The Teacher Tip

What Are Mathematical Habits of Mind?

September 6, 2017

Adapted from Making Sense of Algebra: Developing Students’ Mathematical Habits of Mind by E. Paul Goldenberg, June Mark, Jane M. Kang, Mary K. Fries, Cynthia J. Carter, and Tracy Cordner

Building strong mathematical habits of mind in students is a way of bringing coherence and meaning to mathematics. It also brings texture to the subject, highlighting significant insights over convention and vocabulary. Students learn that they can use their experiences to build habits—ways of thinking about and approaching problems. They move away from the belief that mathematics is a set of arbitrary rules and procedures to apply and begin to see mathematics as being about making sense of and solving complex problems. In the transition from arithmetic to algebra, students learn a powerful new language for expressing numerical ideas and for describing pattern and structure.

Some important mathematical habits of mind include:

  • the I-can-puzzle-it-out disposition
  • using precision in thought and communication; characterizing problems and solutions in precise ways
  • subdividing and exploring problems by posing new and related problems
  • tinkering with problems (concretely or with thought experiments)
  • seeking, articulating, and using underlying structure
  • choosing approaches both strategically and flexibly.

To learn more about Making Sense of Algebra, and to download a free sample chapter, visit

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