Math Proficiencies

Five Strands of Math Proficiencies (NRC, 2001)

• Conceptual understanding – and understanding of concepts, operations and relations.  Conceptual understanding frequently results in students comprehending connections and similarities to interrelated facts.
• Procedural fluency – flexibility, accuracy and efficiency in implementing appropriate procedures.  Skill in proficiency includes the knowledge of when and how to use procedures.  This includes efficiency and accuracy in basic computations.
• Strategic competence – the ability to formulate, represent and solve mathematical problems.  This is similar to problem solving.  Strategic competence is mutually supportive with conceptual understanding and procedural fluency.
• Adaptive reasoning - the capacity to think logically about concepts and conceptual relationships.  Reasoning is needed to navigate through the various procedures, facts and concepts to arrive at solutions.
• Productive disposition – refers to positive perceptions about mathematics. Productive dispositions develop as students gain more mathematical understanding and become capable of learning and doing mathematics.

National Research Council. (2001). Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.