The Importance of Finding Mistakes.

  My students hate looking back at any problems they made a mistake on.  As far as they are concerned, they answered the problem and its done.  Who cares if its correct.  I don't spend enough time on helping them learn to identify mistakes and verbalize the reason for making the mistake.

One common error I constantly see is in using the distributive property, they only multiply the first term in parenthesis.  If they remember to do something with the second term, they usually add the numbers rather than multiplying.

Unfortunately, my students have it ingrained in their heads that anything they do must be graded or its not worth anything.  They do not want to correct mistakes because there are no points associated with the activity, therefore its worthless in their minds.

One of the first steps I have to do is convince them that it is important for them to find their basis of their misconception which causes them to make the same mistake over and over again.  The important thing about making mistakes is that it is part of the learning process.  To identify the cause of the error is a step to gaining understanding and deeper learning.

I don't do this enough but I plan to do more of this activity next semester.  During warm-ups, I plan to put a problem with mistakes and ask students to identify what was done incorrectly and how should the problem have been done.  This way, they get practice identifying mistakes and correcting them.

Here are some reasons why making mistakes is a good thing and what they help you learn.
1.  Making mistakes show everyone you tried.  The student may not fully understand how to do it but when they don't try, there is no chance of learning.

2.  Trying the problems help exercise their brain because the brain likes solving challenging problems.

3. When they understand why certain mistakes occur, it means that they are able to do that type of problem using a deeper understanding.

4.  When a student finds the error and is able to correct it, experiences personal satisfaction.  It also helps build the persistence necessary to work through more complex problems.  It also helps them increase their motivation to learn.

5. Teachers can mistakes as a form of assessment because analyzing the type of mistake can give the teacher information for scaffolding or reteaching a topic if the majority of students are making the same error.  Mistakes are multifaceted and offer so many possibilities for assessment.

6. Create an environment where it is acceptable to make mistakes and where students are not afraid to make them.  Make them aware that it is fine to make a mistake but once the mistake is identified, they need to continue working until they have a correct answer.

7. Provide timely feedback on the mistake.  As part of the process, it is important to determine if the mistake is a misconception, systematic error, or careless mistake so students know what to look for the next time they work a problem.

8.  It is equally important to provide students the chance to correct mistakes on their own. By looking to find the root cause of the mistake, it helps develop conceptual understanding.

9. Use technology that helps support mistakes by providing immediate feedback.  I've discovered I need to train my students to look at the feedback, otherwise they ignore it and move on.

These are some reasons students need to be allowed to make mistakes and to make corrections including a short comment on why the mistake was made.

Let me know what you think.