The Standards for Mathematical Practice are informed by two important resources:

the National Council of Teachers of Mathematics (NCTM)  process standards and

the National Research Council’s (NRC) report Adding it Up Adding: Helping Children Learn Mathematics.

The five NCTM process standards highlight ways of acquiring and applying content knowledge:


  • problem solving

  • reasoning and proof

  • communication

  • representation

  • connections


Additionally, the NRC report describes five strands of mathematical proficiency:

  • conceptual understanding - comprehension of mathematical concepts, operations, and relations

  • procedural fluency- skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

  • strategic competence- ability to formulate, represent, and solve mathematical problems

  • adaptive reasoning- capacity for logical thought, reflection, explanation, and justification

  • productive disposition- habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

The NRC report stresses that the strands are interwoven and interdependent in the development of proficiency in mathematics. These strands provide a framework for discussing the knowledge, skills, abilities, and beliefs that constitute mathematical proficiency.