Department of Mathematics Education

Introduction

The department aims at providing an academic background for students pursuing careers in teaching mathematics. We prepare highly capable prospective secondary school teachers by training them to have knowledge of mathematics and teaching skills. The detailed objectives are to prepare:

1. Well-trained professionals who have a wide scientific knowledge in the various fields of mathematics
2. Innovative professionals who have systematic teaching abilities by training them in logical and analytical thinking
3. Excellent professionals who can conduct independent research in Mathematics Education.

This department also supervises and sponsors the Research Association of Mathematics Education and Technology (RAMET). This creates a great variety of output to be utilized in Engineering Education for Mathematics with initiatives to develop instruction methods and to introduce innovative approaches to teaching mathematics at secondary school level.

Currently, the department has five outstanding professors who majored in Analysis, Algebra, Geometry, and Mathematics Education. They provide advanced theoretical and practical knowledge in these diverse fields of mathematics, leading students to become accomplished experts.

History

The Department of Mathematics Education was established in October 1981 and the current yearly enrollment is 30. Since our first graduation in 1986, we have been continuously preparing competent secondary school math teachers and over 600 have graduated as of now. Most graduates are working as math teachers in public and private secondary schools, as research fellows, or as professionals in the corporate sector.

Job Prospects

Most of our graduates are teachers at secondary school level. They have found employment all across the nation, including Daegu, Ulsan, Incheon, Gyeongbuk, and Gyeonggi. Some have completed graduated school and are working as professors while others are employed at research institutes and business corporations.

The strength of the department is that many well-educated graduates have passed the teacher certification examination. In 2012, fifteen students passed the national examination for public middle schools and high schools and six students became teachers at private secondary schools. One student who graduated from our department in 2011 recorded the highest national examination score in the Daegu school district. Our graduates are skilled teachers whose expertise is based on in-depth mathematical knowledge and a passion for student guidance.

Faculty

Jin Hwan Kim, Professor

- Yeungnam Univ., Geometry
kimjh@ynu.ac.kr
Park Sun Yong, Professor

- Seoul National Univ., mathematics education
polya@yu.ac.kr
Cho,Cheong-Soo, Professor

- Oregon State Univ. , Mathematics Education
chocs@ynu.ac.kr
Choi, Youngook, Professor

- Univ. of California at Riverside, Algebra
ychoi824@yu.ac.kr

※ sorted by the position and Korean name

Curriculum

Curriculum
1-1	CALCULUS I Calculus(1) covers the following: Sequences, limits and continuity of functions of single variable, derivatives, properties of derivatives, differentiation rules, higher order derivatives, applications of derivatives, definite integrals, indefinite integrals, properties of integrals, integration rules, applications of integrals, infinite series power series.
1-1	SEMINAR FOR ACADEMIC LIFE 1. Summary of the course This course is to assist university freshmen in CRM designing to adapt university life well through the instruction and counselling of supervising professor. (This course is composed of self analysis, personality type test, career research, instruction for the success of university life, career plan and direction setting, CRM designing method and CRM designing. The course should be teaching in classes of the students by supervising professor.) 2. Course objectives This course is to motivate the students before the mid term exam and provide students with self analysis, personality type test (MBTI or TCI) and career research (YAT test). Also, this course shall has a plan to instruct the students to enhance the efficiency of university life through career and time management. In addition, this course is to make a chance for the students to have practical assistance to university life by providing study method, report designing strategy and the information on academic system and various kinds of internal programs of the university. After the mid term exam, the students will be instructed to set the direction of career designing through continuous counselling of supervising professor and the students will be able to establish CRM designing and execution plan.
1-1	SOFTWARE AND AI Software and AI (Artificial Intelligence) course aims to educate the basic concepts of software and computational thinking to use them in various applications. It allows students of various majors to experience the core technologies of the 4th industrial revolution, such as big data, machine learning, and AI. It also introduces various applications of AI so that students can easily apply these technologies to their field of study. This course classifies the lecture types into three categories, and adjust the lecture difficulty according to the student's academic ability.
1-1	STATISTICS(1) This course defines events and probabilities, conditional probabilities and independence to evaluate probabilities. Elementary probability distributions such as binomial distribution, geometric distribution, Poisson distribution, and normal distribution are also introduced. The concepts of sample distribution of the statistic and the central limit theorem are introduced. The statistical inference including estimation and hypothesis testing of the mean and the standard deviation will be discussed.
1-1	INTRODUCTION TO EDUCATION This course is an introductory course in Education for prospective teachers, regardless of their major and/or special subjects. This is one of the necessary requirements for teacher candidates being educated in colleges other than the college of education in Korea. The course is to study the various paradigms and concepts of education, representing different views on aim, content and method of education. A particular emphasis is given to identifying theoretical questions of education in order to grasp the problems of Korean education and find out their solutions.
1-2	CALCULUS II Calculus(2) covers the following: vector valued functions, curves in spaces, limits and continuity of functions of multi variables, partial derivatives, properties of partial derivatives, partial differentiation rules, higher order partial derivatives, applications of partial derivatives, double and triple integrals, properties of multiple integrals, applications of multiple integrals, line integrals, Green's theorem, surface integrals, Stokes' theorem, divergence theorem.
1-2	COMMUNICATION SKILL The ability to communicate effectively in speaking and writing is one of the most important skills for educational and career success. This course gives students opportunities to discuss, practice, and eventually master the skills involved in oral and written communication. The topics include theory and practice of effective communication, making speeches, presentation skills, principles of persuasion, and writing skills.
1-2	KOREAN HISTORY This lecture treats total Korean history internationally and help Koreans to have necessary knowledge and to establish their own identity in order to play in a global socity. This lecture is formed to assist people who study history for entering various government's organizations and large companies or Korean history cerification test.
1-2	SOCIAL CONTRIBUTION AND SERVICE This course is to cultivate community sense as members of society and the global village for students in order to develop the basic knowledge required as global citizens. Especially, this course is to foster the spirit of cooperation, sharing, service, and creativity and study the social contribution and leadership to solving the challenges the global community faces. As a liberal arts course, it is centered to nurture a leader having the global capability to contribute to community development through learning the knowledge and the case on the value & logic of social responsibility focused on environmental preservation, social contribution, and good governance(ESG). This course aims to foster a generous mind, learn knowledge and technology and build the capacity to contribute to building a society towards a safer and happier world through the study of theory and practice.
1-2	DATA SCIENCES AND STATISTICS EDUCATION In line with the era of big data, this subject improves the statistical knowledge necessary for pre-service teachers. By addressing Bayesian statistics as well as traditional descriptive statistics and exploratory data analysis, this subject deals with stochastic updating processes based on the accumulation of data and information. In addition, these entire contents are related to statistical education in secondary schools. Specifically, conditional probabilities and distributions, Bayesian theorem and probability distributions, Bayesian paradigms, and inference will be dealt with.
1-2	SET THEORY Set theory treats the classes and sets, functions, relations, partially ordered sets, the Axiom of choice and related equivalent principles, and cardinalities of sets and the natural number.

Curriculum
2-1	DIGITAL EDUCATION This course addresses the understanding and practice of digital and Al education that future pre-service teachers must know, by learning the concepts and principles of digital and Al, and the reflective and critical perspective on the proper use and ethical practice of digital and Al technologies. This course also focuses on expanding digital and Al experiences in the educational field by understanding the concept of digital and Al convergence and ut1l1zation education that can enhance the effectiveness of education and by encountering related cases.
2-1	EDUCATIONAL ADMINISTRATION & MANAGEMENT This course is an introductory course in the Educational Administration and School Management for prospective teachers. This is one of the necessary requirements for teacher candidates being educated in colleges other than the college of education. The course is to study the classical organizational thoughts in relation to education, definitions, basic concepts, and hypotheses regarding educational administration, major tasks and process of educational administration, and theories of administrative behaviors, and to understand the school and classroom management.
2-1	PREVENTION OF SCHOOL VIOLENCE AND UNDERSTANDING OF SCHOOL CULTURE Students will acquire an understanding of the various factors, actual state, the legislative system of school violence. Students will have an opportunity to relate this knowledge about prevention and measures of school violence to school environment using students guidance, parents interview, and human lights education. This information about violence behavior, student cultures, counseling methods, and the implications that social and contemporary legislative policies play will create greater understanding in the field of school violence.
2-1	ARTIFICIAL INTELLIGENCE AND MATHEMATICS Using various cases dealt with mathematics in artificial intelligence, the purpose of this course is to develop the ability of preservice math teachers for mathematical representations, data classification and prediction, and reasonable decision making through optimization. Also this course puts emphasis on developing the ability of reasoning and communication in mathematically, STEAM thinking and information processing in the 4th industrial revolution.
2-1	INTRODUCTION TO ANALYSIS This course is intended for students to tool, modern analysis as relates to further study in mathematics. We treat real numbers, limit, sequences and series, continuity, differential, uniform convergence, open sets and closed sets.
2-1	NUMBER THEORY In this course we deal with the factorization of integers, congruences, properties of polynomials and solving polynomial congruences, divisibility, greatest common divisors, quadratic residues, prime numbers, divisors and arithmetic functions.
2-1	LINEAR ALGEBRA Linear algebra is an important subject in mathematics and has a variable applications in both engineering and social science. This course introduces vector spaces, bases, linear transformations and to help the student to apply their knowledges in various areas.
2-1	LOGIC AND ESSAY WRITING IN MATHEMATICAL EDUCATION The purpose of this course is to develop and enhance student's writing ability on mathematically logical statements with mathematical contents and materials. In this course, students discuss a given specific topic and write in logical and persuasive while reading materials about algebra, analysis, geometry, probability and statistics, history of mathematics, and modern mathematics and its development.
2-2	EDUCATIONAL PSYCHOLOGY This course is an introductory course in the Educational Psychology for prospective teachers being educated in colleges other than the college of education in Korea. It is an undergraduate course to help prospective teachers understand the basic principles of psychological processes involved in the various aspects of educational practices. It includes learner? characteristics, educational environment, learning and instruction, and evaluation of instructional outcomes.
2-2	EDUCATIONAL SOCIOLOGY This course is an introductory course in the Sociology of Education for prospective teachers being educated in colleges other than the college of education in Korea. This is one of the necessary requirements for teacher candidates. An emphasis is given to the understanding of basic concepts and theories in the field.
2-2	GUIDANCE This course is a study of fundamental philosophies, knowledge, and techniques for guiding adolescents toward their better lives. It is to study the practical considerations for the growth of adolescents affective, humanistic domains. A course designed to learn foundational concepts, major principles, major treatment of guidance and counseling, and to discuss its theoretical and practical implications. Emphasis is placed on providing theoretical foundations to deal with human problems through educational counseling, and to pursue counseling theories, practical processes, and techniques.
2-2	INSTRUCTION AND LEARNING OF DISCRETE MATHEMATICS In this course, students build mathematical models for finite or discontinuous discrete situations and develop their ability to handle them logically and creatively, Also we understand the characteristics of the discipline of discrete mathematics and explore instructional principles.
2-2	INTRODUCTION TO FOUNDATIONS OF MATHEMATICS EDUCATION Provides the foundational knowledge of mathematics education by studying the nature and historical development of mathematics, learning psychology of mathematics, various instructional strategies, assessment and evaluation techniques, and technology for school mathematics for the prospective teachers.
2-2	LINEAR ALGEBRA AND SECONDARY SCHOOL MATHEMATICS This course is a continuation of linear algebra course. It deals with inner product space, eigenvalues, and eigenvectors and its related theorems, such as Cauchy-Schwarz inequality and Gram-Schmidt theorem. Also, in this course, we discuss about the diagonalization of a matrix and prove that a symmetric matrix is always orthogonal similar to a diagonal matrix. As an application of this theorem, students have a deep insight on the quadratic curves, i.e. circle, elliptic curve, parabola, and hyperbola. Also, through this course, students have an easy solution for the maximum and minimum value of quadratic forms, which is very important problemsin high school.
2-2	TECHNOLOGY AND SECONDARY SCHOOL MATHEMATICS In order to prepare for the future society based on artificial intelligence and big data, teaching and learning of secondary school mathematics will use various engineering tools (Computer Algebra calculator, GeoGebra) and coding language (Python). For this purpose, it is a practice-oriented course that uses engineering tools to learn mathematics in order to cultivate fluency.
2-2	REAL ANALYSIS AND SECONDARY SCHOOL MATHEMATICS EDUCATION Analysis and Mathematics in School aims at developing pre-service teachers’ pedagogical content knowledge in addition to enhancing their literacy for analysis. This course consistently deals with the didactic transposition between real analysis and secondary school mathematics.

Curriculum
3-1	EDUCATIONAL METHODS & TECHNOLOGY This course is an introductory course in the Teaching Method and Educational Technology for prospective teachers. This is one of the necessary requirements for teacher candidates being educated technology course for the subject matter oriented education students. A general information of the field, theory, and profession of instructional technology will be introduced. The definition of instructional technology, the history of the field, and the current trends and issues in the area will be investigated. Students develop competencies in appling media and technologies to instruction. This course emphasize the method of instruction as well as educational technology.
3-1	EDUCATIONAL PHILOSOPHY & HISTORY This course in one of the necessary requirements for teacher candidates being educated in colleges other than the College of Education in Korea. Hence, its main purpose lies in the introduction to the general history and philosophy of education both in the East and in the West from the ancient to the modern ages. Historical development of educational system, philosophical thoughts of education, and their influences and implications to our modern education are to be understood.
3-1	INTRODUCTION TO SPECIAL EDUCATION This lecture is for leading students in the field of education to effective education with which students(pre-teachers) can better understand and perform the integrating education. Therefore this lecture aims to train students(pre-teachers) to develop an ability of understanding students with disabilities and of performing integrating education.
3-1	COMPLEX ANALYSIS In this course, the main aim is to study the continuity series expansion, analyticity and integration for complex variable functions defined on complex plane from those concepts for real variable functions.
3-1	INTRODUCTION TO DIFFERENTIAL GEOMETRY The first course in differential geometry. This course explores tangent vectors, directional derivatives and covarient derivatives, isometries on Euclidean space, the theory of space curves, and then explores surface concept and various examples of surfaces.
3-1	INTRODUCTION TO GENERAL TOPOLOGY Topolgical structure of R^n, definition of topology, base, subbase, neighborhood, derived set, continuous functions, homeomorphisms and metrics spaces.
3-1	MODERN ALGEBRA This course is intended for students to learn the fundamental concepts of group theory. We deal with several kinds of group-cylic group, symmetric group and factor group and then we study the group homomorphisms between groups. From this course, you will get the Fundamental theorem of finitely generated Abelian group, and three isomorphis theorems of groups.
3-1	PEDAGOGY FOR TEACHING SECONDARY SCHOOL MATHEMATICS This course is to focus on learning a variety of teaching methods and strategies for effective instruction in secondary school mathematics and analyzing various contents in mathematics textbook. In addition, students will practice and apply various theories in mathematics education though teaching practicum.
3-2	ACTUAL AFFAIRS FOR TEACHING PROFESSION This course is for future teacher to understand actual affairs for teaching profession such as classroom management, teaching technique, guidance and counselling, processing official documents, etc.
3-2	EDUCATIONAL CURRICULUM This course emphasizes on general principles and procedures of construction, development and evaluation of school curriculum. Students are expected to develop a sense of reality with regard to the actual curriculum implementation in elementary and secondary schools.
3-2	EDUCATIONAL EVALUATION This course emphases on the relations between school learning and appropriate types of evaluation. It includes theories of reliability and validity, achievement test construction, and interpretation of test results. Introduction to modern theories of measurement techniques and instruments for cognitive, affective and psycho-motor domain; practical introduction to the techniques of tests, such as construction of tests, scoring, reliability, validity, and item analysis.
3-2	ABSTRACT ALGEBRA In this course, we discuss on the basic ring theory and field extension theory. First, it deals with the irreducibility of the polynomials over a given field and then we learn aobut the algebraic extension, finite fields.
3-2	CURRICULUM AND EVALUATION OF SCHOOL MATHEMATICS Students will study various theories of curriculum development and learn the course of school mathematics curriculum and the directions and the views of curriculum of foreign countries. Students will learn the theories of alternative assessments and apply various assessment methods and procedures to secondary school mathematics classroom.
3-2	TOPICS IN COMPLEX ANALYSIS In this course, we study Cauchy's theorem, residue theorem, Liouville's theorem, Rouch's theorem, maximum modulus theorem.
3-2	DIFFERENTIAL GEOMETRY This subject continues introduction to differential geometry. This course examines theory of surfaces in Euclidean space, it will contain as follows : properties of surfaces, shape operators, various curvatures, compact surfaces and Euler characteristics, geodesics and Gauss Bonnet theorem.
3-2	GENERAL TOPOLOGY As an extended course of Introduction to General Topology, this course is intended for students to learn concepts of topological property. We treat countability axioms, separation axioms, Urysohn's lemma, compactness, connectness, product spaces and quotient spaces.

Curriculum
4-1	SCHOOL FIELD PRACTICE School field practice is a field education subject where students actually experience the roles and functions that teachers must perform in the secondary school. In this course,students can develop their preparatory skills as a teacher by accumulating practical experiences on overall school education such as teaching - learning guidance, life guidance, class management and so on through experiences in the field of education.
4-1	MODERN ALGEBRA AND MATHEMATICAL MODELLING Modern Algebra and Mathematical Modelling aims at developing pre-service mathematics teachers’ pedagogical content knowledge of Modern algebra their mathematical modelling competence using that knowledge in various situations. In this course, we deals with special rings-unique factorization domain and Euclidean domain- and then introduce the Galois group of a field extension. You can learn about splitting field, separability, and automorphism group of a field extension and finally you can get the Galois theorem. Also, we learn how to do modelling several real life problems in the real phenomenon into algebraic equations and try to get solutions of these equations.
4-1	SEMINAR IN MATHEMATICS EDUCATION This course aims at developing pre-service teachers’ mathematical problem solving ability and their teaching competence. Also, this course focuses on connecting mathematical knowledge with the content of secondary school mathematics. We develop the pedagogical content knowledge for secondary mathematics teachers through active problem solving in various virtual classroom situation.
4-1	TEACHING GEOMETRY This course examines the geometry learned as academic mathematics. deal with geometric concepts treated in secondary school mathematics and its backgrounds. Students cultivate subject matter and pedagogical knowledge for geometry as a teacher’s literacy.
4-1	TOPICS IN ANALYSIS This course aims at developing pre-service mathematics teachers’ pedagogical content knowledge of high level calculus and their mathematical modelling competence using that knowledge in various situations. This course deals with the convergency of series of functions, uniformly convergency of power series, term by term integration and differentiation, the Taylor series and so on. At the same time, we learn the mathematical modelling activity such as ‘propagation of heat in solid bodies’ by linking theses theories with the real phenomenon.
4-1	THEORY OF TEACHING SCHOOL MATHEMATICS Provides actual teaching experience of the topics in secondary school mathematics by integrating contents and pedagogical knowledge in mathematics. Students will have opportunities for analysis and discussion of the teaching behaviors using video equipments. Development of practical knowledge of teaching mathematics in analyzing the classrooms of experienced mathematics teachers.
4-2	TOPICS IN ALGEBRA This course introduce some topics related with group theory and field theory. Especially, we learn about the Sylow theorem, its applications and the free abelian groups and then we deal with the insolvability of the quintic polynomials and the constructibility of regular n-polygons.
4-2	PROBABILITY & STATISTICS Distribution of random variable, density function, moment generating function, some special distribution, distribution of functions of random variables, distribution of order Statistics, limiting distributions, Estimation, sufficiency statistic, Cramer-Rao lower bound, Bayes Estimation, confidence intervals, hypotheses testing, uniformly most powerful tests, likelihoods ratio test, chisquare tests, nonparametric tests.
4-1,2	EDUCATIONAL VOLUNTEER ACTIVITIES This subject includes acting as assistant teachers in kindergartens or primary and middle schools, acting as teachers' helpers, or conducting volunteer work. The goal of the course is to help future educators foster the development of educational attainments.

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