• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.375-394
• /
• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• Journal of Elementary Mathematics Education in Korea
• /
• v.15 no.1
• /
• pp.199-219
• /
• 2011

In this thesis, we designed a experimental learning-teaching plan of 'decimal fraction concept' at the 4-th grade level. We rest our plan on two basic premises. One is the fact that a essential concept of decimal fraction is 'polynomial of which indeterminate is 10', and another is the fact that the origin of decimal fraction is successive measurement activities which improving accuracy through decimal partition of measuring unit. The main features of our experimental learning-teaching plan is as follows. Firstly, students can experience a operation which generate decimal unit system through decimal partitioning of measuring unit. Secondly, the decimal fraction expansion will be initially introduced and the complete representation of decimal fraction according to positional notation will follow. Thirdly, such various interpretations of decimal fraction as 3.751m, 3m+7dm+5cm+1mm, $(3+\frac{7}{10}+\frac{5}{100}+\frac{1}{1000})m$ and $\frac{3751}{1000}m$ will be handled. Fourthly, decimal fraction will not be introduced with 'unit decimal fraction' such as 0.1, 0.01, 0.001, ${\cdots}$ but with 'natural number+decimal fraction' such as 2.345. Fifthly, we arranged a numeration activity ruled by random unit system previous to formal representation ruled by decimal positional notation. A experimental learning-teaching plan which presented in this thesis must be examined through teaching experiment. It is necessary to successive research for this task.

• School Mathematics
• /
• v.13 no.2
• /
• pp.267-286
• /
• 2011

In this paper I investigated the historical developments of the algorithms for multiplication of natural numbers. Through this analysis I tried to describe more concretely what is to understand the common algorithm for multiplication of natural numbers. I found that decomposing dividends and divisors into small numbers and multiplying these numbers is the main strategy for carrying out multiplication of large numbers, and two decomposing and multiplying processes are very important in the algorithms for multiplication. Finally I proposed some implications based on these analysis.

• Journal of Elementary Mathematics Education in Korea
• /
• v.18 no.1
• /
• pp.37-62
• /
• 2014

In this thesis, we inquire into teaching method of decimal fraction concept in elementary mathematics education based on measurement activity. For this purpose, our research tasks are as follows: First, we design a experimental learning-teaching plan of 'decimal fraction' unit in 4th grade textbook and verify its effect. Second, after teaching experiment using experimental learning-teaching plan, we analyze the student's status of understanding about decimal fraction concept. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results. First, introduction of decimal fraction based on measurement activity promotes student's understanding of measuring number and decimal notation. Second, operator concept of decimal fraction is widely used in daily life. Its usage is suitable for elementary mathematics education within the decimal notation system. Third, a teaching method of times concepts using place value expansion of decimal fraction is more meaningful and has less possibility of misunderstanding than mechanical shift of decimal point. Fourth, teaching decimal fraction through the decimal expansion helps students with understanding of digit 0 contained in decimal fraction, comparing of size and place value. Fifth, students have difficulties in understanding conversion process of decimal fraction into decimal notation system using measurement activity. It can be done easily when fraction is used. However, that is breach to curriculum. It is necessary to succeed research for this.

• Journal of Elementary Mathematics Education in Korea
• /
• v.20 no.2
• /
• pp.193-213
• /
• 2016

This study has two goals. The First is to develop and apply a step-by-step program and the degree to which students' mathematical skills. The second is to analyze mathematical attitude change around the first grade students was done. The program for learning complement number is composed of series of 5 steps and 11 classes. Play for learning complement number, taking into account the difficulty of the learning steps 1-5 are organized. First step is composed of the classes which fragmented pieces of shapes to complete the entire geometry with fun activities for the entire part of the concept of learning and it maintenance concepts and can naturally learn by associating step. In second step, tools to take advantage of the real world and collecting the conservative concept. 3rd steps is to repair the mathematical concept of the parish in the learning stage of expansion. 4th step is halrigalri, number cards, making ten games etc. 5th step is to verify the concept of complement number and number operation ability. The concept of complement number through fun activities can improve students' mathematical skills, and mathematical attitude change. Early in the program, students use the finger to throw acid in the process. Simple addition and subtraction calculations may take a long time and error, but more and more we progress through the program using the fingers is eliminated and a more complex form calculations was not difficult to act out.