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Mathematics Education In New York
Mathematics education in New York in regard to both content and teaching method can vary depending on the type of school a person attends. Private school math education varies between schools whereas New York has statewide public school requirements where standardized tests are used to determine if the teaching method and educator are effective in transmitting content to the students. While an individual private school can choose the content and educational method to use, New York State mandates content and methods statewide. Some public schools have and continue to use established methods, such as Montessori for teaching such required content. New York State has used various foci of content and methods of teaching math including New Math (1960s), 'back to the basics' (1970s), Whole Math (1990s), 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" starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York (state)
New York, officially the State of New York, is a state in the Northeastern United States. It is often called New York State to distinguish it from its largest city, New York City. With a total area of , New York is the 27th-largest U.S. state by area. With 20.2 million people, it is the fourth-most-populous state in the United States as of 2021, with approximately 44% living in New York City, including 25% of the state's population within Brooklyn and Queens, and another 15% on the remainder of Long Island, the most populous island in the United States. The state is bordered by New Jersey and Pennsylvania to the south, and Connecticut, Massachusetts, and Vermont to the east; it has a maritime border with Rhode Island, east of Long Island, as well as an international border with the Canadian provinces of Quebec to the north and Ontario to the northwest. New York City (NYC) is the most populous city in the United States, and around two-thirds of the state's popul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York State
New York, officially the State of New York, is a state in the Northeastern United States. It is often called New York State to distinguish it from its largest city, New York City. With a total area of , New York is the 27th-largest U.S. state by area. With 20.2 million people, it is the fourth-most-populous state in the United States as of 2021, with approximately 44% living in New York City, including 25% of the state's population within Brooklyn and Queens, and another 15% on the remainder of Long Island, the most populous island in the United States. The state is bordered by New Jersey and Pennsylvania to the south, and Connecticut, Massachusetts, and Vermont to the east; it has a maritime border with Rhode Island, east of Long Island, as well as an international border with the Canadian provinces of Quebec to the north and Ontario to the northwest. New York City (NYC) is the most populous city in the United States, and around two-thirds of the state's population liv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle measure, using a division of circles into 360 degrees. They, and later the Babylonians, studied the ratios of the sides of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of limit, codify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pre-calculus
In mathematics education, precalculus is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework. Concept For students to succeed at finding the derivatives and antiderivatives with calculus, they will need facility with algebraic expressions, particularly in modification and transformation of such expressions. Leonhard Euler wrote the first precalculus book in 1748 called ''Introductio in analysin infinitorum'' (Latin: Introduction to the Analysis of the Infinite), which "was meant as a survey of concepts and methods in analysis and analytic geometry preliminary to the study of differential and integral calculus." H. J. M. Bos (1980) "Newton, Leibnitz and the Leibnizian tradition", chapter 2, pages 49–93, quote page 76, in ''From the Calculus to Set Theory, 1630 – 1910: An Introductory Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation (mathematics)
In mathematics, a transformation is a function ''f'', usually with some geometrical underpinning, that maps a set ''X'' to itself, i.e. . Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific affine transformations, such as rotations, reflections and translations. Partial transformations While it is common to use the term transformation for any function of a set into itself (especially in terms like "transformation semigroup" and similar), there exists an alternative form of terminological convention in which the term "transformation" is reserved only for bijections. When such a narrow notion of transformation is generalized to partial functions, then a partial transformation is a function ''f'': ''A'' → ''B'', where both ''A'' and ''B'' are subsets of some set ''X''. Algebraic structures The set of all transformations on a given base set, together with function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, derived from greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A, B, C and D is sometimes denoted as \square ABCD. Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ''ABCD'' add up to 360 degrees of arc, that is :\angle A+\angle B+\angle C+\angle D=360^. This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180°. All non-self-crossing quadrilaterals tile the plane, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangles
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. The names used for modern classification are eith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
