Tuesday, October 18, 2016

Changing Perceptions of Mistakes Part 2.

Arrow, Problem, Trouble, Difficulty
   Yesterday, I discussed societal perceptions of math being only right or wrong so if you make a mistake you are wrong and a failure but as we've seen that is not always true.  Making a mistake is just a signal letting the individual know it may be a misunderstanding of the math process, it might be a sign that was lost, or numbers switched.

Today, I'm looking at ways to help students learn to identify the type of mistake they are making so they can work on becoming more proficient.  It is not easy to work something else into your day but I figured out how I can use some of these suggestions with my students.

1. Write a problem on the board with several solutions.  Ask students to rank the solutions from best to worst. Next have the student discuss the ranking with their neighbor and create the criteria for ranking the solutions.  Finally, create a list of the most common mistakes and suggest ways to catch them or prevent them.

2.  Assign a select number of problems for students to complete.  Ask them why they think their answer is correct or incorrect.  Ask students questions to help them see different ways of reflecting on their thinking. 

3.  The teacher needs  to monitor student work to see areas of misconceptions so the teacher can help clarify those areas.

4.  Take time in class to create a list of the top ten mistakes they do such as multiply the number by two (the exponent) rather than squaring it.

5.  Help individual students create a list of their own common mistakes to use as they do their work such as switching digits in a subtraction problem so they don't have to borrow.

6.  Have students mark the spot where they run into problems as they work the problem so if their answer is incorrect, they can return to see if that is where the mistake occurred.  This also identifies something they can ask for additional help in learning because it lets them know what they still don't know.

My final thought on this is that I have not explicitly taught my students to learn to analyze their errors.  I have just started including one math problem in their warm-ups that will have an incorrect answer.  Their job will be to determine where the error occurs and what the exact error is.  How can I require them to find their own errors if I have not taught them the process?

Tomorrow, check out teaching students to self-correct.  The first step is to change people's mindset from getting a problem wrong is failure to an incorrect answer is actually just telling us where we need a bit more work.  Teaching them to self-correct is the next step.