The goal of mathematics education should be to produce mathematically powerful students – students who are competent and confident.

Mathematically powerful students:

  • Understand the power of mathematics as a tool for making sense of situations, information and events in their world
  • Are persistent in their search for solutions to complex, “messy” or “ill defined” tasks
  • Enjoy doing mathematics and find the pursuit of solutions to complex problems both challenging and engaging
  • Understand mathematics, not just arithmetic
  • Make connections within and among mathematical ideas and domains
  • Have a disposition to search for patterns and relationships
  • Frequently make conjectures and investigate their validity and their implications
  • Have “number sense” and are able to make sense of numerical information
  • Use algorithmic thinking and are able to estimate and compute accurately, flexibly and efficiently
  • Are able to work both independently and collaboratively as problem posers and problem solvers
  • Are able to communicate and justify their thinking and ideas both orally and in writing
  • Use tools available to them to solve problems and to examine mathematical ideas.

The goal of mathematics education should be to produce learners who are both mathematically competent and confident.  Mathematical competence does not come from simply memorizing rules and procedures.  It comes from understanding mathematical relationships so that you can recognize those relationships and use them to make sense of information, situations, and problems that you encounter.  Mathematical confidence does not come from practicing rote procedures until you can do them automatically.  Mathematical confidence comes from knowing that you understand mathematics and its beauty and utility, from knowing that with persistence you can make sense of information and situations you encounter, and from knowing that you can solve even complex and messy or ill-defined problems.