In mathematics education

Mathematics education

In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....

, 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

Cognition

In science, cognition refers to mental processes. These processes include attention, remembering, producing and understanding language, solving problems, and making decisions. Cognition is studied in various disciplines such as psychology, philosophy, linguistics, and computer science...

. 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

National Council of Teachers of Mathematics

The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....

 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

University Interscholastic League

The University Interscholastic League is an organization that creates rules for and administers almost all athletic, music, and academic contests for public primary and secondary schools in the American state of Texas....

. 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

Magnitude (mathematics)

The magnitude of an object in mathematics is its size: a property by which it can be compared as larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....

, ranking

Ranking

A ranking is a relationship between a set of items such that, for any two items, the first is either 'ranked higher than', 'ranked lower than' or 'ranked equal to' the second....

, comparison

Comparison

Comparison may refer to:-Language:* Comparison , a feature of many languages* Degree of comparison, an English language grammatical feature* Mass comparison, a test for the relatedness of languages-Mathematics:...

, measurement

Measurement

Measurement is the process or the result of determining the ratio of a physical quantity, such as a length, time, temperature etc., to a unit of measurement, such as the metre, second or degree Celsius...

, rounding

Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.Rounding is often done on purpose to...

, percents, and estimation

Estimation

Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain.In statistics,*estimation theory and estimator, for topics involving inferences about probability distributions...

, 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 system
  Metric system
  The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...
  
  s; and
• comparing degrees Fahrenheit
  Fahrenheit
  Fahrenheit is the temperature scale proposed in 1724 by, and named after, the German physicist Daniel Gabriel Fahrenheit . Within this scale, the freezing of water into ice is defined at 32 degrees, while the boiling point of water is defined to be 212 degrees...
  
   and Celsius
  Celsius
  Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...
  
   in real-life situations.

Those concepts are taught in elementary-level education.

See also

• Numerosity adaptation effect
  Numerosity adaptation effect
  The numerosity adaptation effect is a perceptual phenomenon in numerical cognition which demonstrates non-symbolic numerical intuition and exemplifies how numerical percepts can impose themselves upon human brain automatically. This effect was first described in 2008.Presently, this effect is...
  
  
• Order of magnitude
  Order of magnitude
  An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
  
  
• Rounding error
• Numeracy, innumeracy
  Numeracy
  Numeracy is the ability to reason with numbers and other mathematical concepts. A numerically literate person can manage and respond to the mathematical demands of life...
  
  
• Approximate number system
  Approximate number system
  The approximate number system is a hypothetical physiological basis for the intuitive "number sense". As its name suggests, it only provides an approximate sense of number, and is not an accurate symbolic computation system...
  
  
• Pirahã people
  Pirahã people
  The Pirahã people are an indigenous hunter-gatherer tribe of Amazon natives, a subgroup of the Mura, who mainly live on the banks of the Maici River in Brazil's Amazonas state, in the territory on Humaitá and Manicoré municipality....
  
  

External links

• Number Worlds - a site with number sense development materials
• Number Sense iPhone App - A new app for kids between ages 4 to 8 years to develop their basic math skills