The other day, I realized the only time I require students to perform an analysis of their mistakes is when they want to retake a test. Otherwise I don't do it. Its mostly because I literally don't have the time.
To effectively learn the material, it is not a question of how much practice, its more a question of the type of practice done. In other words, its best to determine what is not working and mastering those before moving on.
In school and in math, most students react to mistakes emotionally and often feel stupid. This means we need to look at removing the shame associated with mistakes so students will look at the mistakes to see why it was made rather than hiding.
It is important to get students to look at the errors instead of stating they bombed the test. In math the mistake is something as simple as dropping a sign. One way to help students look past their shame is to take one or two of the most common errors made by the students and analyze them as a whole class. Look at the specific mistake together.
It is said that mistakes have a concrete basis such as ignoring a sign, forgetting your multiplication facts, even forgetting to borrow properly. Teach the students the teachers mark is simply a sign saying hey look at this and see where you made the mistake in the process.
Many teachers do not require that students check their work. Until I read this, I have often allowed them to do the check in their heads but after reading this, I realized its easy to make a mistake in your head. Starting this week, all students will be required to check their work when appropriate. This is not a habit I used in college or in most classes I've taken.
Its interesting that even know for all the discussion we have that students need to learn the concepts and the full process, many of us still promote answers as either right or wrong. When I was enrolled in teacher training classes back in college, there was a huge discussion on do you take the stand of the answer is completely right or wrong?
Other training I took along the way enforced the same idea for tests but with the added idea of having students go through the test and figure out where the mistake was, rewrite the problem so its done correctly and explain where the mistake occurred. It is only as I write this entry that I realized no one has ever talked about teaching students to find their mistakes.
I think that may be the missing key in helping students see that making a mistake is not failure but a step towards seeing it as an indicator of focus to learn that part better. Tomorrow I"m going to discuss ways to teach students to check their work for weaknesses rather than mistakes that caused the calculation to be wrong.