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:
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problem solving
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reasoning and proof
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communication
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representation
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connections
Additionally, the NRC report describes five strands of mathematical proficiency:
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conceptual understanding - comprehension of mathematical concepts, operations, and relations
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procedural fluency- skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
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strategic competence- ability to formulate, represent, and solve mathematical problems
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adaptive reasoning- capacity for logical thought, reflection, explanation, and justification
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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.