CHAPTER misunderstanding, representation and procedure in reasoning and making



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A. Brief Description of the Mathematics Education in Japan

The Japanese Education follows a 6-3-3-4 system: 6 years of elementary, 3 years of Junior/Middle High School (Lower Secondary), 3 years of High School (Upper Secondary), and 4 years of College/University. Compulsory education includes elementary and junior high school. Based on Monbukagakusho (2004), 63.5 percent of those who finished High School pursued post-secondary schools. Pre-school is not mandatory however 70% of 3-5 year olds attend either pre-school/kindergarten or nursery schools.

The Mobukagakusho (also known as monbusho) or MEXT (Ministry of Education, Culture and Sports) sets the number of class periods for the school year, the length of each class period,  the subjects to be taught, and the content (Courses of Study) for all schools; Kindergarten, Elementary, Junior and Senior High School. The course of study aims to set a common standard throughout the entire country and possible curriculum revisions are carefully evaluated before being put into effect. It is revised every 10 years; the course of study for elementary and lower school was last revised in March 2008 while for upper schools in March 2009.

In elementary, the goals and objectives of mathematics education are to develop in students the fundamental knowledge in skills with numbers and calculations, quantities and measurements, geometric figures, and quantitative relations. Beginning lower secondary, students are prepared to get into best high schools and universities. Students are taught numbers and mathematical expressions, geometric figures, functions, and data handling. The course of study gives emphasis on the “balance between acquiring basic and fundamental knowledge and skills and fostering the ability to think, make decision, and express oneself.”  The table below shows the objectives of Mathematics for elementary and high school.

Objectives of Mathematics based on Mathematics Curricula in the Course Study (2008)

Math for Elementary School

Math for lower Secondary School

1. acquire basic and fundamental and geometric figures
2. cultivate their ability to consider phenomena from their daily lives with foresight to generate and organize logical thinking steps to follow through, and to represent those phenomena
3. recognize the joy of mathematical activities and the merit of mathematical manipulation
4. foster a disposition to willingly make use of mathematics in daily life and studies

1. deepen their understanding of principles and rules about numbers, quantities, and geometric figures
2. develop fluency for mathematical representations and procedures
3. foster the disposition to utilize their mathematical misunderstanding, representation and procedure in reasoning and making judgments


In the course study, one of the major considerations when it comes to lesson planning is teaching the content of each grade through mathematical activities. Learning activities involve thinking and explaining using words, numbers, mathematical expressions, diagrams, tables and graphs, and engaging ideas with each other (in elementary); and identifying problem, planning solution strategy, carrying out plan, evaluating result and improving strategy (in lower secondary). In both elementary and lower secondary, these learning activities must provide the students the experience of joy in learning mathematics, make the students realize the importance and necessity of mathematics, and give them opportunities to exchange ideas with each other or share mathematical results.

Teaching methodology focuses on mathematical inquiry (Becker, et. al. 1990) and students are taught through problem solving approach. It aims to “develop an understanding of mathematical inquiry and an appreciation for the depth of and complexity of mathematics involved” among students. While use of technology is believed to be essential in teaching and learning mathematics and enhances students’ learning (6 Principles for School Mathematics, NCTM), use of calculators are not allowed in Japanese elementary and junior high school math classes. One reason is that calculators are also not allowed on entrance examinations for Senior High School.

B. Japan in International Surveys

i. PISA 2015

PISA (Programme for International Student Assessment) is a triennial survey that assesses the extent to which 15-year-olds students near the end of compulsory education have acquired key knowledge and skills that are essential for full participation in modern societies. PISA assesses students’ capability to reproduce knowledge, extrapolate from what they have learned and apply that knowledge in unfamiliar settings, both in and outside of school. Result of PISA 2015 reveals the consistent performance of Japanese students in mathematics, reading, and science. Japan obtained 5th place in PISA 2012 (Mathematics) and obtained 7th place in PISA 2015.


ii. TIMSS 2015 and TIMSS Advanced 2015


Based on TIMSS 2015 International Results in Mathematics participated by 57 countries and 7 benchmarking entities, East Asian countries were the top-performing countries, Japan being the top 5 in both fourth and eighth grade. TIMSS is an international assessment of mathematics and science at the fourth and eighth grades. It has been conducted every four years since 1995. TIMSS has the goal of helping countries make informed decisions about how to improve teaching and learning in mathematics and science.


TIMSS 2015 provides 20-year trend measures for countries that participated in the 1st TIMSS assessments in 1995. In addition, TIMSS Advanced 2015 provides assessment of students enrolled in special advanced mathematics and physics programs/tracks in their final year of secondary. TIMSS Advanced 2015, first conducted in 1995 then 2008, is the only international assessment on students’ achievement in advanced mathematics and physics. It gives emphasis on college and career readiness and increasing global competitiveness in STEM (Science, Technology, Engineering and Mathematics).