• Research in Mathematical Education
• /
• v.1 no.1
• /
• pp.1-5
• /
• 1997

We discuss some aspects of mathematics for teachers such as algebra for teachers, geometry for teachers, statistics for teachers, etc., which can be taught in teacher preparation courses. Mathematics for teachers should consider the followings: (a) Various solutions for a problem, (b) The dynamics of a problem introduced by change of condition, (c) Relationship of mathematics to real life, (d) Mathematics history and historical issues, (e) The difference between pure mathematics and pedagogical mathematics, (f) Understanding of the theoretical backgrounds, and (g) Understanding advanced mathematics.

• School Mathematics
• /
• v.12 no.3
• /
• pp.371-388
• /
• 2010

The goals of this study are to inquire middle school students' understanding about prime number and to propose pedagogical implications for school mathematics. Written questionnaire were given to 198 Korean seventh graders who had just finished learning about prime number and prime factorization and then 20 students participated in individual interviews for member checks. In defining prime and composite numbers, the students focused on distinguishing one from another by numbering of factors of agiven natural number. However, they hardly recognize the mathematical connection between prime and composite numbers related on the multiplicative structure of natural number. This study suggests that it is needed to emphasize the conceptual relationship between divisibility and prime decomposition and the prime numbers as the multiplicative building blocks of natural numbers based on the Fundamental Theorem of Arithmetic.

• The Mathematical Education
• /
• v.49 no.4
• /
• pp.437-462
• /
• 2010

The purpose of this research is to analyze the textbook contents about the natural number concepts in the Korean National Elementary Mathematics Curriculum. Understanding a concept of natural number is crucial in school mathematics curriculum planning, since elementary students start their basic learning with natural number system. The concepts of natural number have various meaning from the perspectives of pedagogical research, and the philosophy of mathematics. The natural number concepts in the elementary math curriculum consist of four aspects; counting numbers, cardinal numbers, ordinal numbers, and measuring numbers. Two research questions are addressed; (1) How are the natural number concepts focusing on counting, cardinal, ordinal, measuring numbers are covered in the national math curriculum? ; (2) What suggestions can be made to enhance the teaching and learning about the natural number concepts? Findings reveal that (1) the national mathematics curriculum properly reflects four aspects of natural number concepts, as the curriculum covers 50% of the cardinal number system; (2) In the aspect of the counting number, we hope to add the meaning about 'one, two, three, ......, and so on' in the Korean Mathematics curriculum. In the ordinal number, we want to be rich the related meaning in a set. Further suggestions are made for future research to include them ensuing number in the curriculum.

• School Mathematics
• /
• v.9 no.2
• /
• pp.291-312
• /
• 2007

As a result of observing the 10-th grade text books on mathematics now in use which show the way of introducing complex numbers for the first time, it is easy to see all the text books on mathematics use a quadratic equation $x^2+1=0$ for a new number i. However, Since using the new number i is artificial, this make students get confused in understanding the way of introducing complex numbers. And students who have problems with the quadratic equation can also have difficulty in understanding complex numbers. On the other hand, by using a coordinate plane with ordered pairs and arrows, students can understand complex numbers better because the number system can be extended systematically through intuitive methods. The problem is that how to bring and use ordered pairs and arrows to introduce complex numbers in highschool mathematics. To solve this problem, in this study, We developed a systematic and visible learning contents which make it possible to study the process of the step-by-step extension of number system that will be applied through elementary and middle school curriculum and all the way up to the introduction of complex numbers. After having applied the developed learning contents to the teaching and learning procedure, we can know that the developed learning contents are more efficient than the contents used in the text books on mathematics now in use.

• Journal of Educational Research in Mathematics
• /
• v.27 no.3
• /
• pp.351-373
• /
• 2017

The meanings of division don't change and rather are connected from whole numbers to rational numbers. In this respect, connecting division of natural numbers, division of fractions, and division of decimal numbers could help for students to study division in meaningful ways. Against this background, the units of division of fractions and division of decimal numbers in fifth grade were redesigned in a way for students to connect meanings of division and procedures of division. The results showed that most students were able to understand the division meanings and build correct expressions. In addition, the students were able to make appropriate division situations when given only division expressions. On the other hand, some students had difficulties in understanding division situations with fractions or decimal numbers and tended to use specific procedures without applying diverse principles. This study is expected to suggest implications for how to connect division throughout mathematics in elementary school.

• The Mathematical Education
• /
• v.51 no.1
• /
• pp.1-19
• /
• 2012

In this study, contents of 'the 2007 revised curriculum handbook' and 16 kinds of mathematics textbooks were analyzed first. The purpose of this study is to examine the understanding state of students at general high schools by making questionnaires to survey the understanding state on contents of chapter of complex number based on above analysis. Results of research can be summarized as follows. First, the content of chapter of complex number in textbook was not logically organized. In the introduction of imaginary number unit, two kinds of marks were presented without any reason and it has led to two kinds of notation of negative square root. There was no explanation of difference between delimiter symbol and operator symbol at all. The concepts were presented as definition without logical explanations. Second, students who learned with textbook in which problems were pointed out above did not have concept of complex number for granted, and recognized it as expansion of operation of set of real numbers. It meant that they were confused of operation of complex numbers and did not form the image about number system itself of complex number. Implications from this study can be obtained as follows. First, as we came over to the 7th curriculum, the contents of chapter of complex number were too abbreviated to have the logical configuration of chapter in order to remove the burden for learning. Therefore, the quantitative expansion and logical configuration fit to the level for high school students corresponding to the formal operating stage are required for correct configuration of contents of chapter. Second, teachers realize the importance of chapter of complex number and reconstruct the contents of chapter to let students think conceptually and logically.

• 한국정보교육학회:학술대회논문집
• /
• 2010.08a
• /
• pp.67-73
• /
• 2010

In information and communications society, the numbers of elementary students who violate copyright law have been growing due to lack of understanding so they are needed to be educated on copyright. However, current education only has focused on copyright infringement, few numbers of educations have instructed copyright oriented examples linked to regular curriculum. Therefore, the purpose of this study is to grow elementary students's understanding of copyright and find new ways of education through designed copyright education program oriented regular curriculum.

• Journal of Korean Medical classics
• /
• v.30 no.4
• /
• pp.49-67
• /
• 2017

Objective : Heavenly stems and Earthly branches is a tool used for understanding the virtue of Yin Yang and Five elements. Korean medicine understands the changes in Wuyun through the Ten Heavenly stems, and understand the changes of Liuqi through the Twelve Earthly branches. An accurate understanding of the definitions of Heavenly Stems and Earthly branches and the concept of each of the 10 stems is of vital importance. Method : The paper first reviews the origin, history, and significance of the Heavenly stems and Earthly branches before studying the definitions of the stems and branches as laid out in the works of Yu Onseo, Lee Samun, and Han Dongseok. The paper then reviewed the concept of the each of the ten stems through researching the texts of Seoulmunhaeja, the annotations of the four great Seolmuns, and the texts of Jeongyeokwonui. Result & Conclusion : Heavenly stems and Earthly branches have been in use since more than 6,000 years ago. The central numbers in the changes of Heaven and Earth are five and six. Each number functions with duality, yin and yang, meaning there are ten Heavenly numbers ($5{\times}2=10$) and 12 Earthly numbers ($6{\times}2=12$) which oversees all of the cosmic changes. Stems become the body and signifies water. Branches become the use and signifies divided fire. The meanings of the letters Gab Eul Byeong Jeong Mu Gi Gyeong Sin Im Gye originate from the one year life of a tree which grows, bears fruits, processes Yang qi, and awaits for the next spring. The reason a tree is used is because there is nothing better in studying in detail the changes of a living being through a year.

• The Mathematical Education
• /
• v.52 no.1
• /
• pp.97-109
• /
• 2013

Research in undergraduate mathematics education has been active very recently. The purpose of the paper is to investigate how college students make ion from some known informations about integer and rational numbers in algebra. Three college students were involved in the study. We analyze student's personal answers in order to find where their misunderstandings and difficulties come from based on the theoretical frameworks on mathematical understanding such as APOS-model and P-K-model. Finally we discuss about constructivist teaching ways for algebra and propose new paradigm for teaching undergraduate mathematics.

• School Mathematics
• /
• v.8 no.1
• /
• pp.1-25
• /
• 2006

To be good at numeration is an important matter in learning mathematics. Unlike the 6-th curriculum, integers are introduced in middle school curriculum for the first time in the 7-th curriculum. Therefore, to help the students team integers systematically and thoroughly, it is necessary that we allow more space for process of introduction, process of operations and practice of operations in the 7-th curriculum text book than that of 6-th curriculum text book. As specific and systemic visualized teaching of operation is especially important in building the concept of operation, by using visualized teaching methods, students can understand the process of operation more fully and systematically. Moreover, students become proficient in operation of positive number and negative numbers by expending this learning process of operations to the operations used absolute value. In 7-th grade mathematics, the expression of positive numbers and negative numbers visually are useful for understanding of operations for numbers. But it is not easy to do so. In this paper we use arrows(directed segments) to express positive numbers and negative numbers visually and apply them to perform the operations for numbers. Using arrows, we can extend the method used in elementary school mathematics to the methods for operations of positive numbers and negative number in 7-th grade mathematics. By experiments, we can know that such processes of introduction for operations are effective and this way helps teachers teach and students learn.