Mathematics Education in Korea

The following sections are included:

• OVERVIEW

• CONTENTS

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’.

The Mathematics Curriculum is the basic document for determining the content and scope of mathematics dealt with in school. The academic curriculum system of Korea is structured in a way in which the government establishes and distributes the curriculum. In this chapter, we will examine the characteristics and main contents of ‘Mathematics Curriculum Revised in 2007’ (the 7th revised mathematics curriculum) reformed and announced in 2007, and progressively applied from 2009 to 2011. We will also examine the backgrounds and the basic directions of revision and main contents of ‘Mathematics Curriculum Revised in 2009’, which was set to reform in 2009 and announced in 2011, and scheduled to be applied starting in 2013.

This chapter introduces current elementary mathematics textbooks in Korea. As Koreans use only one series of elementary mathematics textbooks and almost all Korean teachers use them as their main instructional resource, it is fundamental to probe mathematics textbooks so as to better understand Korean mathematics education. This chapter begins with the basic principles and overall direction to develop textbooks, followed by an overview of the structure of a unit. It then describes seven characteristics of elementary mathematics textbooks along with examples. This chapter closes with some issues on the use of textbooks and their future development.

We will examine trends and issues of curriculum research, and research methods used in the research in Korea and then provide suggestions for future directions in conducting research on mathematics curriculum issues. Results from the review of peer-reviewed research articles suggest that the ways in which the research studies on curriculum in Korea sorted out issues seemed to heavily concentrate on the written and intended curriculum by means of a document analysis. In particular, the topics of curriculum studies were biased in the studies of written curriculum, and a significant number of curriculum studies were related to elementary levels. In addition, regarding the research methods, the findings showed that mixed methods have been rarely used, surveys are mostly used as the form of data collection and only a few studies use the data from interviews and the data from observations. Most of the studies rely on a single data source rather than multiple sources of data such as surveys, interviews, observations, and documents. Based on the review of the literature, we suggest pursuing various research topics and issues on curriculum, balancing weigh on the written and enacted curriculum, and deeper analysis and investigation of textbooks.

In this chapter, we present the future directions for Korean mathematics textbooks. According to the latest reformed curriculum called “Mathematics Curriculum Revised in 2009,” the characteristics of contents and systems of the textbooks are described in this chapter. For the grades from 1st to 9th, it is set as the core mathematics curriculum and for the high school (10th to 12th), the elective curriculum. Some contents are deleted and integrated with relative contents, compared to the previous curriculum, called “Mathematics Curriculum Revised in 2007.” Based on the current requests, we suggested future directions for the development of mathematics textbooks.

This chapter introduces practices for successful implementation of reform-based instruction from the perspectives of the learner, teacher, knowledge, instruction and assessment, and classroom culture. In addition, we examine mathematical instruction practices before, during, and after the 7th National Curriculum. The chapter closes with some implications for improving reform-based instruction.

LCI is one of teaching and learning methods based on constructivism. According to constructivism, even students in elementary school can independently construct abstracts from their actions as well as from concrete phenomena. Constructivists assert that such a created scheme provides students powerful adaptabilities of their knowledge and reasoning abilities, which is investigated in this study. Students in LCI showed statically significant differences in content reasoning tests as well as in understanding the learned mathematical concepts. These students also did not resent mathematical concepts during the experimental treatment, where as those students in traditional centered instruction did.

Korean students learn spatial and geometric knowledge, and reasoning in the context of Euclidean geometry, analytic geometry, vectors, and transformation of figures. Topics to foster spatial sense are included at the elementary level. Students start to learn formal deduction related to congruence of two triangles at Grade 8, and properties and relations on quadrilaterals and circles are taught with their proofs at grade 9. Geometry in senior high school focuses on coordinates methods, transformation, and vectors. Geometry still maintains its former central position in school curricula in Korea. According to previous international studies, Korean students’ average performance in geometry is in top class. For most Korean math teachers, proof means a formal deduction and a tool for verification. Deductive system in school, however, is not so rigorous, and any topics on non-Euclidean geometry including spherical triangles are completely excluded in the secondary school math curriculum. Although demonstration with DGS is shown in textbooks, DGS is used by few teachers in teaching practice.

The purpose of this study is to introduce the practice of teaching and learning mathematics in South Korea. We describe the content of the “probability and statistics” strand of the national curriculum at the elementary school level and examine some of its problems. To address them, we modify a fourth-grade unit titled, “Broken Line Graph” with the theme, “Students Understanding Themselves”. In this unit, students collect their height and weight measures, organize and represent data, and project their height and weight into the future. These lessons demonstrate students’ abilities to investigate the posed problems, communicate ideas, summarize and interpret their findings, and reflect upon the project.

Korean mathematics education is based on authorized textbooks which are developed in accordance with the national curriculum. Teaching and learning practices of problem solving in mathematics classrooms, in this chapter, is investigated through the national curriculum and authorized textbooks and workbooks. Students’ problem solving abilities are cultivated through learning and practice of various problem solving strategies that permeate all school mathematics. Polya’s four problem solving stages and problem posing are also emphasized. In elementary mathematics classes, problem solving is taught in separate units whereas it is integrated into overall content areas in secondary mathematics classes.

In Korea, assessment is highly attended by educators as well as students and parents. Such attention influences the improvement of a test item year after year, which leads to the students’ high level of thinking and high achievement. In this chapter, we look at the assessment in Korea in three different levels; nationwide assessment, local (province/metro) area assessment, and assessment in a unit school. The nationwide assessment is planed, administered, and analyzed by the nation. College Scholastic Ability Test (CSAT), National Assessment of Educational Achievement (NAEA), and High School Entrance Test (HSET) are categorized in this level. There are assessments planned and administered by a local province/metro education office, for example, Subject Aptitude Examination (SAE) for 3rd, 4th, 5th and 7th, 8th grades, and Scholastic Ability Test (SAT) for 10th, 11th, and 12 grades. The school-wide assessment is planed, set, administered, and analyzed by a unit school; students take usually four times a year in a regular time span.

The assessment process in mathematics classes is closely related with teaching and learning process, and gives meaningful information to improve students’ mathematical powers. So many researchers have interested in theories and practices of mathematics assessment at the various levels (national level, province level, school level etc.). In this study we analyze Korean national mathematics curriculum, mathematics textbooks, articles, monographs, and reports concerned with mathematics assessment. So we describe the assessment in mathematics national curriculum, the expertise required of student assessments by mathematics teacher in classes, the reality of the process and assessment of mathematics classes.

The state administered university entrance exam, called the College Scholastic Ability Test, is the most competitive test in Korea. The items of it are developed complying with the national curriculum. Two types of mathematics test are provided for students to choose one according to the subjects they learned at high school and to their future careers. In this chapter, the structure of the test, purposes and characteristics of it, and exemplary items are investigated.