Retakes vs. Test Corrections vs. Neither

Both in person and online, a common topic of discussion among math teachers is the question of “retakes”. Under what conditions should students be allowed to have another chance at taking a test? How does the retake affect the grade? This is an important conversation. Different opinions reflect different values, different attitudes towards assessment, and different understandings of how learning happens. I’ll take a stab at unpacking this, and (as is my wont) I will not be shy about sharing my opinions along the way. I will present this as a discussion with imaginary colleagues, whose contributions are in bold type. 

No retakes!

– The test is an accurate assessment of the student.

Doing well on a test does usually reveal a mastery of what was tested. However doing poorly is not as reliable an indicator of understanding, as the problem may be that the student needed more time, or was not feeling well, or made so-called “careless” mistakes in spite of having a decent understanding of the material. Given all this, I cannot accept that argument.

– If they did poorly, well, they should have prepared better. They’ll never learn responsibility if they keep getting second chances.

Students often say they don’t know how to prepare for math tests. They don’t have this issue in other disciplines. The reason is that doing well on a worthwhile math test requires understanding the underlying concepts. Most students cannot improve their understanding by “studying” — unless the test prioritizes memory over understanding. 

Even if they have the maturity to struggle for understanding while preparing for the test, it may well be that they need help in order to do that successfully. 

– They need to be trained to the harsh reality that colleges do not offer such opportunities.

Bad pedagogy in college is not a valid justification for bad pedagogy in high school. 

– Getting a bad grade will help them take the next test seriously.

More likely, it will convince them they’re not good at math, especially if they see that you consider the test to be an accurate assessment of their ability.

– In any case, I don’t have time to create, schedule, and grade retakes!

That is a valid argument, to which I return below.

Retakes, under certain conditions

– I allow retakes if the score was below a certain threshold 

– I allow this many retakes per grading period

– I allow retakes if the student has shown they are serious (e.g. done their homework, etc.)

Such policies are more complicated, and  less extreme than a simple “no retakes” system, but they are justified with the same arguments. The idea is still that the number of retakes should be reduced, though not completely eliminated. This sort of thinking is based on some assumptions, which are not stated explicitly, and don’t need to be, because they are nearly unquestioned. Here they are: (a) students should have mastered the material by the time the test comes around; and (b) they should be able to show this mastery under time pressure.

But everyone knows that in reality, students learn new math concepts at different rates. And while some adrenaline-fueled students thrive under time pressure, others freeze and get anxious. Those character traits may or may not be related to the student’s understanding of the material. When students tell us they need more time (more days before being quizzed, or more minutes for the quiz), they are often telling the truth. 

Is understanding achieved a few days later less valuable? No! What difference does it make if a student masters a concept a week later?

Does needing a few more minutes to figure something out reveal an inferior understanding?  Why should it matter that Student A could finish the test in 50 minutes, and Student B needed 65 minutes? 

We need a system that

• prioritizes student learning (not concerns about grades)
• does not involve extreme time pressure
• respects teachers’ time

Test corrections

– So what do you suggest?

One way to achieve all three goals is test corrections, done as homework. At my school, we called this a “recycle” of the test. Here is my recycle policy:

• I expect a high standard of explanation, much higher than what can be expected on a timed test. To make clear what I want, I ask students to explain it well enough to convince me they understand, and just as important, to convince themselves they understand. I do not ask them to dwell on their mistake, as I don’t think it’s helpful, and it may even be counterproductive.
• They have a week to do it. They can get help from me, or each other, or another teacher, or a tutor, but everything must be in their own words, and all helpers must be listed. 
• A perfect recycle gets your score half way to 100%. All mistakes should be corrected by all students, whether or not this will affect the grade. (The main purpose of the recycle is learning, not grades chicanery.)
• Extra credit / bonus questions should be recycled.

– How does this respect teachers’ time?

Well, it doesn’t require creating another version of the test. It does not require scheduling and proctoring the retake. And the grading is extremely fast: remember you’re only going over problems you’ve graded before, and moreover, only a small fraction of them, since most students are only recycling a small mumber of problems.

– But this does not tell you how the student would do on a timed retake!

So what? In many disciplines, students are assessed without being subjected to time pressure. Why not do that in math? (Besides, we’ve already had a timed test, the one that is being recycled!)

– But if they are allowed to get help, this does not assess what they can do on their own!

Seeking help when you need it is a good thing, not a bad thing.  A student who works hard on the recycles and turns in high-quality explanations in their own words is sure to learn a lot. Isn’t that our goal?

— Henri

PS: For a more in-depth argument on how to handle the fact that students learn math at different rates, see: Reaching the Full Range. For more thoughts on tests and related topics, see: The Assessment Trap.