Error Analysis

Interestingly enough, as a teacher you’re concerned with students getting correct answers when it comes to math problems. However, a student’s wrong answer can tell you a great deal about what they know and understand.

 Have you ever graded a test, multiple choice or single answer, and found a large portion of students submitted the same wrong answer? If it’s a multiple choice question, hopefully all choices were designed with common student errors in mind. By doing so, you create the opportunity to group students post-test into groups according to the mistake they made.

 This next instructional strategy I’m about to explain is not my own. In fact, I’m not certain who initially came up with this idea, but it is one that I, and fellow teacher s, have used and found very informative. What you do before and after this strategy is up to you as the teacher. This idea simply gives you an idea of how to collect data about what students know and understand.

 Let’s start with a simple concept like solving one-step equations. Provide students with a questions such as x – (-3) = -7. We know the answer to be -10, because subtracting 3 from both sides is the correct step in isolating the variable for this problem. We see this equation to be x + 3 = -7 by use of the definition of subtraction that states a – b = a + (-b). Only after we “clean up” the question are we able to see what operation we need to undo during the solving process. This particular problem is a quite difficult for 7th and 8th grade students who are just learning how to solve equations. Common mistakes are to add 3 to both sides, producing a -4 solution. Other mistakes are to correctly perform the operation to solve only to apply integer operations incorrectly. If students did indeed subtract 3 from both sides, they could come up with -4 or 10 as incorrect solutions. If we play the role of the student when designing question, we can perform error analysis during classroom instruction.

 Using this particular example, we arrived at solutions of -10, -4, and 10. The value of 4 could be justified as an incorrect response if students did not apply integer rules correctly when solving the simpler, yet equivalent, equation x + 3 = -7. Provide students the original question, x – (-3) = -7, and have them solve this equation and show their work. Have the potential answers of -10, 10, -4, and 4 posted around the room inconspicuously. Once students have found an answer, and before you have disclosed the correct solution, have students get up and stand by their response. Give them one or two minutes to discuss as a group how they found their common answer. Next, have one member from each answer group explain to the whole class how they arrived at their answer. After all students have listened to all of the groups’ responses, they must then decide to agree with their original group, or decide to join a new group. They must provide an explanation to why they are choosing to join a new group by stating the mistake they made in their solving process that arrived at a new answer.

 This can be applied to any multistep problem, on in which common misconceptions or error may occur. There may be anywhere from 2 to 5 possible responses students may have, depending on the error they made. Do your best not to make any judgment calls prior to students forming groups and making their final decision on an answer based on each group’s explanation. This provides students the opportunity to evaluate their steps and problem solving process against others in the class. This is a level of analyzing that most of the time does not happen when we, as teachers, simply mark a student’s paper for incorrect responses. Once students become accustomed to this type of discussion and error analysis, they will become leaders in their own education.

 I will caution you on stopping the discussion at disclosing the correct solution for the problem. I encourage you to provide students the reason as to how they could have arrived at the incorrect solutions where predetermined.  You will find students with incorrect answers that do not fall into the anticipated incorrect responses. Take this opportunity to allow the student to perform their own error analysis on their work and have them explain their mistake.

 This is a powerful tool that creates analytical students and better test takers. Of course, it’s important for students to understand how to arrive at correct solutions for problems. However, students can gain a great deal more information from learning what they did incorrectly. It’s important for students to know when they got a question incorrect, but to maximize learning; students must understand how they got a question incorrect.

Please share ways in which you have utilized, or will utilize, this stategy.

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