Why?

  There has been a lot of debate about why is it necessary to have students express their thought process when they do a performance task or other math.  Why not just let them do the math or put the answers down.

I have given that whole topic quite a lot of thought.  Why do they have to explain if they can do it.  Hmmmm.  Well after some thought, I realized that society is turning to the idea that you have to be able to communicate your thought processes.

We share our thinking through blogs, social media, etc.  We are expected to communicate our thoughts.  If you don't have a facebook page, a twitter account, or any other form of social media you are out of step with society.  In addition, people expect you to explain the details involved in a project, or a campaign or even in some sort of research. 

So perhaps the idea behind the common core of having students explain their thinking is the first step to being able to communicate.  Furthermore, students are expected to have reached a certain level of literacy in school and literacy is included in Mathematics.   This is especially important when working with English Language Learners (ELL)

If a student does not have the vocabulary to express their thinking or ideas, then they have trouble formulating the questions to ask when they don't understand something.  Furthermore, its quite possible that when a student explains their thinking, misconceptions will reveal themselves during the explanation so we can identify possible problems.

Several years ago, I had a student who drew a diagram for a fractional problem and discovered at that point she thought that the object just needed to be divided into so many parts.  She didn't realize the divisions had to be equal.  If she had not drawn a diagram to show the problem, I would never have discovered that misconception.  

I sometimes have students draw a diagram of something because that is one way they can express their thinking.  In addition, I found cases where students began explaining something and it suddenly hits them that they approached the problem incorrectly and need to rethink what they did.

I think the bottom line is in how we have students explain their thinking as to whether its a good or bad thing.