# Standards for Mathematical Practice Introduction

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, communication, representation, and connections. 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), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

## Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.

## Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure.

## Attend to precision.

Mathematically proficient students try to communicate precisely to others.

## Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem.

## Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

## Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures.

## Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations.

## Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.

## Standards for Mathematical Practice Introduction

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.