What is it?

Why? Let's Justify discussions are useful as students reflect on general ideas, concepts or strategies.  We know that producing explanations is an important part of making sense of mathematics and can help students build their mathematical understanding.

When and Why is it used?

You may consider doing a Why? Let's Justify discussion when there is a main idea or generalization that we want students to examine.  This type of discussion requires us to press the discussion beyond procedural descriptions and into explanations that include reasoning.  

Research into children's thinking has shown the following forms of justification that students use when they are trying to convince themselves of an idea. (see Lannin,Ellis and Elliott 2011 for a discussion on mathematical reasoning in the elementary and middle school years.)

1. Justification through appeal to authority.

Students may justify an idea because someone or something else told them it was true.

2. Justification through examples.

Students may try to convince themselves that a mathematical statement is true by giving lots of examples that work.  Of course, examples alone can't necessarily justify something is true; all that it takes to refute a mathematical statement is one example where it doesn't hold.

3. Justification through a generic example.

As students gain more experience, specific examples might be replaced with a generic one.  Students may also develop models that help them make their case.  When students start playing with a generic example, they use a specific model but talk about it in a more general way.  These are powerful ways for elementary-aged students to engage in justifying claims.

4. Justification through deductive argument.

In mathematics, justifications are always based on logic.  When students are convinced by the truth of one statement, they can use that agreed upon understanding to connect other statements that follow by logical deduction.  Younger students may rely on physical or visual models more than on symbols to show the way several ideas logically build on each other.

Examples: Planning a Why? Let's Justify Discussion

Use the  Why? Let's Justify  template to think through the following instructional plan using these guidelines that Susan Jo Russell, Deborah Schifter, and Virginia Bastable (2011) provide about how to focus students' attention on justifying a general claim:

• Choose accessible numbers when first trying to make sense of a general idea.

• Use a set of expressions or a true/false equation and focus on the meaning of the expressions instead of just carrying out the computation.

• Ask students to show their ideas using cubes, number lines, arrays, story contexts, or other representations they have been working with.

• Identify general claims worth justifying by listening for the patterns, mathematical relationships, or underlying structure of numbers your students notice as they do mathematics.

Key Components of Why? Let's Justify Discussion

During a Why? Let's Justify discussion, the talk narrows up on a general claim in order to closely examine the mathematics and generate a justification for it.  Certain types of mathematical ideas lend themselves to this type of discussion:

• A rule or "trick" is commonly used, but students may not have a conceptual understanding of why the rule works and therefore may struggle to generalize the rule with accuracy when solving new problems.

• You can connect a strategy students are beginning to use to a visual model or a problem context in order to make sense of how a strategy works regardless of the numbers.  

*We suggest being very specific and narrow in your approach to using this strategy.

This strategy comes from chapter 4 of the book Intentional Talk: How to Structure and Lead Productive Mathematical Discussions by Elham Kazemi & Allison Hintz