Mathematics education in the United States
From kindergarten through high school, the mathematics education in public schools in the United States has historically varied widely from state to state, and often even varies considerably within individual states. With the recent adoption of the Common Core Standards by 45 states, mathematics content across the country is moving into closer agreement for each grade level.
Each state sets its own curricular standards and details are usually set by each local school district. Although there are no federal standards, 45 states have agreed to base their curricula on the Common Core State Standards in mathematics beginning in 2015. The National Council of Teachers of Mathematics published educational recommendations in mathematics education in 1991 and 2000 which have been highly influential, describing mathematical knowledge, skills and pedagogical emphases from kindergarten through high school. The 2006 NCTM Curriculum Focal Points have also been influential for its recommendations of the most important mathematical topics for each grade level through grade 8.
In the United States, mathematics curriculum in elementary and middle school is integrated, while in high school it traditionally has been separated by topic, like Algebra I, Geometry, Algebra II, each topic usually lasting for the whole school year.
Algebra I, also known as elementary algebra or beginning algebra, is the first course students take in algebra. Historically, this class has been a high school level course that is often offered as early as the seventh grade but more traditionally in eighth or ninth grades. The course is also offered in community colleges as a basic skills or remedial course.
Geometry usually requires Algebra I as a prerequisite.
Algebra II, or intermediate algebra, has a prerequisite of Algebra I. Historically, intermediate algebra has been a high school level course.
The Common Core mathematical standards recognizes both the sequential as well as integrated approach to teaching high-school mathematics, which resulted in increased adoption of integrated math programs for high school. Accordingly, the organizations providing post-secondary education updated their enrollment requirements. For example, University of California requires three years of "college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry" to be admitted. After California Department of Education adopted Common Core, the University of California clarified that "approved integrated math courses may be used to fulfill part or all" of this admission requirement.
The above three-course sequence is followed by a course often called pre-calculus for college-bound students. Pre-calculus usually combines advanced algebra (or "Algebra III") and geometry with trigonometry.
Depending on school district, several courses may be compacted and combined within one school year, either studied sequentially or simultaneously. Without such acceleration it may be not possible to take more advanced classes like calculus in high school.
College algebra is offered at many community colleges and generally has a prerequisite of intermediate algebra.
Calculus is sometimes taken in the 12th grade at high school or the first year of university studies. A successfully completed college level calculus course like one offered via Advanced Placement program is a transfer level course—that is, it can be accepted by a college as a credit towards graduation requirements. Other optional mathematics courses may be offered, such as statistics or business math.
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 in the 1990s 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 reform 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 reform 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.
In standards based education reform all students, not only the college-bound, must take substantive mathematics. In some large school districts, this came to mean requiring some algebra of all students by ninth grade, compared to the tradition of tracking only the college-bound and the most advanced junior high school students to take algebra.
A challenge with implementing the Curriculum and Evaluation Standards was that no curricular materials at the time 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 so-called math wars erupted in 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 did 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 2001 and 2009, 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.
Beginning in 2011, most states have adopted the Common Core Standards for mathematics, which were partially based on NCTM's previous work. Controversy still continues as critics point out that Common Core standards do not fully prepare students for college and as some parents continue to complain that they do not understand the mathematics their children are learning.
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.
PISA 2015 Assessment
The Program for International Student Assessment (PISA) conducted the 2015 assessment test which is held every three years for 15-year old students worldwide. In 2012, the United States earned average scores in science and reading. It performed better than other progressive nations in mathematics ranking number 36 out of 65 other countries. The PISA assessment examined the students’ understanding of mathematics as well as their approach to this subject and responses. These indicated three approaches to learning. Some of the students depended mainly on memorization. Others were more reflective on newer concepts. Another group concentrated more on principles that have not yet studied. The U.S. had a high proportion of memorizers compared to other developed countries. During the latest testing, the United States failed to make it to the top 10 in all categories including mathematics. More than 540,000 teens from 72 countries took the exam. Their average score in mathematics declined 11 points.
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.
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