{"id":795,"date":"2016-08-15T20:32:58","date_gmt":"2016-08-15T20:32:58","guid":{"rendered":"http:\/\/timss2015.org\/encyclopedia\/countries\/ireland\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/"},"modified":"2016-10-18T16:01:38","modified_gmt":"2016-10-18T16:01:38","slug":"the-mathematics-curriculum-in-primary-and-lower-secondary-grades","status":"publish","type":"page","link":"http:\/\/timss2015.org\/encyclopedia\/countries\/ireland\/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-ireland\" class=\"carouselmenu\"><a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/ireland\/\" 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\/ireland\/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\/ireland\/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\/ireland\/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\/ireland\/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\/ireland\/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\/ireland\/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\/ireland\/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\/ireland\/suggested-readings\/\" class=\"menu-link main-menu-link menu-item menu-item-type-custom menu-item-object-custom\"><span>Suggested Readings<\/span><\/a><\/li>\n<a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/ireland\/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 mathematics component of the Primary School Curriculum<sup>7<\/sup> is for all children from Junior Infant classes (preprimary) to Grade 6. The mathematics curriculum aims to help all children to:<\/p>\n<ul>\n<li>Develop a positive attitude toward mathematics and to appreciate its practical applications in life<\/li>\n<li>Develop problem solving skills and the ability to use mathematics in everyday life<\/li>\n<li>Use mathematical language effectively and accurately<\/li>\n<li>Understand mathematical concepts and processes at a level commensurate to their development and ability<\/li>\n<li>Become proficient in fundamental mathematical skills and in recalling basic number facts<\/li>\n<\/ul>\n<p>In Grade 4, the curriculum is presented in five areas, known as strands\u2014Number, Algebra, Shape and Space, Measures, and Data. The strands are interrelated, such that student understanding in one strand is dependent on and supportive of ideas and concepts in other strands. The strands are divided into strand units in which student learning is described using content objectives. Unlike the rest of the Primary School Curriculum\u2014in which subject learning content is categorized at four levels, each of which consists of a two year grade band\u2014the content in the Mathematics Curriculum is specified in single year grades.<\/p>\n<p>Exhibit 1 shows the curriculum strands and strand units for Grade 4, and provides some specific examples of the types of skills students are able to develop through their mathematical work. These include Applying and Problem Solving, Understanding and Recalling, Communicating and Expressing, Integrating and Connecting, and Reasoning and Implementing.<\/p>\n<p><strong>Exhibit 1: Summary of Mathematics Curriculum for Grade 4, and Sample Skills<\/strong><\/p>\n<table class=\"tableEncyc\" border=\"0\" width=\"100%\">\n<tbody>\n<tr class=\"heading\">\n<td>Strand<\/td>\n<td>Strand Unit<\/td>\n<td>Mathematical Learning Objectives<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" rowspan=\"4\" valign=\"top\">Number<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Place value<\/td>\n<td class=\"borderBottom\" valign=\"top\">Round whole numbers to nearest 1,000<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Operations<\/td>\n<td class=\"borderBottom\" valign=\"top\">Solve word problems involving adding and subtracting within 9,999<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Fractions<\/td>\n<td class=\"borderBottom\" valign=\"top\">Solve problems involving fractions<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Decimals<\/td>\n<td class=\"borderBottom\" valign=\"top\">Order decimals on the number line<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" rowspan=\"2\" valign=\"top\">Algebra<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Number patterns and sequences<\/td>\n<td class=\"borderBottom\" valign=\"top\">Explore, recognize, and record patterns in number, 0\u20139,999; describe sequences<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Number sentences<\/td>\n<td class=\"borderBottom\" valign=\"top\">Translate a one-step word problem into a number sentence, and solve<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" rowspan=\"4\" valign=\"top\">Shape and Space<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">2-D shapes<\/td>\n<td class=\"borderBottom\" valign=\"top\">Identify, classify, compare, draw, tessellate, and make patterns with 2-D shapes<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">3-D shapes<\/td>\n<td class=\"borderBottom\" valign=\"top\">Identify, classify, and construct 3-D shapes<br \/>\nDescribe relationship of 3-D shapes with constituent 2-D shapes<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Symmetry<\/td>\n<td class=\"borderBottom\" valign=\"top\">Use understanding of line symmetry to complete missing half of a shape, picture or pattern<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Lines and angles<\/td>\n<td class=\"borderBottom\" valign=\"top\">Describe intersecting lines and their angles and classify angles as greater than, less than, or equal to a right angle<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" rowspan=\"7\" valign=\"top\">Measures<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Length<\/td>\n<td class=\"borderBottom\" valign=\"top\">Add, subtract, multiply, and carry out simple division of units of length (m, cm, km)<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Area<\/td>\n<td class=\"borderBottom\" valign=\"top\">Estimate, compare, and measure the area of regular and irregular shapes (cm<sup>2<\/sup>, m<sup>2<\/sup>)<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Weight<\/td>\n<td class=\"borderBottom\" valign=\"top\">Add, subtract, multiply, and carry out simple division of units of weight (kg and g)<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Capacity<\/td>\n<td class=\"borderBottom\" valign=\"top\">Add, subtract, multiply, and carry out simple division of units of capacity (l, ml)<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Time<\/td>\n<td class=\"borderBottom\" valign=\"top\">Work with times and dates; add and subtract hours and minutes<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Money<\/td>\n<td class=\"borderBottom\" valign=\"top\">Add, subtract, multiply, and carry out simple division of money (euro and cent)<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight\" valign=\"top\">Representing and interpreting data<\/td>\n<td class=\"borderBottom\" valign=\"top\">Use data sets<\/td>\n<\/tr>\n<tr>\n<td class=\"borderBottom borderRight headingInside\" valign=\"top\">Data<\/td>\n<td class=\"borderBottom borderRight\" valign=\"top\">Chance<\/td>\n<td class=\"borderBottom\" valign=\"top\">Identify and record outcomes of simple random processes<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A revised syllabus for Junior Certificate Mathematics (lower secondary level) was introduced on a phased basis<sup>a<\/sup> in September 2010 as part of the Project Maths initiative. The syllabus<sup>8<\/sup> comprises five strands:<\/p>\n<ul>\n<li>Statistics and Probability<\/li>\n<li>Geometry and Trigonometry<\/li>\n<li>Number<\/li>\n<li>Algebra<\/li>\n<li>Functions<\/li>\n<\/ul>\n<p>In September 2014, all students at the lower secondary level engaged with all five strands of the revised syllabus for the first time. The syllabus is set out in strands to provide continuity with the primary school curriculum. Teachers are encouraged to teach mathematics in contexts that allow learners to see connections within mathematics, between mathematics and other subjects, and between mathematics and its real life applications. In this way, students can achieve the objectives of lower secondary mathematics and develop proficiency in the following areas of mathematical competence:<\/p>\n<ul>\n<li>Conceptual understanding\u2014Comprehension of mathematical concepts, operations, and relations<\/li>\n<li>Procedural fluency\u2014Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately<\/li>\n<li>Strategic competence\u2014Ability to formulate, represent, and solve mathematical problems in both familiar and unfamiliar contexts<\/li>\n<li>Adaptive reasoning\u2014Capacity for logical thought, reflection, explanation, justification, and communication<\/li>\n<li>Productive disposition\u2014Habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence, perseverance, and one\u2019s own efficacy<\/li>\n<\/ul>\n<p>Problem solving (i.e., engaging in a task for which the solution is not immediately obvious) is integral to the lower secondary mathematics classroom. The syllabus stipulates that problem solving should not be met in isolation; rather, it should permeate all aspects of the teaching and learning experience. Problems may comprise purely mathematical matters or an applied context. In a mathematics problem solving environment, students are expected to:<\/p>\n<ul>\n<li>Make sense of the problem<\/li>\n<li>Make sense of the mathematics they can learn and use when doing the problem<\/li>\n<li>Arrive at a correct solution to the problem<\/li>\n<\/ul>\n<p>In the lower secondary mathematics classroom, teachers focus on helping students to develop mathematical knowledge and skills through the process of solving problems, rather than on helping them to find solutions. They prioritize generating class discussion and facilitating mathematical reasoning as students engage in problem solving. Students learn to analyze problems and break them down into manageable steps, to reflect on their strategies and those of others, and to adjust their own approach where necessary.<\/p>\n<p>Teachers play an important role in helping students develop these kinds of skills. By choosing tasks that present learners with a challenge, they activate learners\u2019 mathematical thinking processes, as opposed to imitative thinking processes. By encouraging them to share, explain, and justify their problem solving strategies, those that work as well as those that do not work, teachers can help learners to develop robust and deep mathematical understanding as well as confidence in their mathematical ability.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Mathematics Curriculum in Primary and Lower Secondary Grades The mathematics component of the Primary School Curriculum7 is for all children from Junior Infant classes (preprimary) to Grade 6. The mathematics curriculum aims to help all children to: Develop a &hellip; <a href=\"http:\/\/timss2015.org\/encyclopedia\/countries\/ireland\/the-mathematics-curriculum-in-primary-and-lower-secondary-grades\/\">Continued<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":142,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"1"},"class_list":["post-795","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/795","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=795"}],"version-history":[{"count":14,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/795\/revisions"}],"predecessor-version":[{"id":6916,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/795\/revisions\/6916"}],"up":[{"embeddable":true,"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/pages\/142"}],"wp:attachment":[{"href":"http:\/\/timss2015.org\/encyclopedia\/wp-json\/wp\/v2\/media?parent=795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}