Mathematics education in the United States

From kindergarten through high-school, the mathematics education in public schools 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 mathematical knowledge and skills until the completion of high school, 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.

Unlike most countries, mathematics is separated by topic at the high school level in most of the United States. Two years are devoted entirely to algebra and one year entirely to geometry. (A few states, such as New York and more recently Georgia, follow an integrated curriculum, as in other countries.) The algebra-geometry-algebra sequence is followed by a course often called pre-calculus for college-bound students. Pre-calculus usually combines advanced algebra (or "Algebra 3") and geometry with trigonometry and other topics in preparation for a course in calculus, which is taken in the 12th grade at high school or the first year of university studies.

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) ^[1]
• Geometry: ages 13+ (Geometry taught at 10th grade on average, or as early as 8th grade as an honors course)
• Algebra II (sometimes called Intermediate Algebra): ages 14+ (usually includes powers and roots, polynomials, quadratic functions, coordinate geometry, exponential and logarithmic functions, probability, matrices, and basic trigonometry)
• Trigonometry and/or Algebra 3 (sometimes called Advanced Algebra) or Pre-Calculus(a combination of trigonometry and Algebra 3): 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

Main articles: Math wars and NCTM

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 research emphasizing the importance of conceptual learning, 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 traditional direct instruction of standard arithmetic methods. 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, NCTM 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 widespread adoption of standards-based curricula, research indicates that the instructional practices of teachers changed very little in the United States during the 1990s.^[2]

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 .^[3] 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.^[4]

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 ^[5] 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.^{[citation needed]}

Conferences

Mathematics education research and practitioner conferences include: NCTM's Regional Conference and Exposition and Annual Meeting and Exposition; The Psychology of Mathematics Education's North American Chapter annual conference; and numerous smaller regional conferences.

See also

• Mathematics education in New York

References

1. ^ "Calif. judge blocks mandatory algebra testing". USA Today. 2008-12-19. http://www.usatoday.com/news/education/2008-12-19-calif-algebra_N.htm. Retrieved 2010-05-12. 
2. ^ Hiebert, James; Stigler, James W. (September). "A proposal for improving classroom teaching: Lessons from the TIMSS video study". The Elementary School Journal 101 (1): 3–20. 
3. ^ Christian Science Monitor
4. ^ Frequently Asked Questions About the Core-Plus Mathematics Project
5. ^ Wall Street Journal, New York Times, Chicago Sun Times