M2 Innovations
“Habits of Mind” Problems
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.

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.