{"id":1011,"date":"2016-08-15T20:33:00","date_gmt":"2016-08-15T20:33:00","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-09-15T14:46:09","modified_gmt":"2016-09-15T14:46:09","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/","title":{"rendered":"The Mathematics Curriculum in Primary and Lower Secondary Grades"},"content":{"rendered":"<div class=\"carouselwrap\"><div id=\"menu-singapore\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Introduction<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>The Mathematics Curriculum in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/the-science-curriculum-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>The Science Curriculum in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/teachers-teacher-education-and-professional-development\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Teachers, Teacher Education, and Professional Development<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/instruction-for-mathematics-and-science-in-primary-and-lower-secondary-grades\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Instruction for Mathematics and Science in Primary and Lower Secondary Grades<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/monitoring-student-progress-in-mathematics-and-science\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Monitoring Student Progress in Mathematics and Science<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/special-initiatives-in-mathematics-and-science-education\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Special Initiatives in Mathematics and Science Education<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/use-and-impact-of-timss\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Use and Impact of TIMSS<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/references\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>References<\/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 #00b2cc 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: #00667f;\n\t\t\tborder: 4px #00b2cc solid;\n\t\t\t\n\t\t\tcolor: #ffffff;\n\t\t}\n\t<\/style>\n\t\n<h2>The Mathematics Curriculum in Primary and Lower Secondary Grades<\/h2>\n<p>The<em> Singapore Mathematics Curriculum Framework<\/em> (Exhibit 2) is used at all the grade levels from primary to preuniversity education, and emphasizes the development of students\u2019 mathematical abilities, with a focus on problem solving.<sup>19<\/sup> Five interrelated components support the development of problem solving abilities: concepts, skills, processes, metacognition, and attitudes. The framework provides directions for the teaching, learning, and assessment of mathematics.<\/p>\n<p><strong>Exhibit 2: Singapore Mathematics Curriculum Framework<\/strong><sup>20<\/sup><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-5410\" src=\"http:\/\/timss2015.org\/encyclopedia\/wp-content\/uploads\/sites\/6\/2016\/08\/T15_E_Singapore_2.png\" alt=\"Exhibit 2: Singapore Mathematics Curriculum Framework\" width=\"900\" height=\"710\" srcset=\"http:\/\/timss2015.org\/encyclopedia\/wp-content\/uploads\/sites\/6\/2016\/08\/T15_E_Singapore_2.png 900w, http:\/\/timss2015.org\/encyclopedia\/wp-content\/uploads\/sites\/6\/2016\/08\/T15_E_Singapore_2-300x237.png 300w, http:\/\/timss2015.org\/encyclopedia\/wp-content\/uploads\/sites\/6\/2016\/08\/T15_E_Singapore_2-768x606.png 768w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><\/p>\n<p>\u00a9 Ministry of Education, Singapore (Reproduced with permission by the Ministry of Education, Singapore)<\/p>\n<p>The Singapore mathematics curriculum comprises a set of syllabi spanning 12 years, from primary to preuniversity education. As mathematics is a hierarchical subject, higher concepts and skills are built upon foundational ones and must be learned in sequence. The curriculum is designed in a spiral manner where concepts and skills in each content strand (e.g., Numbers and Algebra, Geometry and Measurement) are revisited and built upon at each level to achieve greater depth and understanding. Exhibit 3 presents a summary of the concepts and skills to be learned by the end of Grade 8 (Secondary 2). Teachers help their students learn these concepts and skills by adopting age- and grade-appropriate pedagogical approaches. Central to these pedagogical approaches at the primary and lower secondary levels is the Concrete-Pictorial-Abstract (C-P-A) approach, whereby teachers lead students through activities that help build an understanding of abstract mathematical concepts from everyday experiences and meaningful contexts, using concrete and pictorial representations.<\/p>\n<p><strong>Exhibit 3: Mathematics Concepts and Skills<\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr class=\"heading\">\n<td valign=\"top\">Primary Mathematics Grades 1\u20136<\/td>\n<td valign=\"top\">Lower Secondary Mathematics Grades 7\u20138<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\" colspan=\"2\" valign=\"top\">Numbers and Algebra<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"borderRight\" valign=\"top\">\n<ul>\n<li>Whole numbers, fractions, and decimals, and the four arithmetic operations (addition, subtraction, multiplication, and division)<\/li>\n<li>Calculation with calculators<\/li>\n<li>Factors and multiples<\/li>\n<li>Ordering of numbers<\/li>\n<li>Approximation and estimation<\/li>\n<li>Percentage<\/li>\n<li>Ratio<\/li>\n<li>Speed<\/li>\n<li>Algebraic expressions in one variable<\/li>\n<\/ul>\n<\/td>\n<td valign=\"top\">\n<ul>\n<li>Negative numbers, integers, rational numbers, and real numbers, and the four arithmetic operations (addition, subtraction, multiplication, and division)<\/li>\n<li>Calculation with calculators<\/li>\n<li>Prime numbers, highest common factor, and lowest common multiple<\/li>\n<li>Ordering of numbers<\/li>\n<li>Use of symbols including &lt;, &gt;, \u2264, \u2265<\/li>\n<li>Approximation and estimation<\/li>\n<li>Percentage<\/li>\n<li>Ratio, and direct and inverse proportion<\/li>\n<li>Map scales<\/li>\n<li>Rate and speed<\/li>\n<li>Algebraic expressions and formulas<\/li>\n<li>Algebraic manipulation (linear and quadratic)<\/li>\n<li>Functions and graphs (linear and quadratic)<\/li>\n<li>Linear equations with one unknown<\/li>\n<li>Simultaneous linear equations with two unknowns<\/li>\n<li>Quadratic equations<\/li>\n<li>Linear inequalities with one unknown<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\" colspan=\"2\" valign=\"top\">Geometry and Measurement<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"borderRight\" valign=\"top\">\n<ul>\n<li>Measurement of length, mass, volume, time, and angle<\/li>\n<li>Area and perimeter of triangles, squares, and rectangles, area and circumference of circles, and volume of cubes and cuboids<\/li>\n<li>Properties of simple geometric figures<\/li>\n<li>Nets of simple solids<\/li>\n<li>Line symmetry<\/li>\n<li>Ideas of tessellation<\/li>\n<\/ul>\n<\/td>\n<td valign=\"top\">\n<ul>\n<li>Properties and construction of simple geometric figures<\/li>\n<li>Angles associated with parallel lines<\/li>\n<li>Angles of polygons<\/li>\n<li>Congruence and similarity<\/li>\n<li>Area of plane figures, volume and surface area of three-dimensional solids<\/li>\n<li>The Pythagorean Theorem<\/li>\n<li>Trigonometric ratios of acute angles in a right-angled triangle<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"headingInside\" colspan=\"2\" valign=\"top\">Statistics and Probability<\/td>\n<\/tr>\n<tr class=\"borderBottom\">\n<td class=\"borderRight\" valign=\"top\">\n<ul>\n<li>Picture graphs, bar graphs, tables, line graphs, and pie charts (including interpretation and use of information to solve problems)<\/li>\n<li>Average<\/li>\n<\/ul>\n<\/td>\n<td valign=\"top\">\n<ul>\n<li>Data analysis (including interpretation and analysis of various statistical representations)<\/li>\n<li>Probability<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>The Mathematics Curriculum in Primary and Lower Secondary Grades The Singapore Mathematics Curriculum Framework (Exhibit 2) is used at all the grade levels from primary to preuniversity education, and emphasizes the development of students\u2019 mathematical abilities, with a focus on &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/singapore\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":168,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1011","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1011","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/comments?post=1011"}],"version-history":[{"count":16,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1011\/revisions"}],"predecessor-version":[{"id":5953,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/1011\/revisions\/5953"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/168"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=1011"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}