In mathematics education, number sense can refer to "an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations." Many other definitions exist, but are similar to the one given. Some definitions 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".

There are also some differences in how number sense is defined in the field of mathematical 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."

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.

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.

## Concepts involved in number sense

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

• estimating with large numbers to provide reasonable approximations;
• judging the degree of accuracy appropriate to a situation;
• solving real-life problems involving percents and decimal portions;
• rounding (understanding reasons for rounding large numbers and limitations in comparisons);
• choosing measurement units to make sense for a given situation;
• comparing physical measurements within and between the U.S. and metric systems; and
• comparing degrees Fahrenheit and Celsius in real-life situations.

Those concepts are taught in elementary-level education.