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.

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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:

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• 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

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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.