Regardless of which standards guide your math classroom, or the curriculum you follow, you are sure to find the demand of students to 'justify their solutions.' This sounds reasonable, right? We should be able to back up our conclusions with logic, reasoning, and evidence. But experience shows that this process is much more difficult in practice. Entire 45-minute sessions can be consumed by a single justification attempt. How can we encourage understanding and rigor and still get through the mountain of content required in our pacing guide?

At the heart of the 'justification' demand is the desire to empower understanding. Instead of simply repeating a procedure endlessly, justification lets students express their understanding in a deep and meaningful way. But if we make that process inflexible, then all we have done is created another layer of confusion for students.

Read this short blog from Dan Meyer, an inspiring math educator, who considers the tension between understanding and explaining, and how, when misguided, can produce unnecessary and confusing results :

When students use Symphony Math, they see their solutions justified with visual models. This is our way of reinforcing the relationship between number sense and spacial relationships. Below we check a multiplication fact by using a grid (area model):

This technique works for us because it is fast, it is consistent, and it provides a visual justification. If the student has made an error, they can correct their work and see it reflected in the model.

In your math classroom, justification can come in the form of questioning. Consider using some of these questions when students are working:

• "How do we know that this answer is correct?"
• "What strategy did you use when you answered this problem?"
• "Can you represent your solution with a model?"

These questions may lead to interesting math talks, or they may simply be a 20-second confirmation of a known strategy. You might even gain some insight into gaps in understanding. Regardless, your consistent questioning encourages students to understand, question, and justify their solutions.

New behaviors take time. Be patient with yourself and your students. You don't need to demand a written paper for every solution, but you do want to encourage students to engage with, and "own", their math understanding. Will student responses to your questions be messy at times? Probably. But as your routine continues, students will begin to embrace their responsibility, and their expressions will become more organized and more informative.

Good mathematicians can justify their work: in fact, it is a critical part of their success. And with consistent expectations and practice, the ability to justify can become another great tool for your math classroom.