Singapore

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’ mathematical abilities, with a focus on problem solving.¹⁹ 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.

Exhibit 2: Singapore Mathematics Curriculum Framework²⁰

© Ministry of Education, Singapore (Reproduced with permission by the Ministry of Education, Singapore)

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.

Exhibit 3: Mathematics Concepts and Skills

Primary Mathematics Grades 1–6	Lower Secondary Mathematics Grades 7–8
Numbers and Algebra
Whole numbers, fractions, and decimals, and the four arithmetic operations (addition, subtraction, multiplication, and division) Calculation with calculators Factors and multiples Ordering of numbers Approximation and estimation Percentage Ratio Speed Algebraic expressions in one variable	Negative numbers, integers, rational numbers, and real numbers, and the four arithmetic operations (addition, subtraction, multiplication, and division) Calculation with calculators Prime numbers, highest common factor, and lowest common multiple Ordering of numbers Use of symbols including <, >, ≤, ≥ Approximation and estimation Percentage Ratio, and direct and inverse proportion Map scales Rate and speed Algebraic expressions and formulas Algebraic manipulation (linear and quadratic) Functions and graphs (linear and quadratic) Linear equations with one unknown Simultaneous linear equations with two unknowns Quadratic equations Linear inequalities with one unknown
Geometry and Measurement
Measurement of length, mass, volume, time, and angle Area and perimeter of triangles, squares, and rectangles, area and circumference of circles, and volume of cubes and cuboids Properties of simple geometric figures Nets of simple solids Line symmetry Ideas of tessellation	Properties and construction of simple geometric figures Angles associated with parallel lines Angles of polygons Congruence and similarity Area of plane figures, volume and surface area of three-dimensional solids The Pythagorean Theorem Trigonometric ratios of acute angles in a right-angled triangle
Statistics and Probability
Picture graphs, bar graphs, tables, line graphs, and pie charts (including interpretation and use of information to solve problems) Average	Data analysis (including interpretation and analysis of various statistical representations) Probability