Justifying Your Work in Math

We are always telling students to justify their work, explain their work, and show their work but how often do we take time to teach students to do this.  I've been focusing on having students "show" their work because it is a way to communicate their thinking.  I do need to work on having them explain or justify their work and that is a bit different.

First, you need to inform students of your expectations on what constitutes justifying your answer.  Do you want them to label everything?  Do you want them to show only calculations or do you want everything including the drawings or models included.  Do you want them to explain how they arrived at their answers in words discussing each step and their thoughts?  Do they need to explain how they made sure their answer was correct?  Put the answers to all these questions on a chart so they can refer to it every they have to justify their answers.

Second, provide each student with a smaller sized chart of their own containing everything they need to include in their answers.  These are the same things you have on the large chart in your room but every student has an individual copy to use.

Once students have these tools, they need multiple opportunities to practice justifying their answers.  This might be taking a word problem and breaking it down into chunks so students have a chance to answer each part and explain how they arrived at the answer.  Furthermore, it is possible to write the questions so they are differentiated to meet all the abilities of the students.

Regularly incorporate opportunities for students to justify their answer when using word problems and regular problems. Students need practice justifying their answers in both situations because they often need to do this for all sorts of tests.  In addition, they need to develop the vocabulary necessary to communicate their thoughts so others can see their thinking.

In my opinion, justifying your answer is being able to write more than just a phrase or identify the property that allows you to do what you did.  It is being able to show understanding of when and why certain things. are used to solve problems.

Furthermore, this process needs to be started down in elementary school rather than waiting till students reach middle or high school.  If they start early, it will become second nature to students and they won't fight it in the upper levels.  This also helps them develop the ability to ask focused rather than general questions.

Let me know what you think, I'd love to hear.  Have a great day.