Elementary mathematics consists of mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 topics frequently taught at the primary or secondary school

Secondary school

Secondary school is a term used to describe an educational institution where the final stage of schooling, known as secondary education and usually compulsory up to a specified age, takes place...

 levels. The most basic topics in elementary mathematics are arithmetic

Arithmetic

Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...

 and geometry

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

. Beginning in the last decades of the 20th century, there has been an increased emphasis on probability and statistics

Probability and statistics

See the separate articles on probability or the article on statistics. Statistical analysis often uses probability distributions, and the two topics are often studied together. However, probability theory contains much that is of mostly mathematical interest and not directly relevant to statistics...

 and on problem solving.

In secondary school, the main topics in elementary mathematics are algebra

Algebra

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

 and trigonometry

Trigonometry

Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

. Calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

, even though it is often taught to advanced secondary school students, is usually considered college level mathematics.

A mastery of elementary mathematics is necessary for many professions, including carpentry, plumbing, and automobile repair, as well as being a prerequisite for all advanced study in mathematics, science, engineering, medicine, business, architecture, and many other fields.

In the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, there has been considerable concern about the low level of elementary mathematics skills on the part of many students, as compared to students in other developed countries. The No Child Left Behind program was one attempt to address this deficiency, requiring that all American students be tested in elementary mathematics.