{"id":1313,"date":"2016-06-15T14:31:26","date_gmt":"2016-06-15T14:31:26","guid":{"rendered":"http:\/\/timss2015.org\/advanced\/?page_id=1313"},"modified":"2019-07-08T18:24:50","modified_gmt":"2019-07-08T18:24:50","slug":"russian-federation-description-of-advanced-mathematics-programs-and-curricula","status":"publish","type":"page","link":"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/russian-federation-description-of-advanced-mathematics-programs-and-curricula\/","title":{"rendered":"Russian Federation: Description of Advanced Mathematics Programs and Curriculum"},"content":{"rendered":"<div class=\"carouselwrap\"><div id=\"menu-programs-and-curriculum-advanced-mathematics\" class=\"carouselmenu\"><a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/france-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>France<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/italy-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Italy<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/lebanon-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Lebanon<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/norway-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Norway<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/portugal-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Portugal<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/russian-federation-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Russian Federation<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/slovenia-description-of-advanced-mathematics-programs-and-curricula\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Slovenia<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/sweden-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>Sweden<\/span><\/a><\/li>\n<a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/united-states-description-of-advanced-mathematics-programs-and-curriculum\/\" class=\"menu-link main-menu-link menu-item menu-item-type-post_type menu-item-object-page\"><span>United States<\/span><\/a><\/li>\n<\/div><\/div>\t<style>\n\t\t.carouselwrap{\n\t\t\tbackground: #e5eaef;\n\t\t}\t\t\n\t\t.owl-item a{\n\t\t\tbackground: #ffffff;\n\t\t\tborder: 4px #1FA67A solid;\n\t\t\tcolor: #000000;\n\t\t}\t\t\n\t\t.owl-item a:hover,\n\t\t.owl-item a:focus,\n\t\t.owl-item a.current-menu-item{\n\t\t\tbackground: #006544;\n\t\t\tborder: 4px #1FA67A solid;\n\t\t\t\n\t\t\tcolor: #ffffff;\n\t\t}\n\t<\/style>\n\t\n<div><a class=\"aboutTIMSS-download\" href=\"http:\/\/timss2015.org\/wp-content\/uploads\/filebase\/advanced\/advanced-mathematics\/M11.-programs-and-curriculum\/M11_1_adv-math-description-of-advanced-math-programs-and-curriculum.pdf\" target=\"_blank\">Download Description of the Advanced Mathematics Programs and Curriculum<\/a><\/div>\n<h2>Russian Federation: Description of the Advanced Mathematics Programs and Curriculum<\/h2>\n<p>High school programs for mathematics (Grades 10-11) are distinguished by the amount of the material being studied and the amount of instructional time. The Basic level program is designed for those students who plan to learn a profession that is not related to mathematics or plan to use mathematics as an auxiliary \u201ctool\u201d in their professional lives. The Profile level program provides sufficient depth of mathematics study to make it possible for students to enter a profession where mathematics is actively used. It includes a large amount of content and has higher requirements for its mastery. The mastery of this content makes it possible for students to continue to university-level studies in mathematical disciplines. Within the Profile level there is a subset of students in an even more intensive program taking six hours or more of mathematics lessons per week. The sample of students participating in the TIMSS\u00a0Advanced\u00a02015 Advanced Mathematics assessment included both Profile-level students and Intensive-level students. The results for students in the Intensive level were also reported separately as Russian Federation 6hr+.<\/p>\n<p>The Profile level curriculum includes an explanation of the main goals of the program and provide for the organization and planning of mathematics courses, including:<\/p>\n<ul>\n<li>General characteristics of the profile course<\/li>\n<li>Teaching goals<\/li>\n<li>The number of lessons per week and per year<\/li>\n<li>General learning skills and activities<\/li>\n<li>Compulsory content and learning outcomes<\/li>\n<\/ul>\n<p>The content of the Profile course is divided into two sections: Algebra and Calculus, and Geometry. The topics included in each section are listed below.<\/p>\n<table width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\" class=\"CurrTable\">\n<tbody>\n<tr>\n<th colspan=\"2\">Content Areas in Algebra and Calculus<\/th>\n<\/tr>\n<tr>\n<td colspan=\"2\" class=\"bgWhite\">Grade 10<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td width=\"30%\" class=\"headingInside\">\n      Polynomials\n     <\/td>\n<td>\nTransformation of polynomials, factorization; division of polynomials; Horner\u2019s method; roots of polynomials; Bezout\u2019s theorem; converting irrational expressions\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Graphs of Functions <\/td>\n<td>\n    Complex functions; conversion of graphs; graphs of linear-fractional functions, asymptotes; graphs of functions which include a sign of a module (e.g., <span class=\"formulas\">y=<span class=\"fraction\"><span class=\"fup\">2x-6<\/span><span class=\"bar\">\/<\/span><span class=\"fdn\">|3-x|<\/span><\/span><\/span>   or <span class=\"formulas\">y=sin|x|<\/span>); reciprocal functions and their graphs\n     <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Introduction to Calculus <\/td>\n<td>\nNumerical sequences, limits of sequences, limits of functions, theorems on limits of functions; properties and continuity of elementary functions\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Derivatives and their Applications <\/td>\n<td>\nGeometric and physical meaning of the derivative, continuity and differentiability of functions, derivatives of sums, products, quotients, composites and exponential functions; second derivatives and higher order derivatives; application of derivatives to study functions; Lagrange\u2019s theorem and its consequences; drawing graphs of functions\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Trigonometric Functions <\/td>\n<td>\nTrigonometric functions of numeric argument (sine, cosine, tangent and cotangent); trigonometric identities and their consequences; reduction formulas; identical transformation of trigonometric expressions; periodicity of trigonometric functions; properties, graphs, and derivatives of trigonometric functions\n      <\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" class=\"bgWhite\">Grade 11<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Integral and Differential Equations <\/td>\n<td>\nIndefinite integrals; definite integrals and their properties, numerical approximation of definite integrals, approximate computation; Newton-Leibniz formula; application of integrals for calculating areas, volumes, and lengths of arcs in physical problems; solutions of simple differential equations\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Exponential and Logarithmic Functions<\/td>\n<td>\nProperties and graphs of exponential functions; logarithms, definitions, and properties; identical transformations of exponential and logarithmic expressions; exponential and logarithmic equations, inequalities and systems of inequalities, types and methods of solution; derivatives of exponential functions; natural logarithms, radioactive decay\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Complex Numbers<\/td>\n<td>\nAlgebraic form, arithmetic operations, conjugating complex numbers;  solutions of quadratic equations with complex coefficients; the complex plane; trigonometric form of complex numbers, multiplication, division, and raising to power; De Moivre\u2019s formula; complex roots of polynomials; the Fundamental Theorem of Algebra\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Elements of Combinatorics<\/td>\n<td>\nMethods of mathematical induction; proofs of identities; factorials; the basic formulae of combinatorics; combinations and permutations; Binomial Theorem, Dirichlet\u2019s Principle\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Elements of the Theory of Probability and Mathematical Statistics<\/td>\n<td>\nClassic definition of probability, calculating probabilities using combinatorics; conditional probability, the rules of addition and multiplication of probabilities, independent events, Bernoulli distribution; mathematical expectation and variance; the concept of the law of large numbers and a normal distribution law; parent population and sample, levels of significance and reliability; evaluation of probability using frequency; the concept of statistical hypothesis testing\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Equations, Inequalities, Systems<\/td>\n<td>\nGeneral methods and approaches for solving equations; irrational equations; generalized method of intervals for solving inequalities; systems of equations and inequalities, basic methods for solving systems of equations; application of graphs to solve equations, inequalities and systems; approximate methods for solving equations; equations, inequalities, and systems with parameters\n      <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"0\" class=\"CurrTable\">\n<tbody>\n<tr>\n<th colspan=\"2\">Content Areas in Geometry<\/th>\n<\/tr>\n<tr>\n<td colspan=\"2\" class=\"bgWhite\">Grade 10<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td width=\"30%\" class=\"headingInside\">\n      Axioms of Solid Geometry\n     <\/td>\n<td>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n     Parallel Lines and Planes<\/td>\n<td>\n    Mutual arrangement of lines and planes in space; theorems of parallelism of lines and planes\n     <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Perpendicularity of Lines and Planes <\/td>\n<td>\n      Theorems of dependences between parallelism and perpendicularity of lines and planes, the Theorem of the Three Perpendiculars; angles between straight lines and a plane\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Coordinates and Vectors in a Space <\/td>\n<td>\nRectangular coordinate systems on a plane, the formula for distance between points, equations of straight lines and circumference; Cartesian coordinate system in a space, equations of straight lines and a plane; movements in a space and their properties (central symmetry, parallel translation, rotation), similarity in a space\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n     Vectors in a Space<\/td>\n<td>\nDecomposition of vectors into three non-coplanar vectors; scalar products; applications of coordinates and vectors to solve problems\n      <\/td>\n<\/tr>\n<tr>\n<td colspan=\"2\" class=\"bgWhite\">Grade 11<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Polyhedrons <\/td>\n<td>\nConcepts of polyhedrons, prisms, rectangular parallelepipeds, and pyramids; areas of faces and surfaces; sections; regular polyhedrons; dihedral angles<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Solids of Revolution<\/td>\n<td>\nBodies and surfaces of revolution, cylinders, cones, axial sections of cylinders and cones; spheres and solid spheres, sections of solid spheres, equation of a sphere; inscribed and circumscribed cylinder, cone, sphere\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n      Volumes of Bodies<\/td>\n<td>\nVolumes of polyhedrons (prisms, pyramids) and solids of revolution (cylinder, cone, sphere, part of the sphere)\n      <\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\">\n     The Surface Areas of Solids of Revolution<\/td>\n<td>\nAreas of spheres, surface areas of cylinders and cones\n      <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Learning outcomes are described in terms of what students should know and be able to do in each of these areas. Teachers have some discretion as to the introduction of optional topics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Download Description of the Advanced Mathematics Programs and Curriculum Russian Federation: Description of the Advanced Mathematics Programs and Curriculum High school programs for mathematics (Grades 10-11) are distinguished by the amount of the material being studied and the amount of &hellip; <a href=\"https:\/\/timss2015.org\/advanced\/timss-advanced-2015\/mathematics\/programs-and-curriculum\/russian-federation-description-of-advanced-mathematics-programs-and-curricula\/\">Continued<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"parent":1278,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1313","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1313","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/comments?post=1313"}],"version-history":[{"count":21,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1313\/revisions"}],"predecessor-version":[{"id":3052,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1313\/revisions\/3052"}],"up":[{"embeddable":true,"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/pages\/1278"}],"wp:attachment":[{"href":"https:\/\/timss2015.org\/advanced\/wp-json\/wp\/v2\/media?parent=1313"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}