# From the Book: Our Four-Part Model

Argumentation is complex and social; teachers need help implementing it in an organized way. Each part builds on the prior part, so that students build up the means to make arguments.

## Equity

When argumentation is unfamiliar, the four-step model makes it approachable. Specific norms, which may be unfamiliar for math class, can be attached to each stage in the model.

### Generating Cases

When students *generate cases,* they create numeric expressions of geometric shapes in which they look for and examine patterns.

You need something to conjecture about!

### Conjecturing

A *conjecture* is a mathematical statement that you think might be true.

- Fundamental to argumentation
- “Being right” is not required
- “Make bold conjectures” is a norm
- Open ended and creative

You need a specific claim to justify!

### Justifying

Justifying occurs when students present reasons for why a conjecture is true or false.

- A good justification convinces others. It goes beyond a personal exploration of an idea.
- Comes from answering why questions- should happen all the time.
- Logically connected series of statements (but won’t often come out in that order).
- Representations and language are both important.

This is commonly thought of as argumentation.

### Concluding

Concluding has two parts:

- deciding whether a conjecture is true or false and
- summarizing the justification in logical order.

- Additional steps: What is the next related conjecture to explore?

Because argumentation is social, need to know when the class agrees.