The new Common Core State Standards (CCSS) have something that seeks to synthesize the NCTM's Mathematical Process Standards with the NRC's strands of mathematical proficiency: the Standards for Mathematical Practice. What follows is an abridged and modified listing from the CCSS site.

Standards for Mathematical Practice

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

Proficient students consider: the meaning of a problem; information like givens, constraints, relationships, and goals; monitor and evaluate their progress; check their answers to problems using a different method; the approaches of others to solving complex problems; and identify correspondences between different approaches. Proficient students employ strategies like: making conjectures; analogous problems; special cases and simpler forms of the original problem; other representations; technological tools; manipulatives. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. They continually ask themselves, “Does this make sense?”

2. Reason abstractly and quantitatively.

Proficient students make sense of quantities and their relationships. They can abstract or generalize, carry out symbolic manipulation, change representation and choose appropriate units.

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

Proficient students understand the role of assumptions, definitions, and previous results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to use specific reasoning strategies such as: cases, counterexamples, induction, finding logical gaps and flaws, and compare arguments. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose.

4. Model with mathematics.

Proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. They can represent real world information and gain insight through applying mathematics.

Examples:

Use rational functions to model the whelk data or constant rectangle area problems, with one dimension in terms of the other.

5. Use appropriate tools strategically.

Proficient students consider available tools: pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.

6. Attend to precision.

Proficient students try to communicate precisely and appropriately to others. This includes definitions, identifying units, appropriate level of precision in numbers.

7. Look for and make use of structure.

Pproficient students attend to patterns and structure. Both within and among problems, representations and topics. This supports generalization and abstraction.

Examples:

The recognition of which rational functions have vertical, horizontal and oblique asymptotes, and what conditions of the function control their location.

8. Look for and express regularity in repeated reasoning.

Proficient students look both for general methods and for shortcuts. They maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Photo credits: docpop and David Shexnaydre @Flickr

## Standards for Mathematical Practice

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

Proficient students consider: the meaning of a problem; information like givens, constraints, relationships, and goals; monitor and evaluate their progress; check their answers to problems using a different method; the approaches of others to solving complex problems; and identify correspondences between different approaches.Proficient students employ strategies like: making conjectures; analogous problems; special cases and simpler forms of the original problem; other representations; technological tools; manipulatives. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.

They continually ask themselves, “Does this make sense?”

## 2. Reason abstractly and quantitatively.

Proficient students make sense of quantities and their relationships. They can abstract or generalize, carry out symbolic manipulation, change representation and choose appropriate units.## 3. Construct viable arguments and critique the reasoning of others.

Proficient students understand the role of assumptions, definitions, and previous results in constructing arguments.They make conjectures and build a logical progression of statements to explore the truth of their conjectures.

They are able to use specific reasoning strategies such as: cases, counterexamples, induction, finding logical gaps and flaws, and compare arguments.

They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose.

## 4. Model with mathematics.

Proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. They can represent real world information and gain insight through applying mathematics.Examples:## 5. Use appropriate tools strategically.

Proficient students consider available tools: pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.## 6. Attend to precision.

Proficient students try to communicate precisely and appropriately to others. This includes definitions, identifying units, appropriate level of precision in numbers.## 7. Look for and make use of structure.

Pproficient students attend to patterns and structure. Both within and among problems, representations and topics. This supports generalization and abstraction.Examples:## 8. Look for and express regularity in repeated reasoning.

Proficient students look both for general methods and for shortcuts. They maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.Photo credits: docpop and David Shexnaydre @Flickr