Mathematics education in the United States

From kindergarten through high-school, public Mathematics Education in the United States varies widely from state to state, and often even varies considerably within individual states.

Curricular content and age levels

Although there are not any country-wide standards, National Council of Teachers of Mathematics (NCTM) has published educational recommendations in mathematics education. They are particularly well known for the Principles and Standards for School Mathematics which covers both knowledge and skills, and the Curriculum Focal Points, which recommend the most important mathematical topics for each grade level through grade 8.

Different levels of mathematics are taught at different ages. Sometimes a class may be taught at an earlier age as a special or "honors" class. A rough guide to the ages at which the certain topics of arithmetic are taught in the United States is as follows:

• Addition: ages 5-7; more digits ages 8-9
• Subtraction: ages 5-7; more digits ages 8-9
• Multiplication: ages 7-8; more digits ages 9-10
• Division: age 8; more digits ages 9-10

The ages at which other mathematics subjects (rational numbers, geometry, measurement, problem solving, logic, algebraic thinking, probability, statistics, reasoning skills, and so on) are taught vary considerably from state to state.

A typical pre-college sequence of mathematics courses in the United States would include some of the following, especially Geometry and Algebra I and II:

• Pre-algebra: ages 11-13 (pre-algebra is taught in schools as early as 6th grade as an honor course, although algebraic reasoning can be taught in elementary school)
• Algebra I (basic algebra): ages 12+ (Algebra I is taught at 9th grade in general, or as early as 7th or 8th grade for an honors course, although California is embroiled in a legal battle over whether or not to require all 8th grade students to take this class)
• Geometry: ages 13+ (Geometry taught at 10th grade on average, or as early as 8th grade as an honors course)
• Algebra II: ages 14+ (usually includes powers and roots, polynomials, quadratic functions, coordinate geometry, exponential and logarithmic functions, probability, matrices, and basic trigonometry)
• Trigonometry or Algebra 3 or Pre-Calculus: ages 15+
• Statistics: ages 15+ (Probability and statistics topics are taught throughout the curriculum from early elementary grades, but may form a special course in high school)
• Calculus: ages 16+ (usually seen in 12th grade, if at all; some honors students may see it earlier).

Recent controversy over U.S. mathematics education

Main articles: Math wars and National Council of Teachers of Mathematics

Near the end of the 20th century, diverse and changing ideas about the goals and methods of mathematical education led to wide adoption of reform-based standards and curricula funded by the US federal government, and also adopted by other national curriculum standards. These were based on student-centered learning methods and equity in mathematics as the centerpieces of the standards based education reform movement.

The goals for educators since the 1990s have been expanded in the context of systemic standards based education reform in the United States and other nations to promote increased learning for all students. It is a goal to achieve equity and success for all groups in society, as it is no longer acceptable to many in the education community that some have been historically excluded from the full range of opportunities that are open to those who have access to the most advanced mathematics.

With the adoption of reform standards and the development of federally funded curricula during the 1990s, mathematics education became a hotly debated subject. The movement was met with opposition from traditionalists outside the mathematics education research arena, calling for a return to the standard arithmetic method of traditional direct instruction. As a result, after initial adoption of standards-based curricula, some schools and districts supplemented or replaced standards-based curricula in the late 1990s and early 2000s.

The movement had its origins in the 1980s, when research began to support an emphasis on problem solving, mathematical reasoning, conceptual understanding and student-centered learning. About the same time as the development of a number of controversial standards across reading, science and history, the National Council of Teachers of Mathematics of the United States produced the Curriculum and Evaluation Standards for School Mathematics in 1989. These standards included new goals such as equity and conceptual understanding and encouraged a de-emphasis on rote learning. However, in spite of wide-spread adoption of standards-based curricula, research indicates that the instructional practices of teachers changed very little in the United States during the 1990s (see TIMSS video study).

The 1989 NCTM standards recommended teaching elements of algebra as early as grade 5, and elements of calculus as early as grade 9, though this was rarely adopted. In standards based education reform all students, not only the college-bound, must take substantive mathematics. In some large school districts, this means requiring some algebra of all students by the end of junior high school, compared to the tradition of tracking only the college-bound and the most advanced junior high school students to take algebra.

A challenge with the Curriculum and Evaluation Standards soon was that no curricular materials were designed to meet the intent of the Standards. In the 1990s, the National Science Foundation funded the development of curricula such as the Core-Plus Mathematics Project. In the late 1990s and early 2000s the math wars erupted in some communities that were opposed to some of the more radical changes to mathematics instruction. Some students complained that their new math courses placed them into remedial math in college . However, data provided by the University of Michigan registrar at this same time indicate that in collegiate mathematics courses at the University of Michigan, graduates of Core-Plus do as well as or better than graduates of a traditional mathematics curriculum, and students taking traditional courses were also placed in remedial mathematics courses.

In 2000 and 2006, NCTM released the Principles and Standards for School Mathematics (PSSM) and the Curriculum Focal Points which expanded on the work of the previous standards documents. Particularly, the PSSM reiterated the 1989 standards, but in a more balanced way, while the Focal Points suggested three areas of emphasis for each grade level. Refuting reports and editorials that it was repudiating the earlier standards, the NCTM claimed that the Focal Points were largely re-emphazing the need for instruction that builds skills and deepens student mathematical understanding. NCTM spokespeople maintained that it provided more grade band specificity on key areas of study for the coherent and consistent development of mathematical understanding and skill. These documents repeated the criticism that American mathematics curricula are a "mile wide and an inch deep" in comparison to the mathematics of most other nations, a finding from the Second and Third International Mathematics and Science Studies.

Another issue with mathematics education has been integration with science education. This is difficult for the public schools to do because science and math are taught independently. The value of the integration is that science can provide authentic contexts for the math concepts being taught and further, if mathematics is taught in synchrony with science, then the students benefit from this correlation.