Japan's Math Education and the Impact on its
Innovation and Economy
(1) Mathematics is the foundation of modern civilization.
(2) Innovations generate wealth.
(3) Every innovation is a result of an application of mathematics.
High quality math education is absolutely necessary to build a
wealthy nation.
According to a New York Times article, "Is Algebra necessary?",
http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebranecessary.html?pagewanted=all&_r=0,
(1) 25% of 9th graders fail to finish high school. Algebra is the No.1
academic reason.
(2) A national sample of university transcripts: Math courses had over
2 times more F’s and D’s than the other subjects.
High School Graduation Rate (2011)
US 75%
Japan 98%
University Graduation Rate (2011)
US
57.4%
Japan 89%
College Job Placement Rate
1
2010 2011
2012
2013
US
24.9% Unavailable Unavailable Unavailable
Japan 91.8% 91.1% (all 93.6%
93.9%
time low)
http://sankei.jp.msn.com/economy/news/130517/biz13051711120030-n1.htm
The Associated Press April 2012 report: 53.6 % of bachelor's degree-holders
under the age of 25 last year were jobless or underemployed, the highest share in at
least 11 years. The AP reports that students who graduated out of the sciences or
other technical fields, such as accounting, were much less likely to be jobless or
underemployed than humanities and arts graduates.
http://www.theatlantic.com/business/archive/2012/04/53-of-recent-college-grads-arejobless-or-underemployed-how/256237/
According to K.I. West
(p. 77) On the other hand, at the K–12 level, a Michigan State University report
entitled “Breaking the cycle: An International Comparison of U.S. Mathematics
Teacher Preparation” states, “the weak K–12 mathematics curriculum
taught by teachers with an inadequate mathematics
background produces high school graduates who are similarly
weak. Some of them then become future teachers who are not given a strong
preparation in mathematics and then they teach and the cycle continues” (p. 31).
Math Contents at Public HS in Japan
10th Grade: Pre-calculus, Elementary Set Theory and Logic, 2D Vector
Geometry, Elementary Number Theory, Elementary Axiomatic
Geometry, and Combinatorial Probability (Proof by contradiction is taught
in the 10th grade. Throughout the high school years (10th, 11th, and 12th grades),
students are trained in proofs. )
11th Grade: Calculus I, 3D Vector Geometry, Linear Algebra, Discrete
Math
12th Grade: Calculus II, Calculus-based Probability and Statistics
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Note (1): For students in STEM concentration programs
(about 40% of all HS students), 2-year sequence courses
(equivalent to 16 credits in US) in Chemistry, Physics, and
Biology or Earth Science are required.
Note (2): In 2002, the Ministry of Education, Science, and
Technology designated 4 high schools to Super Science High
Schools. In 2013, the number increased to 213. Its English
page is at http://rikai.jst.go.jp/eng/e_about/e_sshs.php .
Additional Aspects of Japan's Public Education System
K-1 through K-12
(1) Length of Vacations
Summer (after 1st term)
40 days
Winter (between 1st and 2nd term) 14 days
Spring (after 3rd term)
14 days
(2) During these breaks, assignments are given in every subject but
music and art. The assignments are due at the beginning of the new
term. In HS, tests based on the assignments are given at the beginning
of the new term.
(3) Every prefecture administers its own teacher employment exam in
each subject. The competition rate ([number of applicants]/[number of
open positions])over the last 10 years ranges between 3 and 44,
depending on the year, prefecture, and subject.
(4) The national average public HS teacher salary = 7.77million JPY
Translation of
http://ksmath.kj.yamagata-u.ac.jp/~m-one/jugyo/jugyo-table.html
Total Credits Needed to Graduate
3
(Yamagata University)
General Education
２６
Breadth Requirements Foreign Languages
８
Subtotal
Mathematics Courses
３４
Required Courses
１６
Electives
６２
Free Electives
１２
Subtotal
９０
Total
１２４
At Graduation: 78 More Credits of Math Courses
Required Number of Credits in the Core Major Courses
(1) Science: 90.
(2) Engineering: 105.
(3) 31 extra credits of Education courses needed to earn a HS Teacher
Certificate.
The Impact on Japan's Innovation and Economy
Japan's Net External Assets World Ranking = No.1 in the World
consecutively since 1991.
4
(a) Japans' Net External Assets = 2.06 times No.2 nation
China's.
(b) Japans' Innovation Index = 2.52 times No.2 nation
Switzerland's.
(c) Japan's Technology Trade Balance Ratio = 2.22 times No.2
nation Norway's.
(d) Japan's Money Stock = 2.24 times No.2 nation US's.
Net External Assets 2012 IMF World Ranking
Rank
1
2
3
193
Country
Japan
China
Germany
US
Amount
($ millions)
$3572.6
$1736.4
$1412.3
–$4416.2
http://imfstatext.imf.org/WBOS-query/Index.aspx?QueryId=6325
Innovation Index World Ranking 2008
Page 13 of http://graphics.eiu.com/PDF/Cisco_Innovation_Complete.pdf
where
Innovation Index = Total Number of Patents per 1 million people
Rank
1
2
3
4
Country
Japan
Switzerland
Finland
USA
Innovation Index
1274.533
505.839
363.298
359.840
5
Technology Trade Balance Ratio 2010
The Export-To-Import Ratio (Technology Export divided by Technology
Import) serves as a barometer of a country's competitiveness in path-breaking
technology.
Rank
1
2
3
4
5
Country
Japan
Norway
Sweden
UK
Austria
US
Technology Trade Balance Ratio
4.6
2.07
1.98
1.8
1.57
1.46
http://www.koreatimes.co.kr/www/news/biz/2012/09/123_119527.html
Money Supply M1 March of 2013
Japan $5515 billions
US $2463 billions
http://www.tradingeconomics.com/japan/money-supply-m1
http://research.stlouisfed.org/fred2/series/M1SL
http://www.federalreserve.gov/releases/h6/current/
Health Care Ranking of 17 Advanced Nations
http://www.conferenceboard.ca/hcp/details/health.aspx
No. 1 Japan
No. 17 US
Rich-Poor Gap
6
UN Human Development Report 2008 was the last to report the Richest 10%
to Poorest 10% ratios (no longer available from 2009). Japan has the smallest rich-poor
gap in the world.
Japan 4.5
US
15.9
Crime Rate
Police Recorded Cases per 100,000 population
www.civitas.org.uk/crime/crime_stats_oecdjan2012.pdf
US
Intentional Homicide 5.0
Rape
28.6
Robbery
133
Assault
262
Burglary
715
Vehicle Theft
258
Japan
0.5
1.1
4
44
117
85
US/Japan Ratio
10
26
33.25
5.955
6.111
3.035
Proportion of Welfare Recipients 2013
Japan 1.7%
US
15.2%
Hiroshima University Math Majors Curriculum
Translation of
http://www.hiroshima-u.ac.jp/sci/gakusei-seikatsu/suugakuka-jugyo/
Year 1
Requirements
1st
Semester
Analysis I
Linear
Algebra I
Outlines of
Year 2
2nd
Semester
Analysis II
Linear
Algebra II
1st
Semester
Analysis
III
Abstract
Algebra I
General
Year 3
2nd
Semester
Analysis IV
1st
Semester
Year 4
2nd
Semester
1st
Semester
Thesis
Research
Abstract
Algebra II
General
7
2nd
Semester
Thesis
Research
Mathematics
Theory of
Math I
Equations
Processing
Practice
Electives
Statistical
Data Analysis
A
Statistical
Data
Analysis B
Introduction
to
Informatics
Theory of
Math II
Computational
Mathematics
Algebra A
Algebra B
Algebra C
Algebra
D
Information
Systems and
Geometry
Data Science
Geometry A
Geometry
B
Geometry
C
Geometry
D
Analysis A
Analysis C
Networks
and
Algebraic
Systems
Networks and
Algebraic
Systems
Mathematics
English
Practice
Analysis
B
Analysis D
Probability
and
Statistics
A
Computational
Mathematics
A
Probability
and
Statistics
B
Phenomenal
Mathematics
Probability
and Statistics
C
Nonlinear
Mathematics
Mathematical
Analysis A
Mathematics
Special
Topics
Mathematics
Special
Lectures
Chaos
Theory
Tsukuba University Mathematics Major Requirements
Translation of http://nc.math.tsukuba.ac.jp/college/syllabus/
Year 1
Course
Advanced Calculus I
Advanced Calculus II
Advanced Calculus III
Linear Algebra I
Linear Algebra II
Linear Algebra III
Advanced Calculus I Problems
Credits
2
2
2
1
1
1
1
8
Computational
Mathematics
B
Mathematical
Analysis B
Mathematics
Special Topics
Mathematics
Special
Lectures
Advanced Calculus II Problems
Advanced Calculus III Problems
Linear Algebra I Problems
Linear Algebra II Problems
Linear Algebra III Problems
Mathematics Special Problems
1
1
1
1
1
2
Mathematics Special LectureⅠ
1
Freshman Seminar
Class Seminar
Mathematics Class Seminar
1
1
1
Year 2
Course
Analysis I
Analysis II
Analysis I Problems
Analysis II Problems
Further Theory of Linear Algebra
Further Theory of Linear Algebra Problems
Introduction to Abstract Algebra
Introduction to Abstract Algebra Problems
Introduction to Set Theory
Introduction to Set Theory Problems
Introduction to Topology
Introduction to Topology Problems
Curves and Surfaces
Curves and Surfaces Problems
Computer Science Problems
Statistics
Foreign Mathematics Documents Reading
Credits
2
1
2
1
2
2
2
2
2
2
1
1
1
1
1
2
3
Year 3
Course
Abstract Algebra I-A
Abstract Algebra I-B
Abstract Algebra I-A Problems
Abstract Algebra I-B Problems
Credits
2
2
2
2
9
Topology I
Topology II
Topology I Problems
Introduction to Differentiable Manifolds
Theory of Functions
Theory of Functions Problems
Real Analysis I
Real Analysis II
Real Analysis I Problems
Real Analysis II Problems
Probability Theory I
Mathematical Logic I
Mathematical Statistics I
Computer Mathematics I
Foreign Mathematics Documents Reading II
Survey Methods
Preliminary Graduation Research
2
2
2
2
2
2
2
1
2
1
2
2
2
2
2
2
3
Year 4
Course
Abstract Algebra II
Abstract Algebra III
Topology III
Differential Geometry
Differential Equations
Real Analysis III
Complex Analysis
Functional Analysis
Probability Theory II
Mathematical Statistics II
Mathematical Logic II
Computer Mathematics I II
Graduation Research
Credits
2
2
2
2
2
2
2
2
2
2
2
2
9
"Strengthening a Country by Building a
Strong Public School Teaching Profession"
10
Kazuko Ito West
Waseda University Institute of Teacher Education
Journal of Mathematics Education at Teachers College
Spring–Summer 2013, Volume 4
Program in Mathematics and Education
Teachers College Columbia University
11