Last weekend, I graded some quizzes on operations with rational numbers (specifically, positive and negative fractions). As I worked my way through, I noticed I was highlighting the same mistakes and missing signs repeatedly. It was no big deal, but I immediately began thinking about how I was going to address misconceptions. I did not want to create another practice activity and I did not want to give students class time to correct their work, which bores the students who only missed a couple points. On the opposite side of the coin, I did not want to move onto something new and expect students who made mistakes to catch onto the processes naturally (which usually doesn’t happen). Basically, I felt torn.
I sat pondering the situation over my third cup of coffee for the morning, then I got an idea so simple that I could not believe I never thought of it in the past. I made a list of all of the mistakes/misconceptions I saw throughout the quizzes, then I completed a blank quiz using all of these errors. By the time I was finished with the paper, it looked like a composite of all of the mistakes I saw from individual papers. Now, I knew what to do for my class. I planned to give each student a copy of this total fail quiz to analyze and correct. Boom. From a brief perusing of student work, I created an almost instant error analysis task.
When I had students pass out the error-ridden quizzes in class, I decided to have some fun with this activity. On the copies (which looked like last week’s quiz), I wrote the names of each student in the class. I asked a couple students to pass back quizzes and sat back to watch the show. After about a minute, students were saying things like, “That’s not my handwriting,” and, “This isn’t my quiz. There isn’t even a grade on it.” I called everyone to attention and clarified, “I said quizzes, not your quizzes.”
After the laugh that followed, I explained to students that the quizzes contained errors on each problem. The task was for students to identify the errors and correct them. I was even up front with describing how I made the page. “Any error you see on the paper is something someone did on last week’s quiz, so there’s no need to be judgmental about mistakes you see.”
Students worked on the error analysis for about 20 minutes and it was interesting to hear the conversations in the room. I allowed students to work in partners to encourage this dialogue, but I was impressed at the level of dedication each student had to the task. Some students admitted they remembered making a particular mistake as they completed a problem, while other students openly said phrases like, “He forgot to rewrite the problem first. I probably made that mistake, too.”
When I passed back the graded quizzes, it was cool to see some of the reactions in the class. A couple students immediately put their corrections next to their quiz to compare, while other students confirmed what they already realized during the error analysis activity.
I share this vignette for a couple reasons. First, I want to remember to do this type of error analysis more often. Second, I liked the personalization of error analysis in this activity. Everyone’s heard of error analysis and I’ve always been a fan of Michael Pershan’s Math Mistakes, but I often end up fabricating fake work for students to pick apart or using work from some anonymous student from a website. The activity I used today reflected errors from actual students, which made the activity more relevant to my students. The best part is that the errors reflect the most prevalent misconceptions for this group of students, which further focused the activity. The activity also lowered the stigma of mistakes. Students were admitting when they saw mistakes they remembered making, but they were fine with it by knowing they would correct the mistake.
Does anyone else do this kind of error analysis? Am I alone in this practice? Let me know!