One of my favorite ways to practice a math skill is to complete error analysis. Regardless of how it is set up, the goal of this activity is to allow students to analyze a problem solved incorrectly, identify & explain the error, then solve it correctly.
Even though the concept is the same, sometimes the actual activity for error analysis looks different. Here are a few variations we have used in our classroom!
- To begin a lesson, we analyze errors from the previous lesson’s exit ticket. Students will try to identify the error on their own, share the error with a partner, and work together to come up with the solution (my favorite is when the student who made the error is the person raises their hand to tell us how to fix it).
- I like to have students solve & explain their thinking at the board (after solving & practicing how they would teach someone else, with an assigned partner). I have mentioned this before, but in our classroom we use non-verbal signals to tell the “teacher” if we agree or disagree with what they are doing. When someone is solving at the board, we nod if we agree with what they are doing. If at some point we disagree with what they are doing, we make a signal that is like brushing something off of our shoulder. If you can identify, explain, & reteach the teacher, you raise your hand while simultaneously doing the action. Before I have one student share with the whole class, I like to have them share at tables or with a partner so they all get a chance to share, then we come back together as a group & help whoever is teaching make that correction at the board.
- Error Analysis: Mission Impossible style! This is my favorite way to do error analysis, especially if I have a bigger chunk of time!
I have read a lot of books about engaging students in the classroom since I became a teacher, and I have always tried to implement what I am reading. I do believe that students can be more successful & willing to work when they are engaged in a task. When we are analyzing errors, it is almost like we are a detective or a spy. We have to look really closely at a problem & think critically about what someone else has done. As I was thinking about this, I decided to do a Mission Impossible style error analysis.
(Side note: Does that even match the detective/spy theme??? I don’t know, I have never seen the movie! I just know the song from my short stint of piano lessons in elementary school).
It took very little prep, but it take a lot reflection on my part. I decided to solve a variety of adding and subtracting mixed numbers problems incorrectly. I wanted it to be meaningful, so I didn’t just make random mistakes. I thought back on my last couple years teaching 5th grade & tried to recreate the most common errors my previous students made.
Some of those errors included not finding a common denominator & completing the operation on both the numerator & denominator, creating an equivalent fraction by multiplying the denominators while keeping the numerators the same, forgetting to add a whole when you simplify an improper fraction, or forgetting to borrow from the whole when your first fraction is less than your second fraction.
I solved each problem on a different piece of paper and hung them in different areas of our classroom. Students moved from problem to problem (in no particular order to eliminate a traffic jam). Here was the catch! They had to move like spies! Having them move like spies made it a little more exciting & less chaotic. I wish I could add a video to show you the creative ways they moved! I had some students who would walk slowly then do a fancy roll on the floor to get to the next problem, some students got low to the ground as if that would help them become less noticeable, while another talented student did a one handed front walk over (after making sure the area was clear of desks, chairs, & classmates, of course). And don’t forget the most important part… The Mission Impossible theme song (on repeat) playing in the background!
When students got to the problem, they would begin analyzing to see if they could find the error. For differentiation, I gave the students the option to discuss with the other students at the problem, but again they had to talk like spies (it was surprising quiet, but if you give them that role, they play it well!) Some might think this turns into one partner doing all the work, but when we help each other in our class, the expectation is to “teach not tell”. We regularly talk about why that is important & they do a great job!
Their recording sheet had two columns. One column gave them space to explain the error & the second was used to solve the problem correctly.
As students work on a more independent task like this, I like to wander around the classroom and ask them questions so I can understand their thinking. As I was walking around during this particular activity, I was realizing how rigorous this was considering their current understanding of adding and subtracting mixed numbers. In the moment it was discouraging, but then I remembered that rigor is okay, pushing them out of their comfort zone is okay, & making them think deeper is okay! Even though it was more on the challenging side, they loved it! They were gritty, had a smile on their face as they moved from problem to problem, & helped each other throughout the task!
I think there is true value in students being able to understand a concept well enough to identify the errors other make while solving a problem. I also believe one of the best ways to learn is from mistakes. I have not done any research on this, but I’ve noticed analyzing others’ mistakes (or our even our own mistakes) makes us more aware of them & we are less likely to make those same mistakes again.
Error analysis has been a staple in my classroom & I see myself continuing to use it for many years to come (that is unless something else better comes along… I’m not against change if it will benefit my students)!!