The Mathematics Curriculum in Primary and Lower Secondary Grades
The national mathematics standards, objectives, and content for primary, lower secondary, and upper secondary education are presented in the Courses of Study.13,14,15
Mathematics is a required subject in primary, lower secondary, and the first year of upper secondary school. Beginning with the 1998 revision of the mathematics curriculum, mathematics activities have been part of the objectives of the curriculum for every grade. In addition, enjoying mathematics is an objective at the primary and lower secondary level, while fostering creativity in mathematics is an objective at the upper secondary level.
The mathematics curriculum consists of three parts: overall objectives for the level (primary, lower secondary, or upper secondary), objectives and content for each grade, and syllabus design. Methods and materials are specified to some extent in the objectives and content for each grade, as well as in the construction of teaching plans and remarks on content. The primary school curriculum prescribes the standard number of class periods per year for mathematics. All schools in Japan are required to address all components of mathematics instruction by formulating an overall plan for mathematics that includes descriptions of the following: objectives and content; qualities, abilities, and attitudes to be fostered; learning activities; teaching methodology and teaching framework; and the evaluation of learning.
In the 2008 revision of the curriculum, the mathematics content in Grades 1 to 6 is composed of four content areas: Numbers and Calculations, Quantities and Measurements, Geometric Figures, and Mathematical Relations. At the lower secondary level, the mathematics content is composed of four areas: Numbers and Algebraic Expressions, Geometrical Figures, Functions, and Making Use of Data
The overall objectives for mathematics at the primary level (Grades 1 to 6) are to use mathematics activities to accomplish the following:16 help students acquire basic and fundamental knowledge and skills regarding numbers, quantities, and geometric figures; foster students’ ability to think logically and express themselves clearly about everyday matters; help students find pleasure in mathematics activities and appreciate the value of mathematical approaches; and encourage students to use mathematics in their daily lives and their learning. Exhibit 1 presents the objectives and content for mathematics in fourth grade.17
Exhibit 1: Mathematics Objectives and Content, Grade 4
| Content Area | Objectives and Content |
| Numbers and Calculations | Understand decimal numbers and fractions and that integers can be expressed using the decimal system; understand round numbers and appropriate contexts for using them; understand division and extend the ability to divide integers accurately; consolidate the ability to calculate integers and extend the ability to use these calculations; deepen understanding of decimal numbers, including adding, subtracting, multiplying, and dividing decimal numbers and using these calculations; deepen understanding of fractions, including adding and subtracting fractions with the same denominator and using these calculations; add and subtract using a soroban (Japanese abacus) |
| Quantities and Measurements | Understand the meaning of units of measurement for area and calculate the area of geometric figures; understand the meaning of units and measurements for angles, and measure angles |
| Geometric Figures | Understand plane figures (e.g., parallelograms, rhombuses) and solid figures (e.g., rectangular parallelepipeds) by observing their elements and exploring the relationships among those elements; recognize the elements and positional relationships of two- and three-dimensional geometrical figures through activities such as observing and drawing these figures |
| Mathematical Relations | Represent and explore the relationships between two numbers or quantities as they vary simultaneously; understand the algebraic expressions that represent the relationships between numbers or quantities and use these expressions; deepen understanding of the properties of the four basic operations; gather and organize data according to purpose, represent data clearly by using tables and graphs, and explore the features of data |
The overall objectives for mathematics at the lower secondary level (Grades 7 to 9) are to use mathematics activities to do the following: help students deepen their understanding of fundamental concepts, principles, and rules regarding numbers, quantities, and geometrical figures; help students acquire skills in mathematical processing and representation so that they can develop their ability to analyze and represent phenomena mathematically; help students enjoy mathematical activities and appreciate the value of mathematics; and encourage students to apply their mathematical understanding and ability when they think and evaluate problems.18 Exhibit 2 presents the objectives and content for mathematics in eighth grade.19
Exhibit 2: Mathematics Objectives and Content, Grade 8
| Content Area | Objectives and Content |
| Numbers and Algebraic Expressions | Develop the ability to discern algebraic relationships in concrete phenomena, represent these relationships in algebraic expressions using letters, and interpret these expressions; understand how to calculate the four fundamental operations with expressions using letters; solve and interpret simultaneous linear equations with two variables |
| Geometric Figures | Through activities such as observing, manipulating, and experimenting, discover the properties of basic plane figures and verify those properties based on the properties of parallel lines; understand the congruence of geometrical figures and verify the properties of geometrical figures based on the conditions for congruence of triangles; develop the ability to think and represent mathematical relationships logically |
| Functions | By exploring concrete phenomena, understand linear functions and develop the ability to discover, represent, and analyze functional relationships |
| Making Use of Data | Develop the ability to understand and use probability through exploring uncertain phenomena and be able to use it to analyze and represent data |