What to Teach
| Number and Quantity | Structure of Number-Use | . | ||
| Natural Number |
Sequence, Law of Composition, Quantitative Interpretation of Decimal Numbers | . | ||
| Rational Number |
Rational Multiple, Law of Composition, Extension of Natural Number, Decimal Form | . | ||
| "Symmetrical System of Number" | Needs of Symmetrical System of Number, Meaning of "Symmetrical System of Number", Absolute Value, Order Relation, Law of Composition, Calculation, Extension of Natural Number and Rational Number | Instruction | ||
| Real Number | Square Root, Irrational Number and Rational Number, Definition of "Real Number" | . | ||
| Complex Number | . | . | ||
| Proportional Relation |
Meaning of "Proportional Relation", Applying Proportional Relation to Problem Solving, Proportional Function on A Number System | . | ||
| Linear Algebra | From Theory of "Quantity" to "Linear Algebra", Linear Map and Matrix | . | ||
| Compound Proportional Relation |
Meaning of "Compound Proportional Relation", Applying Compound Proportional Relation to Problem Solving | . | ||
| Measurement/ Calculation of Quantity |
Measurement | General Discussion | . | |
| Itemized Discussion (Lenght, Weight, Time, Area, Volume, etc.) | ||||
| Calculation | General Discussion | . | ||
| Itemized Discussion (Area, Volume) | ||||
| Expression | . | |||
| Equation | . | |||
| Function | Instruction | |||
| Space | . | |||
| Geometry/ Figure |
Geometry | Euclidean Geometry | Plane Geometry | . |
| Space Geometry | . | |||
| "Figure" and "Space" | . | |||
| "Isomorphic" | Meaning of "Figure", "Isomorphic" | . | ||
| Kinds of "Isomorphism" | Congruity | . | ||
| Similarity | . | |||
| Straight Line | . | |||
| Symmetry | . | |||
| Figures | Simplicial Complex, Angle, Polygon/Polyhedron, Circle/Sphere/Ball, Curve Line, Cone/Cylinder, Pasting, Projection, etc. | . | ||
| Logics | . | |||
| Data Processing/ Statistics |
. | |||
| Probability | . | |||
| Programming | . | |||