Mathematics education in the United States
Encyclopedia
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.
(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:
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:
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.
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.
'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.
Kindergarten
A kindergarten is a preschool educational institution for children. The term was created by Friedrich Fröbel for the play and activity institute that he created in 1837 in Bad Blankenburg as a social experience for children for their transition from home to school...
through high-school, the mathematics education
Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research....
in public schools in the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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 MathematicsNational Council of Teachers of Mathematics
The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....
(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
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
is as follows:
- AdditionAdditionAddition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
: ages 5–7; more digits ages 8–9 - SubtractionSubtractionIn arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
: ages 5–7; more digits ages 8–9 - MultiplicationMultiplicationMultiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
: ages 7–8; more digits ages 9–10 - DivisionDivision (mathematics)right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
: 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
Integrated mathematics
Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and...
, 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-algebraPre-algebraPre-Algebra is a common name for a course in middle school mathematics. In the United States, it is generally taught between the fifth and eighth grades, although it may be necessary to take this course as early as sixth grade in order to advance to Calculus BC by twelfth grade...
: 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) - AlgebraAlgebraAlgebra 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...
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) - GeometryGeometryGeometry 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 ....
: ages 13+ (Geometry taught at 10th grade on average, or as early as 8th grade as an honors course) - AlgebraAlgebraAlgebra 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...
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) - TrigonometryTrigonometryTrigonometry 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...
and/or Algebra 3 (sometimes called Advanced Algebra) or Pre-Calculus(a combination of trigonometry and Algebra 3): ages 15+ - StatisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
: ages 15+ (Probability and statistics topics are taught throughout the curriculum from early elementary grades, but may form a special course in high school) - CalculusCalculusCalculus 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...
: ages 16+ (usually seen in 12th grade, if at all; some honors students may see it earlier).
Recent controversy
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
Whole language
Whole language describes a literacy philosophy which emphasizes that children should focus on meaning and strategy instruction. It is often contrasted with phonics-based methods of teaching reading and writing which emphasize instruction for decoding and spelling. However, from whole language...
, 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 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
Core-Plus Mathematics Project
The Core-Plus Mathematics Project is one of the five NCTM-standards-based high school mathematics curriculum development projects funded by the National Science Foundation. The project has developed, tested, and published a four-year comprehensive high school mathematics textbook series...
. 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
Principles and Standards for School Mathematics
Principles and Standards for School Mathematics are guidelines produced by the National Council of Teachers of Mathematics in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada...
(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.
Conferences
Mathematics education research and practitioner conferences include: NCTMNational Council of Teachers of Mathematics
The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....
'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.