Teaching Error Analysis in Math.

 Many math teachers do not take time to have students analyze errors to learn more.  I know most of my students would rather not look at any problems to see what they've done incorrectly.

Learning to look at errors and analyze them is an important skill. There are several reasons to teach students to perform error analysis.  First, this promotes higher level thinking skills because it requires students to create, analyze, and proving hypothesis, thoughts, and ideas.

Secondly, it helps students connect the conceptual with the steps needed to solve a problem.  When students focus on the process, they often loose sight of the concept associated with the problem.  When they are able to find the mistake in the process and explain the error, they are showing they understand the concept.  Finally, it helps students prepare to take tests with multiple choice questions.  If they find an answer that is not one of the choices, they can review their math to find the errors.

There are some activities one can include in class to help students learn to analyze to find errors.  It is important to use these activities to help students learn to analyze their work for mistakes because most do not know how to do it.  I know from personal experience most of my student's analysis before they learn to do it usually consist of "I didn't know how to do the problem" or "I have no idea".    In addition, learning to analyze mistakes helps students develop their ability to communicate their thinking.

No matter what the error is in the problem, students need to rework the problem correctly so they get the expected answer.  It is not enough just to identify the error but they still need to do the problem correctly.  Both parts are needed for students to complete the error analysis.

One way is to assign a problem to students to work.  Then collect the solutions and check them quickly to find the ones that were done incorrectly.  Choose on of those to have students look and see if they can figure out what was done incorrectly and what needs to be done to do it correctly.  The other choice is to do a problem incorrectly and have students identify the error and how to correct it.  Some textbooks now have problems in each section in which allow students to practice their error analysis.

Create a gallery walk with several problems done incorrectly on them, spaced around the the classroom.  Divide the students up into groups of two or three and have them go through and find the error on each sheet.  You can have them write down their solutions on the sheets or on a separate sheet of paper.  By putting students into small groups, they need to discuss the error and it improves their communication skills.

It is suggested that students stop erasing mistakes as they do the problem.  Instead, have them circle the mistake and explain what it was before continuing to the end of the problem.  This teaches students to avoid making the same mistake in the future and it shows students that making mistakes is a part of the process.  It helps students accept that making mistakes is fine but you need to use those mistakes to learn to do the problems correctly.  Furthermore, students have a way of helping themselves assess their understanding.

My next entry will be about using centers in middle school or high school math because one center can be on analyzing errors.  Let me know what you think, I'd love to hear.  Have a great day.