A
person with the **habits of mind** of a mathematical thinker can use their knowledge to make conjectures, to reason,
and to solve problems. Their use of
mathematics is marked by great
flexibility of thinking together with the strong belief that precise definitions are important. They use both direct
and indirect arguments and make
connections between the problem being
considered and their mathematical knowledge. When presented with a problem to solve, they will assess
the problem, collect appropriate
information, find pathways to the answer, and be
able to explain that answer clearly to others.

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While
an effective mathematical toolbox certainly includes algorithms, a person with well developed **habits of mind** knows both why algorithms work and under what circumstances an algorithm will be most effective.

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