode?

In practice mode, we only want to allow the student to make question B if they actually got question A correct. So by design of our platform, it is impossible to carry an error forward. The sw_answer function still works, and you can use it in various different creative ways if you please.

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