1. Inquiring
   • Inquiring involves discovery or constructing knowledge through questioning or testing hypothesis. Posing questions to stimulate students to discover similarities or differences on different rules or asking students to test mathematical conjectures enables students to participate in a more active role in the learning process.
2. Communicating
   • Communicating involves receiving and sharing meanings by using language, symbols, graphs and aesthetic forms. Listening, speaking, reading and writing are the important elements of communication which help students to interpret others' statements, state their ideas, clarify their meanings, refine their strategies to solve problems, hypothesize and construct simple arguments. Activities such as teachers posing questions for students to answer, small-group work, large-group discussions, presentation of individual and group projects (both written and oral form) provide platforms for students to communicate mathematically. Mathematics in itself can also be considered as other form of language. Teachers can guide students to see the difference of the mathematical language with those languages used in daily life and appreciate the precise nature of the mathematical language.
3. Reasoning
   • Reasoning involves developing plausible or logical arguments to deduce or infer conclusions. It is fundamental to the knowing and doing of mathematics. A mathematician or a student makes a conjecture by generalizing from a pattern of observations made in some particular cases (inductive reasoning) and then tests the conjecture by constructing either a logical verification or a counter-example (deductive reasoning).
4. Conceptualizing
   • Conceptualizing involves organizing and reorganizing knowledge through perceiving and thinking about particular experiences in order to abstract patterns and ideas and to generalize from particular experiences. In teaching, teachers should pay due emphasis on helping students master the basic concepts of mathematics and create link between concepts.
5. Problem-solving
   • The importance of problem solving in mathematics education has well been recognized. It involves understanding the problems;
     ◆ considering possible strategies and choosing an appropriate one to solve the problem;
     ◆ carrying out the plan; and
     ◆ justifying or evaluating the solution.

1. Fundamental Arithmetic and Basic Mathematics
2. Directed Numbers and the Number Line
3. Introduction to Algebra
4. Linear Equation in One Unknown
5. Introduction to Geometry
6. Introduction to Statistics and Statistical Charts
7. Percentages(I)
8. Approximate Values and Numerical Estimation
9. Areas and Volumes (I)
10. Manipulation of Simple Polynomials
11. Angles related to Lines
12. Introduction to Coordinates

1. Errors in Measurement
2. Identities and Factorization
3. Algebraic Fractions and Formulas
4. Angles related to Rectilinear Figures
5. Congruence
6. More about Statistical Charts
7. Rate, Ratio and Proportion
8. Similarity
9. Linear Equations in Two Unknowns
10. Pythagoras' Theorem and Irrational Numbers
11. Areas and Volumes (II)
12. Trigonometric Ratios

1. More about Factorization of Polynomials
2. Laws of Integral Indices
3. Linear Inequalities in One Unknown
4. Percentages (II)
5. Quadrilaterals
6. Special Lines and Centres in a Triangle
7. Areas and Volumes (III)
8. Coordinate Geometry of Straight Lines
9. Trigonometric Relations
10. Applications of Trigonometry
11. Measures of Central Tendency
12. Introduction to Probability

1. Real Numbers and Complex Numbers
2. Quadratic Equations in One Unknown
3. Equations of Straight Lines
4. Functions and Graphs I
5. Functions and Graphs II
6. Exponential and Logarithmic Functions
7. Basic Properties of Circles I
8. Basic Properties of Circles II
9. More about Polynomials
10. More About Equations II

1. More about Equations I
2. Trigonometry I
3. Trigonometry II
4. Trigonometry III
5. Variations
6. Permutation and Combination
7. More about Probability
8. Measures of Dispersion
9. Uses and Abuses of Statistics
10. Arithmetic and Geometric Sequence
11. Locus
12. Inequalities and Linear Programming

(Module 1)

1. Foundation knowledge
2. Limit
3. Differentiation
4. Applications of Differentiation
5. Indefinite Integrals
6. Definite Integrals (I)
7. Definite Integrals (II)

(Module 2)

1. Foundation knowledge (I)
2. Foundation knowledge (II)
3. Limit
4. Differentiation (I)
5. Differentiation (II)
6. Applications of Differentiation
7. Indefinite Integrals (II)
8. Indefinite Integrals (II)