Korea, Rep. of

The Mathematics Curriculum in Primary and Lower Secondary Grades

The 2009 revised mathematics curriculum is designed as a set of courses through which students may acquire mathematical concepts, principles, and laws, enhance their ability to observe and interpret mathematically a range of phenomena occurring in the world, and develop the ability to solve mathematical problems using mathematical reasoning and logical thinking. Korea recognizes the need for continually improving the mathematics curriculum to provide students with rich experiences and relevant activities to foster the development of more comprehensive mathematical thinking processes.⁷

In particular, according to the new revised 2009 mathematics curriculum, students should acquire the core competencies necessary for future success in an increasingly complex and specialized job market. The 2009 mathematics curriculum emphasizes mathematical process standards and highlights such things as mathematical problem solving, communication, and reasoning. The mathematical process implies not only useful instructional methods for improving student understanding but reinforcing understanding of mathematical content.⁸

In addition, the 2009 mathematics curriculum aims to enhance student interest in and curiosity about mathematics, and cultivate a sense of confidence and a positive attitude toward mathematics. The mathematics curriculum aims to help students acquire the following competencies:

• Develop the ability to understand basic mathematical skills, concepts, principles, and laws, and their interrelationships, through the experience of mathematically observing, analyzing, organizing, and representing everyday social and natural phenomena
• Enhance the ability to think and communicate mathematically, and use those skills to develop the ability to solve mathematical problems in logical and creative ways
• Understand the value of mathematics, develop intrinsic motivation toward and interest in mathematics, and develop a positive attitude toward mathematics and positive personal characteristics⁹

The 2009 mathematics curriculum for elementary school comprises five content domains: Numbers and Operations, Figures, Measurement, Patterns, and Probability and Statistics.¹⁰ Exhibit 1 presents a summary of the mathematics topics and skills taught in each grade band.

Exhibit 1: Mathematics Topics Covered, Grades 1–6¹¹

Domain	Grades 1–2	Grades 3–4	Grades 5–6
Numbers and Operations	Numbers of up to four digits Addition and subtraction of two-digit numbers Multiplication	Five-digit numbers and higher Addition and subtraction of three-digit numbers Multiplication Division Four arithmetic operations with natural numbers Fractions Decimals Addition and subtraction of fractions and decimals	Factors and multiples Addition and subtraction of fractions Multiplication and division of fractions Multiplication and division of decimals Fractions and decimals
Figures	Shapes of solid figures Shapes of plane figures Plane figures and their components	The fundamentals of figures Moving plane figures The components of a circle Triangles Quadrangles Polygons	Congruence and symmetry Cuboids and cubes Prisms and pyramids Cylinders and cones Solid figures and spatial sense
Measurement	Comparing quantities Reading time Moment and length of time Length	Time Length Volume Weight Angles Estimation (rounding off, rounding up, rounding down) Comparing numbers (equal to or greater than, equal to or less than, greater than, less than)	The perimeter and area of plane figures Units of weight and area The ratio of the circumference of a circle to its diameter and the area of circles Surface area and volume
Patterns	Looking for patterns	Looking for patterns Patterns and correspondence	Ratio and rate Proportional expressions and distribution Direct and inverse proportions
Probability and Statistics	Classifying Drawing tables Drawing graphs	Organizing data Bar and broken-line graphs	Chance and average Expressing data Ratio graphs (band graphs and pie charts)

The 2009 mathematics curriculum for middle school comprises five content domains: Numbers and Operations, Variables and Expressions, Functions, Probability and Statistics, and Geometry.¹² Exhibit 2 summarizes the mathematics topics and skills for each grade band.

Exhibit 2: Mathematics Topics Covered, Grades 7–9¹³

Domain	Grades 7–9
Numbers and Operations	Prime factorization Greatest common divisor and least common multiple Concepts, comparison of, and the four basic operations with integers and rational numbers	Recurring decimals Relationship between rational numbers and recurring decimals	Concept and properties of square roots Irrational numbers Comparison of real numbers The four basic operations with radical expressions
Variables and Expressions	Using variables Value of expressions Addition and subtraction of linear expressions Linear equations	Law of exponents Addition and subtraction of polynomials Multiplication and formulas for multiplication of polynomials Division of polynomials Modification of equations Simultaneous linear equations Properties of inequalities and linear inequalities Simultaneous linear inequalities	Factorization Quadratic equations
Functions	Concept of functions Ordered pairs and coordinates Graphing functions	Meaning of and graphing linear functions Application of linear functions Relationship between linear functions and linear equations	Meaning of quadratic functions Properties of graphs of quadratic functions
Probability and Statistics	Stem and leaf plots, frequency distribution tables, histograms, and frequency distribution polygons Average from frequency tables Distribution of relative frequency	Number of events Concept and properties of probability Calculation of probability	Median, mode, and average Variance and standard deviation
Geometry	Points, lines, faces, and angles Geometrical relationship among points, straight lines, and planes Properties of parallel lines Constructing triangles Conditions for congruent triangles Properties of polygons Relationship between central angle and arc in sectors Length of arc and area of sectors Properties of polyhedrons and solids of revolution Surface area and volume of solid figures	Properties of isosceles triangles Circumcenter and incenter of triangles Properties of quadrangles Properties of similar figures Conditions for similar triangles Length and ratio of parallel line segments Application of properties of similar figures	The Pythagorean theorem Trigonometric ratios Properties of chords and tangents of a circle Properties of circumferential angles