백정환 Jung Hwan Baek , 고상숙 Sang Sook Koh

DOI: JANT Vol.50(No.3) 263-284, 2011

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We took note of the fact that there were not many studies on improvement of mathematics learning in the field of statistics for the minority students from the families who belonged to the Low-SES. This study was to help them understand the concepts and principles of mathematics, motivate them for mathematics learning, and have them feel familiar with it. The subjects were 12 students from the low-SES families among the sophomores of 00 High School in Gyeonggi-do. Although it could not be achieved effectively in the short-term of learning for the slow learners, their understanding of basic concepts and confidence, interests and concerns in statistical learning were remarkably changed, compared to their work in the beginning period. Our discourse classes using various topics and examples were well perceived by the students whose performance was improved up to the 3rd thinking level of Mooney`s framework. Also, a meaningful instructional model for slow learners(IMSL) was found through the discourse.

박선영 Seon Yeong Park , 김원경 Won Kyoung Kim

DOI: JANT Vol.50(No.3) 285-308, 2011

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The objective of this study is to review how researches on mathematics education are being conducted currently in Korea and overseas and to examine the current state of domestic researches on mathematics education from a broader view. Although many efforts have been made to understand trends in researches on mathematics education, there have been few in -depth studies on research trends in overseas or for comparison between domestic and overseas trends. Thus, this study classified and analyzed 181 domestic articles between 2005 and 2009 in the journals and and 201 overseas articles in the journals and according to year, research area, research contents, school level, research method, and key words using the PME classification system with some modification. Through these analysis, we examined research trends on secondary mathematics education in Korea and overseas. The research findings are as follows. First, "teaching-learning process" was a spotlight area both at home and overseas, and "realistic mathematics" and "social-cultural subjects" were not covered much either at home or overseas. "Mathematical communication" occupied a very small portion in Korea but was a highly interesting area in overseas research. Second, research contents of interest were different between Korea and overseas. Research on general area was the mainstream. But geometry and statistics were mainly studied in Korea and algebra and analysis in overseas. Third, research related to middle school was twice more than that related to high school in Korea, But, research related to middle school was the same as high school in overseas. Fourth, qualitative research was the absolute majority both at home and overseas, and philosophical didactical analysis was used only in Korea. Fifth, the order of key words were problem solving - teacher - curriculum - creativity - textbook in Korea, but teacher - teaching - semiotic - affective factor - proo f- problem solving - technology in overseas.

김창수 Chang Su Kim , 전영배 Young Bae Jun , 노은환 Eun Hwan Roh

DOI: JANT Vol.50(No.3) 309-327, 2011

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In this paper, we extended the division algorithm for the integers to the finite decimals. Though the remainder for the finite decimals is able to be defined as various ways, the remainder could be defined as ``the remained amount`` which is the result of the division and as 『the remainder』 only if ``the remained amount`` is decided uniquely by certain conditions. From the definition of 『the remainder』 for the finite decimal, it could be inferred that ``the division by equal part`` and ``the division into equal parts`` are proper for the division of the finite decimal concerned with the definition of 『the remainder』. The finite decimal, based on the unit of measure, seemed to make it possible for us to think 『the remainder』 both ways: 1) in the division by equal part when the quotient is the discrete amount, and 2) in the division into equal parts when the quotient is not only the discrete amount but also the continuous amount. In this division context, it could be said that the remainder for finite decimal must have the meaning of the justice and the completeness as well. The theorem of the division algorithm for the finite decimal could be accomplished, based on both the unit of measure of 『the remainder』, and those of the divisor and the dividend. In this paper, the meaning of the division algorithm for the finite decimal was investigated, it is concluded that this theory make it easy to find the remainder in the usual unit as well as in the unusual unit of measure.

김성숙 Sung Sook Kim , 강미경 Mee Kyung Khang

DOI: JANT Vol.50(No.3) 329-335, 2011

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There has been an ongoing symbiotic relationship between the history of the International Commission on Mathematical Instruction(ICMI) and the broader history of mathematics education since 1908. Similarly, the International Congress on Mathematical Education(ICME) has played an important role in the direction of Mathematics education since its first congress in 1969. ICME-12 is due to be held in Seoul, Korea from July 8th to 15th 2012. To date, there has been no research paper concerning the history of the ICMI published in any Korean journal. In readiness for the upcoming ICME-12, this paper aims to provide a comprehensive overview of the history of the IMCI from the perspective of Mathematics education.

김경미 Kyung Mi Kim , 황우형 Woo Hyung Whang

DOI: JANT Vol.50(No.3) 337-354, 2011

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The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students` understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

강미광 Mee Kwang Kang

DOI: JANT Vol.50(No.3) 355-365, 2011

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The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students`s low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers` and students` understanding of radian.

김정하 Jeong Ha Kim

DOI: JANT Vol.50(No.3) 367-381, 2011

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It is important to concern about individual difference on every subject and every class. How can we know the individual difference? It is helpful for that to find out students` math learning style and learning type. In this paper, I conducted a survey to look for math learning style and math learning type of 4th, 5th and 6th grade students, and analyzed those data. The research findings are summarized as follows; First, 4th, 5th and 6th grade students prefer the visual learning style to the verbal style, and they have more wholistic tendency than analytical tendency in the domain of the cognitive learning style . Second, they prefer the authoritative and goal-oriented learning style to the practical and recreational learning style, and they have more interior-oriented than exterior-oriented in the domain of affective learning style. Third, the representative math learning type of 4th, 5th and 6th grade students is visual/holistic/authoritative and goal-oriented /interior-oriented. The math learning styles of students have a lot of influence on their learning, so that an appropriate teaching method for each student could arouse a maximum effect in the math study.

이승우 Seung Woo Lee

DOI: JANT Vol.50(No.3) 383-394, 2011

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This paper analyzes subjects related to Math/Stat and studies teaching effect on subject development connected Math/Stat in software curriculum. Among many subjects related to the software, this paper shows exemplary applications of Math/Stat in the software curriculum. Thereby this opens potential application fields of Math/Stat. This confirms that Math/Stat is not only an essential subject to improve competitiveness but also a strategic element in the field of software. Therefore, by maximizing the academic outcome through the interdisciplinary combination of software and Math/Stat, it is possible to educate more competitive and skilled professionals.