(1) Conceptual understanding refers to the “integrated and functional grasp of mathematical ideas”, which “enables them [students] to learn new ideas by connecting those ideas to what they already know.” A few of the benefits of building conceptual understanding are that it supports retention, and prevents common errors.
(2) Procedural fluency is defined as the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.
(3) Strategic competence is the ability to formulate, represent, and solve mathematical problems.
(4) Adaptive reasoning is the capacity for logical thought, reflection, explanation, and justification.
(5) Productive disposition is the inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. (NRC, 2001, p. 116)
National Research Council. (2001). Adding it up: Helping children learn mathematics. J Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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