November 8th, 2013

# 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.

• ATM

I think I like the idea of the revision model a great deal, but I would be interested to hear a little more about your experience with it. Has it substantially increased your grading load? Have you used the method in higher-level classes, where tests tend to have fewer (and more involved) problems? What grade would you assign to a student who turned in a blank test on his first try and a perfect test on the revision?

• Kelly Jackson

I will answer the last question first. In most cases, I only give points worth the partial credit I would have given for the problem. If it is blank, I would not have given any partial credit, therefore it would not be an item they could gain points for. On a low stakes assessment like a quiz, I might allow half-credit for a revision. A zero could come up to a 50% with perfect revisions (A lot of work in the 3 right for 1/2 credit model). I have found that my midterm exam grades have really improved, especially for my B and C students. By not providing detailed grading feedback to a student on the original test, since they will have to correct the item, my grading time on tests goes down. Grading the corrections, does take time, but because most of the items are correct, it goes quickly. Grading right answers is always easier than giving feedback for wrong answers. In my view, my showing them the right steps is less of a learning experience for them than doing the corrections themselves. I want them to take more responsibility for their learning.

• Lis

I like your strategy. As an English person, I've seen students learn more from revising their own work, than from new writing. I also keep the exit criteria sound, but provide a lot of opportunities for students willing to do extra work. Our goal is that students learn the material. This is a great tool to have in our teaching toolbox.

• Andrea McCann

As an instructor I find the area of tests and exams frustrating. Students choke, some are great at memorization, and there is little room to learn from their mistakes. It is hard to be creative when everyone is pushing us to conformity. When one doesn't want to do the extra work, there is little room for change.
In my classes, I always allow for corrections, if the students choose. I like projects that require research into what they require, and an association with the area of life that interests them. they have guidelines, but they do the work in the area they choose. Wherever possible they can do test corrections for marks and I do give partial marks when part is correct! Then they will work harder to reach a higher goal, and LEARN more! Students long after have told me the value of the assignments and the test corrections.

• Tara Quinn

As an instructor of beginning calculus classes where I give no partial credit on quizzes or tests I'm happy to see other math instructors are like minded.

The biggest resistance I hear from other instructors is that of student confidence. They believe that if students aren't given partial credit they will get lower grades and then feel worse about themselves. So, to protect their egos and self-confidence in math we must give them partial credit. In fact, I've seen the opposite to be true.

I don't give partial credit but allow students to correct their work and resubmit. I then average the two grades. I've done this for three semesters. Students have been very receptive. In mid-class and end of class review students indicate that they like this method- that it challenges them and enables them to learn from their mistakes. Many indicate they used to make the same mistakes over and over but don't now because they've learned to identify them. They indicate to me all they have learned from making corrections.

So I say why not challenge them? Why let students think that close enough is good enough because we don't think they can do it all right? They can be careful, they can do well, they can fully succeed in math with no partial credit.