# Habits of Mind of a Mathematical Thinker

Across all of the mathematics courses is an overarching goal of helping middle level mathematics teachers develop mathematical habits of mind. Mathematical habits of mind represent an enriched view of what it means to do mathematics, based on orientations mathematicians bring to their work, and the expectations for mathematical understandings for preK-12 students articulated in dimensions of mathematical proficiency and the NCTM process standards. As a project, we continue to construct and reconstruct our own understanding of the phrase. This table represents the projectâ€™s current working definition, presented as a set of skills and dispositions of a mathematical thinker.

A mathematical thinker with well-developed habits of mind:

- Understands which tools are appropriate when solving a problem
- Is flexible in his or her thinking
- Uses precise mathematical definitions
- Understands there exist multiple paths to a solution
- Is able to make connections between what one knows and the problem
- Knows what information in the problem is crucial to its being solved
- Is able to develop strategies to solve a problem
- Is able to explain solutions to others
- Knows the effectiveness of algorithms within the context of the problem
- Is persistent in his or her pursuit of a solution
- Displays self-efficacy while doing problems
- Engages in meta-cognition by monitoring and reflecting on the processes of conjecturing, reasoning, proving, and problem solving