State Standards
The Common Core State Standards - Standards for Mathematical Practice describe habits of mind 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.
Below are the eight Standards for Mathematical Practice. For more information on each one, visit www.corestandards.org.
Make Sense of Problems and Persevere in Solving Them
Mathematically proficient students analyze problems, identify solution strategies, and persist in finding answers, adjusting their approach as needed while ensuring their solutions make sense.
Reason Abstractly and Quantitatively
Students understand and manipulate mathematical relationships by decontextualizing problems into symbols and contextualizing those symbols to ensure meaning and accuracy.
Construct Viable Arguments and Critique the Reasoning of Others
Proficient students create logical arguments, justify their reasoning with evidence, and evaluate others’ arguments by identifying strengths, weaknesses, and areas for improvement.
Model With Mathematics
Students apply mathematical concepts to real-world situations, making assumptions, using representations like graphs and equations, and refining their models to improve accuracy.
Use Appropriate Tools Strategically
Mathematically proficient individuals select and use tools such as calculators, diagrams, and technology effectively to explore, solve problems, and verify their solutions.
Attend to Precision
Students communicate mathematical ideas clearly, use accurate calculations, specify units and labels appropriately, and ensure their reasoning is logically sound.
Look for and Make Use of Structure
Proficient students recognize patterns, break down complex problems into simpler components, and use structural insights to find solutions more efficiently.
Look for and Express Regularity in Repeated Reasoning
Students identify repeated calculations or reasoning patterns, generalizing methods and shortcuts while maintaining oversight to ensure accuracy.
At each grade level, students practice skills and deepen conceptual understanding in each of the five mathematical domains:
- Counting and Cardinality
- Operations and Algebraic Thinking
- Number and Operations in Base Ten
- Measurement and Data
- Geometry