Finding Errors

  As I mentioned yesterday, its hard for students to find the error they made if they do not get the correct answer.  I've been wondering about techniques I can include to help students learn to find their errors.

It seems that once the student has completed a problem, their mind shuts the door on it and moves on because they are finished with it and don't need to check it.

One suggestion I ran across is to have a poster in the classroom for the top 11 errors made in math calculations hung somewhere in the room so they can check it before they move on.

1.  Did not distribute the outside term to both terms inside the parenthesis. This includes not distributing the negative sign with the number.

2. Multiplying by 2 instead of squaring.  In other words they multiply by the exponent, instead of applying the power.

3. Adding instead of subtracting or vice versa.

4. Adding instead of multiplying or vice versa.

5. Misplacing or loosing a decimal.

6. Making a rounding error.

7. Forgetting to carry a number or to borrow.

8. Forgetting to change the inequality sign when dividing or multiplying by a negative.

9. Making a mistake when cross multiplying ratios.

10.  Making a mistake when adding/subtracting/multiplying/dividing a fraction.

11. Omitting units or incorrectly converting units. 

I think I'm going to run this list of common mistakes off and give each student a copy so they can use it to double check their steps.  Of course, I'll have to model its use but if I use it regularly, perhaps they will choose to use their list.

It is also suggested that the teacher change the way they identify mistakes for students.  Rather than saying  "You made a mistake", say "I'm glad you made the mistake, it means you are thinking about the problem and you can learn from it."  I tend to let the student know they missed a step when solving it, so go back and check to see if they can tell where they missed the step. 

In addition it is good for the teacher to make a mistake, correct it, and let the students know what the mistake was and why they did it.  It shows that teachers are not infallible. Teachers are human.  Too often students are under the mistaken impression that math teachers are extremely smart, like Einstein.  Its important to show them we are human.  Make it normal to look at mistakes so they are no longer something to be feared but celebrated.

When a student makes a mistake, it is important to correct it but also to understand why the mistake was made.  By correcting the error and knowing why it was made, it gives the student a personal sense of success. Furthermore, the type of the mistake provides an assessment for the teacher.  The mistakes let the teacher know, what has not been mastered yet.

In a sense, this is something that should be started in elementary but it isn't always so it is necessary to work with students in high school.

Let me know what you think.  I love to hear from my readers.  Have a good day.