Why Is It Important To Analyze Mistakes?

I work with students who come to high school with the idea they do not need to show their work and once it is turned it, its all over.  When I return the work, all they want to do is throw it out.

Consequently, they really do not know how to examine their work to find the errors nor do they use the mistakes to help them learn the material better.

I admit, I'm partially at fault because I do not require them to analyze then their mistakes nor do I have them verbalize why they made the mistake.  Thus they continue to make the same mistake as they progress through the course.

Its a bit late this year to start this since school ends in about a month but I can make it part of the course requirements next year.  If students learn to identify the types of mistakes they are making, it means they can learn to identify it when they check their work.  In fact, most of my students have never learned to check their work before turning it in. 

I read somewhere recently, where the teacher required her students to go through all returned papers, identify the type of error they made and record it in their journals as a way of keeping track of this.  Other teachers only use this for tests where they have students write down the problem, correct it, explain what the mistake was before they can retake the test.

It is said that understanding where you go wrong and how you go wrong can lead to better understanding and improved grades.  In addition, it  is a habit good math students have.  Furthermore, as a teacher, you can write your next test to that it contains problems based on student errors.  We have to teach students to analyze their errors so they can improve.

Most errors fall into five categories:

1. Mechanical errors such as transposing numbers, dropping a sign, being too much in a hurry, or making a simple mathematical mistake such as 2 x 3 = 5.

2. Application errors such as misapplying a step in the process.

3. Knowledge based error where they do not understand the concept or do not understand the term.

4. Order of operation error where they do not understand when they can do things slightly out of the traditional order.  The elementary school has Order of Operation posters made by students hanging on the wall and they all have addition, subtraction, multiplication, and division in that order without the left to right based on what comes first.  This means students arrive in high school thinking they have to add before they can subtract, multiply before they can divide.

5. They have incomplete knowledge so they need to practice to get it.

It is recommended students keep a journal for analyzing all mistakes, patterns of errors, review concepts that give a student problems, review all previous assignments and tests, ask for help as soon as possible, and always diagnose problems immediately.