## Tuesday, March 12, 2013

### Error Analysis for Enrichment and Critical Thinking

This year, working with a wide variety of students, many needing either extra help or extra enrichment and extensions, I have been doing a lot of reading about all different levels of need.  One of my absolute FAVORITE ideas for enrichment this year has been error analysis.  I have done it with my 3rd, 4th, and 5th graders on different topics, and they are a big hit.

Why I love Error Analysis
• The Research I began creating Error Analysis sheets for my students after reading about Marzano's New Taxonomy (Systems of Knowledge).  Under Analysis, he lists Error Analysis as an exceptional way to promote thinking and learning.  As soon as I read this, I knew error analysis would be incredibly meaningful for both enrichment purposes AND reteaching purposes.
• Students Love It! My students LOVE, LOVE, LOVE the challenge error analysis poses, and I have even seen kids take error analysis sheets out to recess because they are determined to figure out what error took place or the perfect wording to describe what happened.
• It Encourages Critical Thinking  So much of what students are asked to do in math is all about solving the problem and finding the answer.  That's important, but students need to look at math in different ways to truly grasp a complete understanding of concepts.  If we only ask students to solve problem after problem, we end up with a very surface-level understanding of a concept.  When we give them error analysis tasks, students are challenged to figure out the error, explain the error in their own words, rework the problem, and attempt to give advice to the student who made the mistake.  That's a lot of critical thinking going into one problem and really increases their depth of understanding!
• Students Can Analyze Their Own Mistakes  When I see that a student has made a mistake on his/her work (especially when I am conferencing individually with them), I always ask them to find their error rather than telling them what they did wrong. Before I explicitly taught error analysis, it was rare that students could find their error, especially if it wasn't super obvious.  After having the direct practice of error analysis, students are much better able to look through their work, step-by-step and identify the error.
• It Prevents Students From Making the Same Mistakes  Although I usually assign error analysis tasks toward the end of a unit, when students have nearly full conceptual understanding of a concept, it always amazes me how SEEING an error first hand can prevent students from making that same mistake in their own work.

How I Create Error Analysis Tasks

I research different errors that are commonly made in whatever concept we are working on, I pull from common errors I have seen before, and I take errors that my kids are currently making.   Then, I make a page with a problem that has an error, and it is the student's job to figure out what the error is. This is not easy for students, but oh my, it sure stretches their thinking!  You can easily take any student error and turn it into an error analysis task.

I teach students how important it is to walk through the problem step-by-step.  They need to figure out if the student has made a basic computational mistake or if the student has made an even bigger, more significant conceptual mistake.

Once they figure out what the problem is, they have to give the "student" who made the mistake some advice on avoiding making the same error next time.  This is also challenging for the kids, but I have seen so many amazing new understandings come out of this type of thinking.  Finally, students have to rework the problem on their own.

At the beginning of the year, we complete several error analysis examples together.  My FREE addition error analysis is a good place to start, no matter the grade level. I show them the process of walking through the problem and how best to complete an error analysis task.

From that point forward, I have students complete error analysis tasks for just about every math concept It each.  I usually do one or two examples with the kids first so that they know my expectations and so that they can warm up their brains to the types of errors that might be made in a specific math concept, and then they are begging me to pass them out and send them off on their own.

Ways to Use Error Analysis
You can use these error analysis tasks in so many different ways.  For my talented and gifted kids, I have used them as an assessment when they have shown mastery of a unit during other tasks.  For kids in the regular classroom needing enrichment, I usually have them complete the tasks in a center or with a partner.

For students needing extra support, we complete error analysis in small groups.  We go step-by-step through the concept and they are always able to eventually identify what the error is.  It is so empowering to students when they finally figure out the error-- AND it helps prevent them from making the same error in the future.

I have even sent these home as homework, which the kids love!

I have included the addition with regrouping error analysis for free because it's the perfect place to start, no matter the grade.  Try them in your class, and if you do, let me know how it goes!

Updated 2017:  When I originally posted this in 2012, I never imagined how much I would TRULY fall in love with Error Analysis!  Since then, I have created error analysis tasks for almost every math concept I teach, and my students beg for them!  Click the image below to find all of my error analysis tasks: