What would make my claim valid?
Use a variety of tools and strategies to figure out if a mathematical claim can be made valid.
Time To Complete
I Can Statements
- Use a variety of tools and strategies to systematically tinker with a mathematical claim.
I will know my tinkering with claims is of high quality when it:
- Systematically uses a variety of tools and strategies.
In the case that one student believes that the claim is true while the other believes that it must be altered, these students should present their cases to their peers for a full class discussion.
Encourage students to use their empirical examples as a starting point to think about what they need to change. In particular, disconfirming examples may all have a particular characteristic that, if excluded, could make the claim valid.
Ask students to intentionally create an invalid claim and share the invalid claim with a neighbor. The students discuss why the claim is invalid and any insights they gain that can be applied to tinkering with their claim.
As students come up with wrong answers or make missteps, share them with the class using ‘My Favorite No’. A related strategy is for the instructor to present an incorrect proof/solution, and then have the students discuss what insights we can learn from it. My Favorite ‘No’: http://www.redesignu.org/design-lab/learning-activities/my-favorite-no
Share and discuss articles about the importance of making mistakes in math.
Provide students with both examples and non-examples and ask them to sort them and record their strategies and processes as they do so. Once they are sorted, ask students to reflect on the process and strategies they used.
Articles on the importance of making mistakes in math