Mathematics education in New York
Encyclopedia
New York State Math education in regards to both content and teaching method can vary depending on the type of school a person attends. Private school math education varies from school to school whereas New York has State wide public school requirements where standardized tests are used to determine if the teaching method and educator are effective in transmitting content to the student. While an individual private school can choose the content and which educational method to use, New York State mandates content and methods state wide. Though, some public school have and continue to to use established methods, such as Montessori for teaching state required content. New York State has used various foci of content and methods of teaching math including New Math (1960's), "back to the basics" (1970's), Whole Math (1990's), Integrated Math and Everyday Mathematics.
How to teach math, what to teach and its effectiveness has been a topic of debate in New York State and nationally since the "Math Wars" started in the 1960's. Often, current political events influence how and what is taught. The politics in turn influence state legislation. California, New York State and several other states have influenced text book content produced by publishers.
In the United States
, the state of New York
has implemented a novel curriculum for high school
mathematics
.
The courses Integrated Algebra, Geometry, and Algebra II/Trigonometry are required course
s mandated by the New York State Department of Education for high school
graduation
Students will learn to how write, solve, and graph equation
s and inequalities. They will also learn how to solve systems of equations, quadratic
s, as well as exponents, exponential function
s, polynomial
s, radicals
, and rational expressions. Other topics included are probability
and statistics
At the conclusion of this one year course, students take the New York State regents exam in Integrated Algebra. The first administration of this exam was in June 2008.
Geometric concepts such as right triangle
s are introduced. The course will also cover topics such as perpendicular
and parallel lines
, triangles, quadrilateral
s, and transformations
At the conclusion of this one year course, students take the New York State regents exam in Geometry. The first administration of this exam was in June 2009.
This course covers concepts that can be found in trigonometry
and advanced algebra
, as well as preparing students for pre-calculus and calculus
and reviewing old topics. During their year of study, students will learn different theorem
s, graph complex number
s and vectors, as well as reviewing topics such as exponential function
s, systems of inequalities, and radical
s. As the year progresses, students will be expected to relate these functions
to the real world, create conjecture
s through their own research
, and begin a classroom
discussion about these topics.
At the conclusion of this one year course, students will take the New York State regents exam in Algebra II/Trigonometry. This is the last regents exam in mathematics students will ever take. Like the former "Math B" regents, it is considered one of the hardest regents of high school, along with the Physical Setting/Chemistry regents and the Physical Setting/Physics regents. The first administration of this exam was in June 2010.
, while Math A covers a whole range of topics.
In Math A, students will learn to how write, solve, and graph equation
s and inequalities. They will also learn how to solve systems of equations, quadratic
s, as well as exponents, exponential function
s, polynomial
s, radicals
, and rational expressions. Other topics included are probability
and statistics
. Geometric concepts such as right triangle
s are also introduced. The course works in conjunction with New York State's Standards for Mathematics.http://www.emsc.nysed.gov/ciai/mst/pub/mststa1_2.pdf The course will end after three semesters, in which students will take the Regents Math A Examination.
, while Math A/B focuses on a whole range of topics. Math A/B serves as a bridge between the Math A and Math B courses.
Math A/B stays true to its geometric roots, as the first half of the course will cover topics such as perpendicular
and parallel lines
, triangles, quadrilateral
s, and transformations
. After the first semester, students will take the New York State Math A Regents exam. June 2008 was the last administration of this exam. For the second half of the year, students will begin Math B. They will cover logic
, geometric figures, and an introduction to trigonometry
.
. Math B focuses on a whole range of topics. It is taken after the student has completed and passed Math A.
A regents exam is taken at the end of the -year course. The Math B regents is often considered one of the most difficult New York State regents.
Math B covers concepts that can be found in trigonometry
and advanced algebra
, as well as preparing students for pre-calculus and calculus
and reviewing old topics. During their year of study, students will learn different theorem
s, graph complex number
s and vectors, as well as reviewing topics such as exponential function
s, systems of inequalities, and radical
s. As the year progresses, students will be expected to relate these functions
to the real world, create conjecture
s through their own research
, and begin a classroom
discussion about these topics. At the end of their studies, they will take the New York State Math B Regents Examination. The last administration of this exam will be in August 2010.
http://www.emsc.nysed.gov/osa/mathre/new_mathregents.htm about the State's requirements for high school graduation as related to mathematics. The committee recommended that:
The move was praised by many who thought the changes to the original draft curriculum were unnecessary.
How to teach math, what to teach and its effectiveness has been a topic of debate in New York State and nationally since the "Math Wars" started in the 1960's. Often, current political events influence how and what is taught. The politics in turn influence state legislation. California, New York State and several other states have influenced text book content produced by publishers.
In the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
, the state of New York
New York
New York is a state in the Northeastern region of the United States. It is the nation's third most populous state. New York is bordered by New Jersey and Pennsylvania to the south, and by Connecticut, Massachusetts and Vermont to the east...
has implemented a novel curriculum for high school
High school
High school is a term used in parts of the English speaking world to describe institutions which provide all or part of secondary education. The term is often incorporated into the name of such institutions....
mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
The courses Integrated Algebra, Geometry, and Algebra II/Trigonometry are required course
Course (education)
The very broad dictionary meaning of the word course is the act or action of moving in a path from point to point . There are multiple meanings for this word, some of which include: general line of orientation, a mode of action, part of a meal, a mode of action, and many more. This article focuses...
s mandated by the New York State Department of Education for high school
High school
High school is a term used in parts of the English speaking world to describe institutions which provide all or part of secondary education. The term is often incorporated into the name of such institutions....
graduation
Graduation
Graduation is the action of receiving or conferring an academic degree or the ceremony that is sometimes associated, where students become Graduates. Before the graduation, candidates are referred to as Graduands. The date of graduation is often called degree day. The graduation itself is also...
Integrated Algebra
This is the first course in the new three year curriculum. It replaced "Math A".Students will learn to how write, solve, and graph equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s and inequalities. They will also learn how to solve systems of equations, quadratic
Quadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
s, as well as exponents, exponential function
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
s, polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s, radicals
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
, and rational expressions. Other topics included are probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics 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....
At the conclusion of this one year course, students take the New York State regents exam in Integrated Algebra. The first administration of this exam was in June 2008.
Geometry
This is the second course in the new three year curriculum. It replaced part of "Math A" and part of "Math B"Geometric concepts such as right triangle
Right triangle
A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...
s are introduced. The course will also cover topics such as perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
and parallel lines
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...
, triangles, quadrilateral
Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on...
s, and transformations
Transformation (mathematics)
In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...
At the conclusion of this one year course, students take the New York State regents exam in Geometry. The first administration of this exam was in June 2009.
Algebra II/Trigonometry
This is the final course of the new three year curriculum. It replaced the elements of "Math B" not covered in geometry.This course covers concepts that can be found in trigonometry
Trigonometry
Trigonometry 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 advanced algebra
Algebra
Algebra 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...
, as well as preparing students for pre-calculus and calculus
Calculus
Calculus 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...
and reviewing old topics. During their year of study, students will learn different theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s, graph complex number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
s and vectors, as well as reviewing topics such as exponential function
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
s, systems of inequalities, and radical
Nth root
In mathematics, the nth root of a number x is a number r which, when raised to the power of n, equals xr^n = x,where n is the degree of the root...
s. As the year progresses, students will be expected to relate these functions
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
to the real world, create conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
s through their own research
Research
Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
, and begin a classroom
Classroom
A classroom is a room in which teaching or learning activities can take place. Classrooms are found in educational institutions of all kinds, including public and private schools, corporations, and religious and humanitarian organizations...
discussion about these topics.
At the conclusion of this one year course, students will take the New York State regents exam in Algebra II/Trigonometry. This is the last regents exam in mathematics students will ever take. Like the former "Math B" regents, it is considered one of the hardest regents of high school, along with the Physical Setting/Chemistry regents and the Physical Setting/Physics regents. The first administration of this exam was in June 2010.
Math A (former course)
Math A replaces the former "Course 1" curriculum which focused solely on the topic of algebraAlgebra
Algebra 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...
, while Math A covers a whole range of topics.
In Math A, students will learn to how write, solve, and graph equation
Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign , for examplex + 3 = 5\,asserts that x+3 is equal to 5...
s and inequalities. They will also learn how to solve systems of equations, quadratic
Quadratic equation
In mathematics, a quadratic equation is a univariate polynomial equation of the second degree. A general quadratic equation can be written in the formax^2+bx+c=0,\,...
s, as well as exponents, exponential function
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
s, polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
s, radicals
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
, and rational expressions. Other topics included are probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics 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....
. Geometric concepts such as right triangle
Right triangle
A right triangle or right-angled triangle is a triangle in which one angle is a right angle . The relation between the sides and angles of a right triangle is the basis for trigonometry.-Terminology:The side opposite the right angle is called the hypotenuse...
s are also introduced. The course works in conjunction with New York State's Standards for Mathematics.http://www.emsc.nysed.gov/ciai/mst/pub/mststa1_2.pdf The course will end after three semesters, in which students will take the Regents Math A Examination.
Math A/B (former course)
Math A/B takes the place of the former "Course 2" curriculum, which focused almost solely on geometryGeometry
Geometry 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 ....
, while Math A/B focuses on a whole range of topics. Math A/B serves as a bridge between the Math A and Math B courses.
Math A/B stays true to its geometric roots, as the first half of the course will cover topics such as perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...
and parallel lines
Parallel (geometry)
Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The assumed existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not...
, triangles, quadrilateral
Quadrilateral
In Euclidean plane geometry, a quadrilateral is a polygon with four sides and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon , hexagon and so on...
s, and transformations
Transformation (mathematics)
In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term "transformation" refers to a function from X to itself that preserves this structure.Examples include...
. After the first semester, students will take the New York State Math A Regents exam. June 2008 was the last administration of this exam. For the second half of the year, students will begin Math B. They will cover logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, geometric figures, and an introduction to trigonometry
Trigonometry
Trigonometry 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...
.
Math B (former course)
Math B is required to receive a High School Regents Diploma with Advanced Designation. The course replaces the former "Course 3" curriculum, which focused almost solely on trigonometryTrigonometry
Trigonometry 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...
. Math B focuses on a whole range of topics. It is taken after the student has completed and passed Math A.
A regents exam is taken at the end of the -year course. The Math B regents is often considered one of the most difficult New York State regents.
Math B covers concepts that can be found in trigonometry
Trigonometry
Trigonometry 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 advanced algebra
Algebra
Algebra 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...
, as well as preparing students for pre-calculus and calculus
Calculus
Calculus 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...
and reviewing old topics. During their year of study, students will learn different theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
s, graph complex number
Number
A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....
s and vectors, as well as reviewing topics such as exponential function
Exponential function
In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
s, systems of inequalities, and radical
Nth root
In mathematics, the nth root of a number x is a number r which, when raised to the power of n, equals xr^n = x,where n is the degree of the root...
s. As the year progresses, students will be expected to relate these functions
Function (mathematics)
In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
to the real world, create conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
s through their own research
Research
Research can be defined as the scientific search for knowledge, or as any systematic investigation, to establish novel facts, solve new or existing problems, prove new ideas, or develop new theories, usually using a scientific method...
, and begin a classroom
Classroom
A classroom is a room in which teaching or learning activities can take place. Classrooms are found in educational institutions of all kinds, including public and private schools, corporations, and religious and humanitarian organizations...
discussion about these topics. At the end of their studies, they will take the New York State Math B Regents Examination. The last administration of this exam will be in August 2010.
Future changes
In November 2004, the Mathematics Standards Committee made a report to the Board of RegentsBoard of Regents
In the United States, a board often governs public institutions of higher education, which include both state universities and community colleges. In each US state, such boards may govern either the state university system, individual colleges and universities, or both. In general they operate as...
http://www.emsc.nysed.gov/osa/mathre/new_mathregents.htm about the State's requirements for high school graduation as related to mathematics. The committee recommended that:
- The curriculum should return to its old format as a one-year course with a regents exam taken at the end of the year, with the new exam to be administered no earlier than June 2007. Math A would have its name changed to Integrated Algebra.
- In addition to the current regents exam at the end of the Math B course, there should be another regents exam, at the end of the first half of Math B study (currently Math A/B), to be administered no later than June 2006, bringing the total number of regents exams to three.
- The course's name be changed to Geometry for the first half of the course, and Algebra II and Trigonometry for the second half of the course (currently Math B). Integrated is only used in the new Algebra course.
-
- The State of New York has announced that these changes will be implemented in the 2009/10 scholastic year.
The move was praised by many who thought the changes to the original draft curriculum were unnecessary.