Learning from Mistakes: A Different Approach to Partial Credit

When you are a math teacher you are often faced with the dilemma of whether to assign partial credit to a problem that is incorrect, but that demonstrates some knowledge of the topic. Should I give half-credit? Three points out of five? My answer has typically been to give no credit…at first. However, taking a page from my colleagues in the English department (and grad school), I do allow for revisions, which ends up being a much better solution.

My approach is simple. If a problem is not completely correct, no points are assigned up front. The student is allowed to resubmit their test with corrections. For any wrong answer they must:

  1. Write the original problem (with directions)
  2. Write down their original answer
  3. Write down the correct solution to the problem
  4. Write two additional problems with correct solutions similar to the test item
  5. Identify if their mistake was secretarial, computational, procedural, conceptual

I then assign the partial points. Students will never receive full credit for an item, even with corrections, if the original item was wrong on the test. They can, however, earn back some credit. They typically do their corrections as an in-class activity (to reduce the chance that someone else does the work). For their additional problems they may use examples from their notes, from the text, from online homework, or they can even make up and solve a similar problem. The key is that they have to do it correctly three times to get the partial credit. In reality they are getting no more points than I would have given them had I given the partial credit up front, they are just getting the credit for correct work.

I find that this strategy helps students in three ways. First, of course, is that their grade on the test is improved by a few points. Second, they fill in learning gaps so that they are better prepared for their midterm and final exams. Finally, by identifying the type of error for each item and noting if there is a pattern, they can better prepare for their next test. When a student miscopies, mis-aligns, or misreads a problem, it’s more of a clerical error. When they do one of the four basic operations incorrectly, it is a computational error. These two types of mistakes are more about “during the test” issues. Whether it is going too fast, a disability issue, or carelessness, it is typically not about preparation. To fix these errors the student has to make adjustments DURING the test. When a student completes the steps out of order or doesn’t completely finish a problem, they are struggling with procedure. When they leave a problem blank or use the wrong formula or technique, their deficiency is conceptual. These latter two error-types are more about preparation. To fix these, one has to better prepare BEFORE the test, and I do talk to students in detail about test preparation and test taking strategies. But I also like to focus on the “after.”

Learning from mistakes is a powerful tool. I don’t let students correct every test. Sometimes I limit the number of items they may correct, the number of total points they may earn back, or the number of letter grades they can jump. However, I never give a student full credit for an item that was not correct to start with, so no student can get a 100% even if their revisions are perfect. I also don’t allow corrections for credit for my midterm or final exams.

In my mind, the traditional model of partial credit enables bad behavior, whereas allowing students to make revisions provides another opportunity for learning. My goal is to avoid the “everyone gets a trophy” model of grading, where I feel obligated to give some points if anything written down is partially correct. Taking the traditional model to the extreme, a student could get an 80% without getting a single problem entirely correct, so long as most of their work is in the ball park. We then end up with students in the next level of math who are underprepared. In the revision model a student only receives partial credit for completely correct work. This leads to better prepared students at both the current and next level.

Kelly A. Jackson is a professor of mathematics at Camden County College.