The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.
The first of these are the NCTM process standards of:
- Problem solving
- Reasoning and proof
The second are the strands of mathematical proficiency specified in the National Research Council’s report, "Adding It Up":
- Adaptive reasoning
- Strategic competence
- Conceptual understanding (comprehension of mathematical concepts, operations and relations)
- Procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately)
- Productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)
Math Practice 1 — Make sense of problems and persevere in solving them.
Math Practice 2 — Reason abstractly and quantitatively.
Math Practice 3 — Construct viable arguments and critique the reasoning of others.
Math Practice 4 — Model with mathematics.
Math Practice 5 — Use appropriate tools strategically.
Math Practice 6 — Attend to precision.
Math Practice 7 — Look for and make use of structure.
Math Practice 8 — Look for and express regularity in repeated reasoning