Number sense

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In mathematics education, number sense can refer to "an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations".[1] Other definitions of number sense emphasize an ability to work outside of the traditionally taught algorithms, e.g., "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms".[2]

Psychologists believe that the number sense in humans can be differentiated into the approximate number system, a system that supports the estimation of the magnitude, and the parallel individuation system, which allows the tracking of individual objects, typically for quantities below 4.[3]

There are also some differences in how number sense is defined in math cognition. For example, Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons."[4][5][6]

In non-human animals, number sense is not the ability to count, but the ability to perceive changes in the number of things in a collection.[7] All mammals, and most birds, will notice if there is a change in the number of their young nearby. Many birds can distinguish two from three.[8]

Researchers consider number sense to be of prime importance for children in early elementary education, and the National Council of Teachers of Mathematics has made number sense a focus area of pre-K through 2nd grade mathematics education.[9] An active area of research is to create and test teaching strategies to develop children's number sense. Number sense also refers to the contest hosted by the University Interscholastic League. This contest is a ten-minute test where contestants solve math problems mentally—no calculators, scratch-work, or mark-outs are allowed.[10]

Concepts involved in number sense[edit]

The term "number sense" involves several concepts of magnitude, ranking, comparison, measurement, rounding, percents, and estimation, including:[11]

  • estimating with large numbers to provide reasonable approximations;
  • judging the degree of precision appropriate to a situation;
  • understanding the hidden meaning of numbers through analytical and critical thinking (e.g., Freakonomics[12]);
  • rounding (understanding reasons for rounding large numbers and limitations in comparisons);
  • choosing measurement units to make sense for a given situation;
  • solving real-life problems involving percentages and decimal portions;
  • comparing physical measurements within and between the U.S. and metric systems; and
  • comparing degrees Fahrenheit and Celsius in real-life situations.[11]

Those concepts are taught in elementary-level education.

See also[edit]


  1. ^ "number sense".
  2. ^ "What is number sense?".
  3. ^ Piazza, M. (2010). "Neurocognitive start-up tools for symbolic number representations". Trends in Cognitive Sciences. 14 (12): 542–551. doi:10.1016/j.tics.2010.09.008. PMID 21055996. S2CID 13229498.
  4. ^ "Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities".
  5. ^ "Making Sense of Number Sense: Implications for Children With Mathematical Disabilities".
  6. ^ "Stages in Development of Number Sense - Harvard Education Letter".
  7. ^ "Number Systems".
  8. ^ Dantzig, Tobias. Number: The Language of Science. New York: Macmillan Company, 1930.
  9. ^ "Understanding a Child's Development of Number Sense".
  10. ^ "UIL Number Sense".
  11. ^ a b "Unit 1: Number and Number Sense" (20-day lesson),, St. Tammany Parish School Board, Covington, LA (USA), 2009, overview webpage: ST-MathGrade7Unit-topics.
  12. ^ "".

External links[edit]