Conceptual understanding is a term frequently employed in education, particularly in reference to mathematics. At its most basic definition, conceptual understanding is the student’s comprehensions of mathematical concepts, operations, and relations. The overall goal of elementary mathematics education is to develop conceptual understanding as part of mathematical proficiency.
Students who master conceptual understanding are able to learn more than isolated facts and methods. Knowledge is organized into a coherent whole, one that allows the student to connect new ideas to previously learned knowledge and skills. This further supports retention, as students who can connect information are able to better use and recall such knowledge.
Students are said to be able to demonstrate conceptual understanding when they can recognize, label and generate examples of mathematical concepts, identify and apply principles, and apply the various signs, symbols and terms of mathematics that represent various concepts.
Many countries, such as the United States, are integrating conceptual understanding into their national mathematical standards. Students must be taught which particular ideas are key to all mathematics, why and how such ideas aid in problem solving, by demonstrating the systematic nature of mathematics and adapting learned concepts to new problems.