### Description

**How do I know it works and how do I convince others?**

Provide evidence and reasoning to convince others that your claim is valid.

### Time To Complete

### I Can Statements

I can

- Explain how my mathematical argument accurately addresses my claim.
- Apply correct reasoning to make my mathematical argument.
- Provide a mathematical basis for my argument.

I will know that my articulation of the effectiveness of my mathematical argument is of high quality when it:

- Explains how my mathematical argument accurately addresses my claim.
- Applies correct reasoning to make my mathematical argument.
- Provides a mathematical basis for my argument.

Ask students to use Jo Boaler’s three levels of being convincing: convince yourself, convince a friend, convince a skeptic. Have students begin with the first level and work up to the final level, adding more detail or explanation as they go along.

Provide examples of convincing mathematical arguments. Have students evaluate exemplars with rubric-specific feedback to help solidify what they need to do for the task. Exemplars can be coded as well, using indicators to mark necessary parts of the argument.

Ask students to generate counter-examples or to introduce false claims, which they can discuss with a partner. They should then reflect on how exploring false claims and counter examples can help them clarify their own argument.

### Resources

- Proof as a tool for learning mathematics: http://web.mit.edu/bskow/www/215-S12/knuth_proof-as-a-tool-for-learning.pdf
- Introduction to mathematical arguments: https://math.berkeley.edu/~hutching/teach/proofs.pdf
- Some Remarks on Writing Mathematical Proofs: http://www.math.washington.edu/~lee/Writing/writing-proofs.pdf
- Sample math sentence starters: https://elementarynumbertalks.files.wordpress.com/2016/08/math_talk_sentence_starters.pdf
- Several tips for promoting mathematical argumentation: http://www.nctm.org/Publications/Teaching-Children-Mathematics/2016/Vol22/Issue7/Promoting-Mathematical-Argumentation/