What is it?

As teachers help students gain mathematical knowledge, confusion and partial understandings may occur.  Engaging in discussions about these confusions and partial understandings help teachers and students make sense and work through stumbling blocks together.    This work can be delicate in nature as publicly sharing their errors and revising their thinking can be challenging.  It is essential to build a mathematics environment where learning from errors together is a postitive experience.

When and Why is it used?

Troubleshoot and Revise can be initiated by a teacher or by one or more students.  In either case, the teacher or the students have noticed something that is awry and can seek the collective engagement of the class to figure out what needs to be revised.  Troubleshoot and Revise may be initiated for a variety of reasons:

• students might recognize they have partial understanding and are stuck

• they may notice a strategy they used, which seemed to make sense, resulted in an answer different than that of their classmates

• the teacher may notice a misunderstanding bubbling up and worthy of attention

Teachers can use errors as opportunities for advancing mathematical thinking.  We want students to know that thoughtful mathematicians voice their confusions; thinking collaboratively through errors can help everyone better understand the mathematics.  

Examples: Planning a Troubleshoot and Revise Discussion

Use the  Troubleshoot and Revise template to think through the plan when you have the opportunity to realize students have partial understanding or are stuck:

• Identify the confusion or misunderstanding that needs to be addressed

• Identify the mathematical insight you need students to understand

• Identify problems, diagrams or questions that may be helpful in the discussion

• determine an exit ticket or assessment to check for understanding

Key Components of Define and Clarify Discussion

This structured process allowing students or a group of students to think aloud together to make sense of mathematics.  Sometimes the confusion is minimal and does not require a large group, but sometimes the confusion is greater.  A targeted discusison is useful to slow the conversation down to uncover the confusion and bring new understanding.  Troubleshoot and Revise discussions are great for when:

• you observe several students in your class grappling with an idea, and you think other students could help clarify the confusion

• a student comes to you with the idea he or she is willing to put in front of the class and you believe the class has the resources to support the student in thinking through the idea

• you want to support norms for revising one's thinking

This strategy comes from chapter 7 of the book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi & Allison Hintz