history of mathematics curriculum in korea

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CHAPTER 1

HISTORY OF MATHEMATICS CURRICULUM IN KOREA

Joongkwoen Lee

Department of Mathematics Education, Dongguk University

Phil Dong 3 Ga, Joong Gu, Seoul, Korea

E-mail: [email protected]

The beginning of mathematics curriculum in Korea started in 1885.

The modern meaning of mathematics curriculum in Korea started

in 1945. The 1st mathematics curriculum (1955~1963) can be

characterized as real life experience centered curriculum. The focus of

the 2nd mathematics curriculum (1964~1972) was systematic learning.

The 3rd mathematics curriculum (1973~1981) was influenced by New

Math Movement. The 4th mathematics curriculum (1982~1988) started

from the failure of New Math and the emergence of the Back to Basics

Movement in the U.S. The 5th mathematics curriculum (1989~1994)

basically maintained the tradition of the 4th curriculum. The 6th

curriculum (1995~1999) increasingly stresses mathematical thinking

abilities by the way of fostering mathematical problem-solving

abilities. The 7th mathematics curriculum (2000~2006) are represented

by the implementation of ‘differentiated curriculum’.

1. The Quickening of Mathematics Curriculum in Korea

(1885~1945)

The beginning of mathematics curriculum in Korea started in 1885.

Hansung High school (4years) and Hansung girls’ High school taught

mathematics from 1885. The schools’ syllabus of lecture is the

following.

From 1910 to 1945, there were lots of changes in mathematics

curriculum in Korea. 5 years middle school (current middle school and

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high school) taught mathematics as two parts - numbers and figures. It

was a higher level compared to the earlier curriculum. The syllabus of

lecture dealt with 1st order equations, 1st order functions, 2nd order

equations, and 2nd order functions.

Table 1-1. Syllabus of Lecture

School

Grade High school Girls’ High school

1 arithmetic, algebra (6hours) integer, fraction (2hours)

2 algebra, geometry (5hours) fraction, decimal, abacus (2hours)

3 algebra, geometry, bookkeeping

(4hours) ratio, summation, abacus (2hours)

4 geometry, bookkeeping (4hours)

The modern meaning of mathematics curriculum in Korea started in

1945. The government made known to the public a guide line of general

education system and teaching hours of mathematics per week.

Table 1-2. Mathematics Hours (Elementary School)

grade 1 2 3 4 5 6

hours 6 6 6 5 5 5 Table 1-3. Mathematics Hours (Middle School)

grade 1 2 3 4

hours boys 4 4 4 4

girls 3 3 3 3

History of Mathematics Curriculum in Korea 3

At that time, middle school and high school were not divided. 4years

middle school covered middle and high school curriculum. Boys learned

mathematics one more hours per week than girls.

2. The Period of a Syllabus of Lectures (1946~1954)

2.1. Elementary School

The syllabus of lectures for elementary school mathematics presented

overall mathematics subjects. Counting was emphasized for the first

grade students. The second grade textbooks showed two digit numbers

addition and subtraction. For the 3rd grade students, divisions and

fractions were introduced. The 4th grade students learned abacus, time,

area, and volume. For the 5th grade students, making equation,

mensuration, the circular constant were introduced. Ratio, rotation

figures, power, and movement were taught for the 6th grade students.

2.2. Middle School

The syllabus of lectures for middle school mathematics arranged in a raw

the items of mathematics subjects without educational goals and

assessment plans. The hours teaching mathematics per week were

5hours for lower level middle school, and 1st grade 5hours, 2nd and 3rd

grades of liberal art class 0~2hours, and 2nd and 3rd grades of science

class 6~7hours for high level middle school students. The following

Table 1-4 shows mathematics contents and hours.

There were many problems in the period of a syllabus of lectures

(1946~1954). The content of mathematics was too difficult for the

students who were not ready to study. The system of mathematics

curriculum was not well organized.

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Table 1-4. Mathematics Contents and Hours

lower level middle school high level middle school

1

compulsory(175hours)

measurement(35h)

statistics(40h)

basic figure(35h)

character(35h)

table(20h)


demonstration

geometry(plane)(50h)

statistics(55h)

series and continuous change(70h)

2


changing and modifying equation(75h)

magnify reduction movement of figures(40h)

characteristic of figures(30h)

triangle and trigonometric function(30h)

selective(175hours)

plane triangle(30h)

algebra(40h)

plane analytic geometry(35h)

differential integral calculus(70h)

3


trigonometric function(45h)

approximate calculation(35~40h)

algebra(35~40h)

trajectory(50~60h)

selective(175hours)

differential integral

calculus(105~125h)

solid geometry(50~70h) 3. The 1st Mathematics Curriculum (1955~1963)

The 1st mathematics curriculum can be characterized as real life

experience centered curriculum, which was influenced by Progressivism

in the U.S. which valued learner's experience in real life. Because this

curriculum regards the school subject mathematics as a tool for the

betterment of living, the structure or the system of mathematics was

ignored. Thus, the contents of the mathematics curriculum were in low

level and mainly life-problem oriented.

Lenience and ignorance in the mathematics structure of the 1st

mathematics curriculum caused the decline of students’ mathematics

achievement, which necessitated the 2nd curriculum revision.


The 1st grade curriculum provided basic concept of fraction and real life

mathematics which were not showed in the period of a syllabus of


lectures (1946~1954). The 2nd grade students learned fractions and the

9 × 9 multiplication table. The 3rd grade students dealt with 3 digit

numbers for addition, subtraction, multiplication, and division. The 4th

grade students learned revenue and expenditure. For the 5th grade

students symmetry and center, probability and permutation, combination,

mensuration, and the circular constant were eliminated. They just

handled plane concept of figures and measures. The 6th grade students

learned number, calculation, fraction and ratio, measure, tables, problem

solving in real situation, and figures. The 1st mathematics curriculum

(1955~1963) lowered the overall levels compared to the period of a

syllabus of lectures (1946~1954).

3.2. Middle School

The 1st grade students learned the concept of approximate value and

decimal point, and a prime factor. They used characters to present

equations. The 2nd grade students began with real life mathematics

problems. Character and expression, simple 1st order equation, measure

and error and approximate value also introduced for the 2nd grade

students. The 3rd students dealt with discount insurance, tax, and check.

They learned inequality expression and basic demonstration knowledge.

3.3. High School

The 1st grade students learned function, trigonometry function, measured

value, probability, statistics, economy and finance, figures and it nature.

There were number and calculation of expressions, algebra function,

algebra, trigonometry function, probability, statistics, series, and integral

in the analytic calculus. In the geometry geometric system, linear type,

circle, trajectory, solid figures, coordinate and equation were founded.

4. The 2nd Mathematics Curriculum (1964~1972)

The focus of the 2nd curriculum was systematic learning, which was

based on Herbart’s Essentialism (Park, 1998). The 2nd curriculum placed

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great value on the logical and theoretical aspects of mathematics, and

pursued the improvement of students' mathematical abilities.


For the 1st grade students fraction was added to number chapter. In

calculation part multiplication and division were introduced. The 2nd

grade students combined number and fraction. They emphasized

multiplication and division. The 3rd grade students learned addition

and subtraction of integers, fractions, and decimals. Introduction of

abacus was eliminated for the 4th grade students. They stressed

multiplication and division. The calculation using abacus appeared at

first time in the 5th grade. They faced the circular constant. In the 6th

grade curriculum the notations of { }, ●, [ ] were appeared. They learned

time and velocity.

4.2. Middle School

The 1st grade students learned using characters, positive negative

numbers, measure, measured number and error that came from 2nd grade

level. For the 2nd grade students the law of calculations was introduced.

They reduced skills of calculation. For the 3rd grade students learned

mathematics 2~4hours per week.

4.3. High School

Common mathematics dealt with number and expression, approximate

value, equation and inequality expression, function, equation of curve,

plane figures and its’ nature. Mathematics I (for liberal art students)

treated of calculation of log, series, probability, statistics, differential and

integration, 3-dimension space. Mathematics II (for science students)

handled equation and inequality expression, exponent and log,

trigonometry function and vector, series, probability, statistics,

differential and integration, figures.


5. The 3rd Mathematics Curriculum (1973~1981)

The 3rd mathematics curriculum was influenced by New Math, which

occurred as the result of the discipline centered curriculum and

mathematics modernization movement. The 3rd curriculum attempted to

introduce abstract but fundamental ideas (for example, sets) early in the

curriculum and to continually return to these ideas in subsequent lessons,

relating, elaborating, and extending them. Bruner’s discovery learning

was also crucial element in the 3rd curriculum.


The 1st grade students learned the concept of relation and set that was

not appeared in the 2nd mathematics curriculum (1964~1972). For the

2nd grade students, correspond relation was newly introduced. They

learned unit of money. In the 3rd grade curriculum, the symbol of set

was appeared. They treated of one to one correspondence in terms of

function relations. The error of true value and approximate value was a

special feature of the 4th grade curriculum. The whole set, complement

set, empty set, relation of ratio appeared for the 5th grade students. The

6th grade students studied the law of exponent and frequency distribution

table. They did not learn abacus at the 6th grade.

5.2. Middle School

Ratio and unit of ratio, metric unit, statistics table, shape of basic figures

which are in the 1st grade curriculum moved to elementary curriculum.

However, vertical, parallel, negative number, positive number, the law of

calculation, 1st order equation, coordinate plane, volume of solid figures,

surface area of solid figures moved into the 1st grade curriculum from

the 2nd grade curriculum. Set, algebraic structure of number system,

product set and function, number of cases, and probability were newly

added in the 2nd grade curriculum. In the 3rd grade curriculum, addition,

subtraction, multiplication, division of fraction expression, fraction

equation, ratio, projected figure were eliminated. Algebraic structure of

real number system, binomial operation, residue class, 2nd order

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equation and relation, sample survey, topological nature of figures were

newly adopted in the 3rd grade curriculum.

5.3. High School

Set, conditional statement, true value table, mathematical induction, flow

chart, polynomial, rational expression, irrational expression, 3rd and 4th

order equation, synthetic division, remainder theorem, ellipse, hyperbola,

region of inequality, approximate value of integral were added in the

mathematics I. Error of approximate value moved to middle school

curriculum. Plane figures and its' nature moved to mathematics II. We

can find 3rd and 4th order inequality expression, rational inequality,

matrix, axiom structure of plane geometry, directional cosine, directional

ratio, length of curve in mathematics II. Monogram, slide rule, projected

figure were eliminated in mathematics II.

6. The 4th Mathematics Curriculum (1982~1988)

The 4th mathematics curriculum started from the failure of New Math

and the emergence of the Back to Basics Movement in the U. S.

Students’ basic computation skills were weakened due to the structural

approach to mathematics of the 3rd curriculum. Thus the 4th curriculum

reduced contents, lowered the level of difficulty, and emphasized

obtaining of minimal competencies in mathematics.


The introduction of set in the 1st grade curriculum was expurgated. They

adopted corresponding relation and comparing numbers by paring and

making expression. The 3rd grade students treated four digit numbers

calculation. The equivalent relation of sets was deleted for the 4th grade

mathematics curriculum. The introduction of subset, whole set, and

empty set moved from chapter of number to chapter of relation for 5th

grade students. The raw of exponent was erased in the chapter of number

for the 6th grade curriculum.


6.2. Middle School

Addition and subtraction of binary system and quinary system, the law of

calculation, and its nature, relation of two sets were expurgated for the

1st grade curriculum. Simultaneous inequalities, transformation of

figures were eliminated for the 2nd grade curriculum. Corelation moved

from 3rd grade curriculum to the 2nd grade curriculum. Binary

operation, residue class, and sample survey were erased in the 3rd grade

curriculum.

6.3. High School

In the 4th mathematics curriculum, there is no new mathematical subject

that added to high school mathematics curriculum. The principle of log

rule, operation of function, approximate value of integral, formula of

Heron were deleted in mathematics I. Axiomatic construction of plane

geometry was eliminated in mathematics II. 3rd order matrix was

reduced to 2nd order matrix in mathematics II.


The 5th mathematics curriculum basically maintained the tradition of the

4th curriculum. The main direction of revision was to emphasize

students’ mathematical activities in mathematics class, and to consider

affective aspects of learning mathematics. From this period, keeping in

step with the current social trends, the mathematics curriculum started to

take the information society into account.


The 1st grade mathematics curriculum treated finding unknown terms in

simple addition and subtraction using materials. The 2nd grade

mathematics curriculum emphasized the relation of multiplication and

division, applying multiplication and division. Segment, half line,

straight line, and congruence of segments were expurgated in the 3rd

grade mathematics curriculum. Drawing figures, set, elements, subset,

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and symbols ({ }, ∈, ⊂, ⊃) were deleted in the 4th grade mathematics

curriculum. The 5th grade mathematics introduced set, elements, subset,

cup, and cap. Finding area of obtuse triangle, and regular polygon

were deleted in the 5th grade mathematics curriculum. Development

figures of prism and cylinder were added to the 6th grade mathematics

curriculum.

7.2. Middle School

Calculation of approximate value was eliminated in the 1st grade

mathematics curriculum. The basic concept of circle moved from

the 3rd grade curriculum to the 1st grade mathematics curriculum.

The law of exponent was treated within natural number in the 2nd

grade mathematics curriculum. Probability moved from the 3rd grade

mathematics to 2nd grade mathematics curriculum. The 3rd grade

mathematics curriculum did not handle algebraic structure, solving

2nd order equation by using graphs, position relation of basic figures.

Irrational number moved from the 2nd grade to the 3rd grade curriculum.

7.3. High School

The 5th mathematics curriculum for high school reduced the number

of mathematics subjects. Specially, true table, true value, sum of logic,

product of logic, and composite of propositions were deleted in the

general mathematics. Mathematics I adopted Gauss elimination. Ellipse,

hyperbola moved from general mathematics to mathematics II.


The 6th mathematics curriculum is not so much different from the

previous one. The 6th curriculum increasingly stresses mathematical

thinking abilities by the way of fostering mathematical problem-solving

abilities. This curriculum period especially emphasized the necessity of

discrete mathematics in school mathematics.



Comparing width, weight, and volume were added to the 1st grade

mathematics curriculum. The 2nd grade mathematics curriculum deleted

the concept of circles. Problem solving in relation chapter was

emphasized in the 3rd grade mathematics curriculum. Acute angle,

obtuse angle, acute triangle, and obtuse triangle were newly appeared in

the 4th grade mathematics curriculum. Set was eliminated for the 5th

grade students. Parallel displacement and symmetric displacement were

newly adopted in the 5th grad mathematics curriculum. Subtraction of

integer was added to the 6th grade mathematics curriculum. However,

abacus, regular polygon, and width were eliminated in the 6th grade

mathematics curriculum.

8.2. Middle School

The 1st grade mathematics curriculum expurgated equivalence, constant,

tree. They reduced set, integer and rational number, calculation of

expression. The 2nd grade mathematics curriculum reduced probability.

Approximate value and error moved from the 1st grade to 2nd grade

mathematics curriculum. The 3rd grade mathematics curriculum

eliminated maximum value and minimum value of 2nd order function

within limited range, applying 2nd order function, relationship of 2nd

order function and 2nd order equation, and perfect square number.

8.3. High School

Parabola moved from common mathematics to mathematics II.

Mathematics I eliminated Gauss elimination. Mathematics I and

mathematics II were separated in terms of dealing with subjects.

Mathematics II added differential of inverse function and function

expressed with parameters.

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The core characteristics of the 7th mathematics curriculum are

represented by the implementation of ‘differentiated curriculum’, which

can be one of the alternative ways of alleviating such problems of our

education as instruction of mathematics is carried out without

considering students’ abilities and aptitudes in the classroom. The

following will show the rationale for the revision of the 6th mathematics

curriculum and the main features of the current ‘differentiated

curriculum’, namely the 7th mathematics curriculum.

9.1. General Features of the 7th Curriculum

The Korean educational period consists of the two periods: ‘Compulsory

Period (10 years from grade 1 to 10)’ and ‘Elective Period (2 years from

grade 11 to 12)’. Otherwise, to prevent the redundancy and inefficiency

of math contents, and to pursue the consistency of mathematics

education, previous school level distinction is abolished even though the

distinction in terms of administration still exists. Mathematics in the

‘Compulsory Period’ is organized in a stepwise and level-referenced

manner that allows the teacher to consider the rate of the student’s

cognitive development and to thereby select core contents of the

curriculum based on a learning hierarchy and difficulties. Moreover, the

curriculum would separate ‘basic’ and ‘enriched’ content to make it

possible for each student to maintain his or her own learning pace and to

have a creative learning experience.

In the mathematics curriculum, ‘level based differentiated

curriculum’ manner is applied because the school subject mathematics is

relatively hierarchic, structured, and creates severe individual differences

among pupils in the process of instruction. Thus, the mathematics

curriculum is organized and implemented in a ‘level based differentiated

curriculum’ manner in the ‘Compulsory Period’ (from grade 1 to 10; 10

levels and each level with 2 sub-levels A and B). In ‘Elective Period’

(from grade 11 to 12; 2 levels and each level with 2 sub-levels A and B),

the ‘subject selection differentiated curriculum’ manner is applied for

the students to select their own subjects based on their own needs and


capacities. In the mathematics curriculum, this curriculum manner is

applied to all the students in grades 11 and 12. In these two grades

various mathematics subjects are available such as ‘Practical

Mathematics,’ ‘Mathematics I,’ ‘Mathematics II,’ ‘Calculus,’

‘Probability and Statistics,’ and ‘Discrete Mathematics’.

9.2. The Flow and Basic Structure of the 7th Curriculum

For each of the two educational periods, i.e. ‘Compulsory Period (10

years from grade 1 to 10)’ and ‘Elective Period’ (2 years from grade 11

to 12), corresponding mathematics curriculums are developed. Each of

these two mathematics curriculums are composed of 5 parts, such as

characteristics, objectives, contents, teaching & learning methods, and

evaluation. During the ‘Compulsory Period (from grade 1 to grade 10)’,

mathematics is compulsory, which means all students are required to

take the same mathematics courses. But, during grades 11 and 12,

tracking in mathematics is available.

9.3. Synopsis of the 7th Mathematics Curriculum

The 7th mathematics curriculum is organized and implemented in a

‘level based differentiated curriculum’ manner in the ‘Compulsory

Period’ (from grade 1 to 10; 10 levels and each level with 2 sub-levels A

and B). On the other hand, in the ‘Elective Period’ (from grade 11 to 12;

2 levels and each level with 2 sub-levels A and B), ‘subject selection

differentiated curriculum’ manner is applied for the students to select

their own subjects based on their needs and capacities.

9.3.1. Compulsory Period

The ‘Compulsory Period’ mathematics curriculum consists of the

following six content domains: ‘Numbers and Operations’, ‘Geometric

Figures’, ‘Measuring’, ‘Probability and Statistics’, ‘Letters and

Expressions’, and ‘Patterns and Functions’. In the domain of ‘Numbers

and Operations’, students can understand the concepts of natural

numbers, integers, rational numbers, and real numbers. Also, they can

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correctly add, subtract, multiply, and divide those numbers in the

elementary and middle school levels. Also, the importance was

continuously emphasized in Principles and Standards for School

Mathematics (NCTM, 2000). Similarly, in our mathematics curriculum,

almost every step from grade 1 to 6 contains ‘spatial perception’ as an

important content. This ‘spatial perception’ content mainly consists of

space movement related contents, so called a ‘motion geometry’, which

could be instructed through the learners’ own positive learning activities

dealing with concretely contrived geometric devices, so that they would

contain purposed geometric concepts. Instruction of ‘spatial perception’

is expended such an order as: experiencing the various spatial senses;

operating spatial senses mentally; and utilizing and expressing the spatial

sense mathematically.

The second notable change is actually not about content itself but

about ‘something noteworthy in instructing’ which was described in the

curriculum document. So to speak, in dealing with proposition proof, this

curriculum urges not straight proof but referring to intuitions or to

considering related problematic situations.

The domain of ‘Geometric Figures’, students can understand the

concepts and the nature of plane figures and solid figures. In the domain

of ‘Measuring’, students can understand and apply the concepts of length,

time, weight, angle, width, volume, and trigonometric rate. In the domain

of ‘Probability and Statistics’, students can understand the concepts of

the numbers of cases, probability, and can organize and represent data in

tables and graphs. In the domain of ‘Letters and Expressions’, students

can use the letters in representing mathematical ideas to solving

expressions and understanding the concepts of equations and inequalities.

In the area of ‘Patterns and Functions’, students can explore patterns and

understand the basic concepts of correspondence, linear functions,

quadratic functions, rational functions, irrational functions and

trigonometric functions, and can use problem-solving strategies.

9.3.1.1. ‘Number and Operation’ Domain As we can find easily in following table, the quantity of the contents of

‘Number and Operation’ domain begins to steeply decrease at grade 8.


This ‘Number and Operation’ domain has been separated into two

domains such as ‘Number’ and ‘Operation’ up to the 6th curriculum.

Considering the fact that these two domains have traditionally contained

main contents in elementary school mathematics, it is natural that this

domain has become an abnormally large domain that is a prime

consideration for teachers.

In the aspect of a shift in contents occurred in those mathematics

curriculums including the present curriculum, the content “set” is

regarded as the most dynamically changed one. Thus we do not hesitate

to mention sets as a representative content in discussing the changes in

school mathematics curriculum in Korea. In the third curriculum initiated

in 1973, sets first appeared in grade 2. After that first appearance,

however, sets were continuously moved to upper grades following

changes in the curriculum revise. After all, in the 7th curriculum sets

disappeared in elementary school mathematics, and appeared first in the

7th grade.

9.3.1.2. ‘Geometric Figure’ Domain The ‘Geometric Figure’ domain, which traditionally has been a solid

one, now undergoes big changes in the 7th curriculum. The first

remarkable change is that ‘spatial perception’ is newly introduced and

emphasized especially in the elementary level. The content ‘spatial

perception’ was prescribed by the NCTM (1989) in Curriculum and

Evaluation Standards for School Mathematics as a subject that should be

included in the mathematics curriculum at the elementary and middle

school levels. Also, the importance was continuously emphasized in

Principles and Standards for School Mathematics (NCTM, 2000).

Similarly, in our mathematics curriculum, almost every step from grade 1

to 6 contains ‘spatial perception’ as an important content. This ‘spatial

perception’ content mainly consists of space movement related contents,

so called a ‘motion geometry’, which could be instructed through the

learners’ own positive learning activities dealing with concretely

contrived geometric devices, so that they would contain purposed

geometric concepts. Instruction of ‘spatial perception’ is expended such

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an order as: experiencing the various spatial senses; operating spatial

senses mentally; and utilizing and expressing the spatial sense

mathematically.

The second notable change is actually not about content itself but

about ‘something noteworthy in instructing’ which was described in the

curriculum document. So to speak, in dealing with proposition proof, this

curriculum urges not straight proof but referring to intuitions or to

considering related problematic situations.

9.3.1.3. ‘Measuring’ Domain Strongly interrelated domain with ‘Geometric Figure’ is the domain

‘Measuring’. For instance, even though both domains deal with the

common geometric figures ‘Geometric Figure’ domain handles the

constituent elements and the properties of the geometric figures. On

the other hand, ‘Measuring’ domain talks about the length, area, and

volume of the geometric figures.

9.3.1.4. ‘Probability and Statistics’ Domain In the 7th

mathematics curriculum, stem-and-leaf plots have been

introduced for the first time. Stem-and-leaf plots provide efficient ways

of showing information, as well as comparing different sets of data.

Moreover, they are very easy and interesting for the elementary students

to learn.

9.3.1.5. ‘Letters and Expressions’ Domain In the ‘Letters and Expressions’ domain the main features of the contents

are separated into two parts according to the school level. One is the

‘problem solving’ which runs throughout the elementary school level

(grade 1 through 6), and the other one is the ‘equation and inequalities’

which runs throughout the middle and high school level (grade 7 through

10). In fact, in the elementary school level, the concept of real

mathematical ‘letters’ or ‘expressions’ are not proper to learn and the

‘problem solving’ could not either be properly included in the domain.


Thus, the content ‘problem solving’ was included in the domain just for

convenience’ sake. Considering the fact that problem solving could not

be treated as simply a mathematical content but as a way to teach and

learn mathematics, it is not a proper way to locate the ‘problem solving’

in the middle of the curriculum as if it would be one of the normal

mathematics contents.

9.3.1.6. ‘Patterns and Functions’ Domain Finding patterns in mathematics is a powerful problem-solving strategy.

This pattern was newly systemized into the 7th school mathematics

curriculum. Instructions of patterns in this curriculum are categorized

into three topics such as: experiencing various patterns and finding rules;

representing and creating patterns; and expressing patterns into

mathematical rules and making use of them.

Up to the 6th curriculum the function was defined in such manner

as not the dependence of quantities, but the fact of the correspondence

itself, on the basis of which certain objects are regarded as being

assigned to other certain objects. The concept of a function is reduced

to set-theoretical definitions. However, in this curriculum the function

is explained as a variable quantity that is dependent upon another

variable quantity. Thus the essence of the concept is the dependence of

quantity.

9.3.2. Elective Period

In mathematics curriculum, this ‘selective’ curriculum manner is applied

to all the students in grades 11 and 12. In these two grades various

mathematics subjects are available such as ‘Practical Mathematics,’

‘Mathematics I,’ ‘Mathematics II,’ ‘Calculus,’ ‘Probability and

Statistics,’ and ‘Discrete Mathematics’.

9.3.2.1. Practical Mathematics ‘Practical Mathematics’ is an optional course offered to students who

want to learn mathematics for daily life without having to complete the

10th level. This subject enables students to apply the basic concepts and

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rules of mathematics, to consider various types of problem solving in real

life situations. The contents emphasize the application of mathematics in

the four domains: the calculator and the computer, economic life,

everyday statistics, and problem solving. The contents use easy and

interesting material from real life, which are based on the mathematics

lower than the 10th level.

9.3.2.2. Mathematics I ‘Mathematics I’ is the first course to be offered to students who wish to

study advanced mathematics after completing level 10 of ‘Mathematics’

in the Compulsory Period. Through this course, students understand

basic mathematical concepts, principles, and laws, and develop

mathematical thinking ability, logical reasoning ability, and reasonable

and creative problem-solving ability. This course is a prerequisite for

‘Mathematics II’.

The contents consist of an ‘algebra’ domain, including exponents and

logarithms, matrixes and sequences; and ‘analysis’ domain, including

the limits of sequences, exponential functions, logarithmic functions;

and a ‘probability and statistics’ domain, including permutation and

combination, probability, and statistics.

9.3.2.3. Mathematics II ‘Mathematics II’ is a course to be offered to the students who want to

study more advanced mathematics after ‘Mathematics I’. Through this

course students can attain deeper mathematical knowledge and better

develop their mathematical thinking ability, logical reasoning ability, and

then develop abilities and attitudes to solve problems reasonably. This

course is suitable for students who wish to study the natural sciences or

technological sciences at the college level.

The contents of ‘Mathematics II’ consist of an algebra domain,

including equations and inequalities; an analysis domain, including limits

and the continuity of a function, the differentiation and integration of

polynomial functions; and a geometry domain, including quadratic

curves, space figures and coordinates of space.


9.3.2.4. Differentiation and Integration ‘Differentiation and Integration’ is a course designed for students who

want to study advanced differentiation and integration of various

functions after having completed ‘Mathematics II’. In this course

students will be able to gain advanced knowledge in differentiation and

integration. They will develop their mathematical thinking, logical

reasoning, and problem-solving ability. This course is appropriate for

students who want to study the natural sciences or technology at the

college level.

The contents consist of trigonometry, the limits of trigonometry, the

limits of exponential functions and logarithmic functions, differentiation

and integration of various functions, and the application of differentiation

and integration.

9.3.2.5. Probability and Statistics ‘Probability and Statistics’ is an optional course offered to students

who wish to study applied probability and statistics without having to

have completed level 10 mathematics. This subject enables students to

improve their data processing ability and their inferential ability

necessary for the information age. It will enable them to understand the

statistical phenomena in society and nature and, hence, to improve their

analytical ability. It is suitable for students who need to use probability

and statistics in real life situations through experimental and operational

activities.

The contents consist of real life examples in the following four

areas: descriptive statistics, probability, random variables, probability

distributions, and statistical estimation, all of which are based on the first

10 levels.

9.3.2.6. Discrete Mathematics ‘Discrete Mathematics’ is offered to students regardless of whether they

have completed Level 10 mathematics or not. In ‘Discrete mathematics’,

using basic mathematical concepts, principles, and laws will develop the

student’s abilities and aptitude to analyze mathematically, to think

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logically and to solve reasonably finite or discontinuous discrete problem

situations. This is a course needed for students who want to have

experience in discrete mathematical knowledge.

The contents consist of four domains: selections and arrangements,

graphs, algorithms, and decision making and optimization. For each of

these domains, various real world problems should be utilized to lead

students to easy and interesting discrete mathematical situations.

References

1. Kang, O. K. (1997). The 7th elementary and secondary school mathematics

curriculum of republic of Korea. Seoul: The Ministry of Education. [in Korea]

2. Lee, J. K. (2004). Mathematics curriculum in Korea. Seoul: KyungMoonSa. [in

Korea]

3. National Council of Teachers of Mathematics (1989). Curriculum and evaluation

standards for school mathematics. Reston, VA.: The Author.

4. National Council of Teachers of Mathematics (2000). Principles and standards for

school mathematics. Reston, VA.: The Author.

5. Paik, S. Y. (2004). Mathematics curriculum in Korea. Paper presented at ICME10,

Copenhagen, Denmark, 2004.

6. Park, K. M. (1997). Mathematics curriculum in Korea. Research in Mathematical

Education, 1(1), 43–59.

7. Park, K. M. & Leung, K. F. S. (2002). A comparative study of the mathematics

textbooks of China, England, Hong Kong, Japan, Korea, and the United States. Paper

presented at the ICMI comparative study conference, the University of Hong Kong,

20th–25th October, 2002.

8. Park, K. M. (2003). Issues related to the mathematics curriculum revision. Paper

presented at the MathLove Seminar on mathematics curriculum, Seoul, 14th June,

2003. [in Korea]

history of mathematics curriculum in korea

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