Representation

Presented by Group 5

Principles and Standards for School Mathematics describes a future in which all students have access to rigorous, high-quality mathematics instruction, including four years of high school mathematics. Knowledgeable teachers have adequate support and ongoing access to professional development. The curriculum is mathematically rich, providing students with opportunities to learn important mathematical concepts and procedures with understanding. Students have access to technologies that broaden and deepen their understanding of mathematics. More students pursue educational paths that prepare them for lifelong work as mathematicians, statisticians, engineers, and scientists.

INDONESIA

By the turn of the current education curriculum to

be KTSP, then its curriculum characteristics is also

different. KTSP characteristics can be known, among

others, of how schools and education units to

optimize performance, learning, learning resource

management, professionalism of staff, as well as

the assessment system.

Thus, it can be argued some of the characteristics

of KTSP as follows:

Granting broad autonomy to schools and

education units.

Community and parent participation is high.

Democratic leadership and professional.

Team work is compact and transparent.

South KoreaModern school system in South Korea is divided into 6 years of

primary school, three years each for junior high and high school.

Program for International Student Assessment (Program for

International Student Assessment) which is run by a recent OECD

study puts South Korea ranked 11th in the world. Although school

students often occupy South Korea rank high on international

comparative tests, the education system is often criticized for

applying a passive way of learning and too much memorization.

South Korea's education system is quite disciplined and structured

is the influence of Confucianism that has long been embedded in

Korean society. His students rarely have enough time to relax

because of the pressure to do well and get in top universities.

INDONESIACurrently in Indonesia has been established that the curriculum used is the Education Unit Level Curriculum (KTSP). KTSP is an idea about developing a curriculum that is placed in the position closest to the learning, the school and education units. Empowerment schools and education units by providing greater autonomy, in addition to showing the responsiveness of government to the demands of society, is also a means of improving the quality, efficiency, and equity of education.

On KTSP system, the school has "full authority and responsibility" in setting the curriculum and learning in accordance with the vision, mission, and goals of education unit. To realize the vision, mission, and goals, schools are required to develop standards of competence and basic competences in the competence indicators, develop a strategy, set priorities, manage a variety of potential schools and empower neighborhoods, and accountable to the people and Government in KTSP, curriculum development done by teachers, principals, and school committee and the board of education.

SOUTH KOREACurriculum in South Korea has long been reformed with an emphasis on engineering and technology utilization. Long learning in school pupils South Korea, on average lasts for 15 hours / day. School hours in place starting at 07.00 and ending up at 22:00 and every student class numbered only 25 children. It was still divided into two groups, each numbering 12 and 13 children.One interesting thing, the schools that have names in Korea, it was founded by well-known industry companies such as Hyundai, Samsung, and LG. The government only supports the subsidy funding.Such learning systems, facilitate the graduates, who obviously intelligent and master the skills, can be recruited into the workforce in the company concerned.

INDONESIASystem administration / education hierarchy in Indonesia is divided into several educational pathways which are further subdivided into several types and forms of education. Educational pathway consists of: (1) formal education and (2) non-formal education.

Basic EducationPrimary education is education that underlies secondary education. Every citizen aged seven to fifteen years of compulsory basic education. Government and Local Government guarantee the implementation of compulsory education for every citizen over the age of 6 (six) years in the basic education without charging a fee. Basic education in the form:•Elementary School (SD) and Madrasah Ibtidaiyah (MI) or other forms of the same level,

•Junior High School (SMP) and Madrasah Tsanawiyah (MTs), or other forms of equals.

Secondary EducationSecondary education is a continuation of basic education. Secondary education consists of: general secondary education, and vocational education.Secondary education in the form:1. Senior High School (SMA),2. Madrasah Aliyah (MA),3. Vocational School (SMK), and4. Madrasah Aliyah Vocational (MAK), or other forms of equals.

Higher EducationHigher education is education after secondary education includes diplomas, bachelor's, master's, specialist, and doctoral degrees are held by the college. Universities may take the form:1. academy,2. polytechnics,3. high school,4. institute, or5. University

Organized non-formal education for citizens who require educational services that serves as a replacement, addition, and / or complement formal education in support of lifelong education. Non-formal education serves to develop the potential of students with an emphasis on the mastery of knowledge and functional skills as well as personality development and professional attitude.Non-formal education includes:1. life skills education,2. early childhood education,3. youth education,4. educational empowerment of women,5. literacy education,6. vocational education and job training,7. educational equality, and8. Another study aimed to develop the ability of learners.

SOUTH KOREAIn general, the education system in South Korea consists of four levels, namely formal education: elementary school, high school junior high, high school and higher education. This is the fourth level of education: grade 1-6 (elementary), grades 7-9 (junior), 10-12 (high school), and grade 13-16 (high school / program S1), as well as post-graduate program (S2/S3 ).

INDONESIA•Sifat-Sifat Operasi Hitung•Perpangkatan dan Penarikan Akar Pangkat Tiga •Menentukan FPB dan KPK •Satuan Volume •Satuan Debit•Luas Bangun Datar •Bangun Ruang

SOUTH KOREA•Division of fraction•Division of decimals•Mixing calculations of fractions and decimals•The properties of prisms and pyramids•The properties of cylinders and cones•Various solid figures•Ratio of the circumference of a circle to its diameter and area of a circle•Surface area and volume•The surface area and volume of a cylinder•Ratio graphs•Number of cases and probability•Equations•Proportional expressions•Continued ratios and proportional distribution•Direct proportion and inverse proportion•Problem solving methods

Content standard is a written description of what students should know and be able to do in a particular content or subject area. The expectations articulated in the content standard outline the knowledge, skills, and abilities for all students in the subject area.

Representation includes the ways that students

depict their mathematical thinking as well the

process they use to put their thinking into that

form. Representations can include a variety of

written formats, oral explanations, models with

manipulative materials, or even the mental

process one uses to do mathematics.

Before students are ready to

use these conventional forms, they

need opportunities to express their

thinking using their own invented,

non-conventional forms

of

representation.

Create and use representations to organize,

record, and communicate mathematical ideas;

Select, apply, and translate among mathematical

representations to solve problems;

Use representations to model and interpret

physical, social, and mathematical phenomena.

Representations can help students organize their thinking. Students'

use of representations can help make mathematical ideas more

concrete and available for reflection. In the lower grades, for example,

children can use representations to provide a record for their teachers

and their peers of their efforts to understand mathematics. In the

middle grades, they should use representations more to solve problems

or to portray, clarify, or extend a mathematical idea.

Representations can help students organize their thinking. Students'

use of representations can help make mathematical ideas more

concrete and available for reflection. In the lower grades, for example,

children can use representations to provide a record for their teachers

and their peers of their efforts to understand mathematics. In the

middle grades, they should use representations more to solve problems

or to portray, clarify, or extend a mathematical idea.

1. Create and use representations to organize, record, and communicate mathematical ideas

For example: Find greatest common divisor (GCD) of two integer numbers 12 and 32.

Solution :

First, we find the factor of each integer number by using factor tree

Different representations often illuminate

different aspects of a complex concept or

relationship. For example, students usually learn

to represent fractions as sectors of a circle or as

pieces of a rectangle or some other figure.

2. Select, apply, and translate among mathematical representations to solve problems

For example:

Compare from this below fractions, which is greatest fraction ?

To decide the greatest fraction from that above problem, we

can use a circle. For the first fraction , it means that a circle

which divided into 2 parts which equal size then one of both

parts is shaded. Then for the second fraction , it means that a

circle which divided into 4 parts which equal size then three

of fourth parts is shaded.

For example:

Compare from this below fractions, which is greatest fraction ?

To decide the greatest fraction from that above problem, we

can use a circle. For the first fraction , it means that a circle

which divided into 2 parts which equal size then one of both

parts is shaded. Then for the second fraction , it means that a

circle which divided into 4 parts which equal size then three

of fourth parts is shaded.

...

• Like this below picture :

• The term model has many different meanings. So it is not

surprising that the word is used in many different ways in

discussions about mathematics education. For example, model

is used to refer to physical materials with which students work

in school—manipulative models.

• The term model has many different meanings. So it is not

surprising that the word is used in many different ways in

discussions about mathematics education. For example, model

is used to refer to physical materials with which students work

in school—manipulative models.

3. Use representations to model and interpret physical, social, and mathematical phenomena

• Representations can include a variety of written formats, oral explanations, models with manipulative materials, or even the mental process one uses to do mathematics.

• Representations can help students organize their thinking. Students' use of representations can help make mathematical ideas more concrete and available for reflection.

• The term mathematical model, which is the focus in this context, means a mathematical representation of the elements and relationships in an idealized version of a complex phenomenon. Mathematical models can be used to clarify and interpret the phenomenon and to solve problems.

• In South Korea, its educational system is the same with Indonesia. Six years for elementary school (SD), three years for junior high school (SMP), and six years in senior high school (SMA). Now, we will compare them according to subject matter and content standard.

• The content standards of elementary school in Indonesia are bilangan, geometri dan pengukuran, dan pengolaan data whereas in South Korea are numbers and operations, geometry, statistics and probability, figures, and patterns and problem solving.