According to Wikipedia.org, throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils. In modern times there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In England , for example, standards for mathematics education are set as part of the National Curriculum for England , while Scotland maintains its own educational system. Ma (2000) summarised the research of others who found, based on nationwide data, that students with higher scores on standardised math tests had taken more mathematics courses in high school. This led some states to require three years of math instead of two. But because this requirement was often met by taking another lower level math course, the additional courses had a “diluted” effect in raising achievement levels. In North America, the National Council of Teachers of Mathematics (NCTM) has published the Principles and Standards for School Mathematics . In 2006, they released the Curriculum Focal Points , which recommend the most important mathematical topics for each grade level through grade 8. However, these standards are not nationally enforced in US schools.
Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or "honors" class. Elementary mathematics in most countries is taught in a similar fashion, though there are differences. In the United States fractions are typically taught starting from 1st grade, whereas in other countries they are usually taught later, since the metric system does not require young children to be familiar with them. Most countries tend to cover fewer topics in greater depth than in the United States.
In most of the US, algebra, geometry and analysis (pre-calculus and calculus) are taught as separate courses in different years of high school. Mathematics in most other countries (and in a few US states) is integrated, with topics from all branches of mathematics studied every year. Students in many countries choose an option or pre-defined course of study rather than choosing courses à la carte as in the United States. Students in science-oriented curricula typically study differential calculus and trigonometry at age 16-17 and integral calculus, complex numbers, analytic geometry, exponential and logarithmic functions, and infinite series in their final year of secondary school.