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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
> Journal Vol & Issue
The Mathematical Education
Journal Basic Information
Journal DOI :
Korea Society of Mathematical Education
Editor in Chief :
Volume & Issues
Volume 48, Issue 4 - Nov 2009
Volume 48, Issue 3 - Aug 2009
Volume 48, Issue 2 - May 2009
Volume 48, Issue 1 - Feb 2009
Selecting the target year
A case study on differentiated curriculum for the university calculus and the curriculum development using a numerical software
Choi, Enn-Jeong ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 213~234
College students have a diverse educational background with the recent multiplicity in university admissions standards and procedures. As a result, their mathematical preparation and performance varies widely. Teaching calculus to such a diverse student group is a demanding task. Differentiated curriculum has been conducted for the university calculus course in Yonsei university for the past five years. A case study on the differentiated curriculum in Yonsei university is presented for the curriculum improvement. With its ideal purpose, the differentiated curriculum has created issues and problems in practice. As an alternative to the ideal differentiated curriculum, this study shows that a computer-based approach using a numerical software could give aids to overcoming the difficulty of inadequately prepared students in the learning process while mathematically sophisticated students could keep interested in the course. This study also presents the useful topics in calculus that can be implemented for computer-based calculus education and provides guidelines for the effective usage.
The Impact of Children's Understanding of Fractions on Problem Solving
Kim, Kyung-Mi ; Whang, Woo-Hyung ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 235~263
The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.
A study on science and mathematics articles in Hansungsunbo and Hansungjubo
Lee, Kyung-Eon ; Shin, Hyun-Yong ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 265~285
In this study, we investigate the science and mathematics articles in Hansungsunbo and Hansungjubo which are the first modernistic newspapers in Korea. Hansungsunbo was published from October 31, 1883 to December 4, 1884 and Hansungjubo was issued from January 25, 1886 to July, 1888. While these papers were published, Korea had concluded a treaty with America(1882), England(1883), Germany(1883), Russia, and France(1884). Therefore, Korea had a lot of problems with commercial relations, the civilization and enlightenment of the Korean society. In this situation, some leaders who had the enlightenment thought published these two papers in order to inform the Korean people of the worldwide news on the politics, economy, history, science and technology, and so on. In this paper, we bring up the title and the contents on the science articles and the mathematics test problems of 'Dongmoonguan' and 'Chunjinmoobi School'.
Children's sense-making of triangle congruence conditions
Son, So-Hyun ; Yim, Jae-Hoon ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 287~302
This study investigated how 5th grade students found and understood triangle congruence conditions (SSS, SAS, ASA). In particular, this study focused on children's processes of discovering triangle congruence conditions and the obstacles which they encountered in the process of making sense of these conditions. Our data indicates that inquiring the cases in which less than three factors of triangle are given is helpful for children to guess triangle congruence conditions and understand the minimal characteristic of these conditions. And the degree of difficulty of discovering each congruence condition is different. Children discovered SAS condition and ASA condition easily, but it was hard for them to discover and understand that SSS was also a triangle congruence condition because they connected the length of a given side with the use of a scaled ruler not a compass.
The change of mathematical representations and behavioral characteristics in the class using manipulative materials - Focused on teaching regular polytopes -
Choi, Jeong-Seon ; Park, Hye-Sook ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 303~328
In this study, we developed the teaching methods using manipulative materials to teach regular polytopes, and applied these to first-year student of middle school who is attending the extra math class. In that class, we focused on the change of the mathematical representations -especially verval, visual and symbolic representations- and mathematical behavioral. By analyzing characterstics the students' work sheets, we obtained affirmative results as follows. First, manipulative materials played an important role on drawing a development figure of regular polyhtopes describing the verval representation definition of regular polytopes. Second, classes utilizing manipulative materials changed students verbalism level of representations the definition of regular polytopes. For example, in the first class about 60% of students are in the
vervalism level, but in the third class, about 65% of students are in the
level. Third, classes utilizing manipulative materials improved visual representation about development figure. After experiences making several development figures about regular octahedron directly, and discussion, students found out key points to be considered for draws development figure and this helped to draw development figures about other regular polytopes. Fourth, students were unaccustomed to make symbolic representations of regular polytopes. But, they obtained same improvement in symbolic representations, so in fifth the class some students try to make symbol about something in common of whole regular polytopes. Fifth, after the classes, we have significant differences in the students, especially behavioral characteristics in II items such as mind that want to study own fitness, interest, attachment, spirit of inquiry, continuously mathematics posthumously. This means that classes using manipulative materials. Specially, 'mind that want to study mathematics continuously' showed the biggest difference, and it may give positive influence to inculcates mathematics studying volition while suitable practical use of manipulative materials. To conclude, classes using manipulative materials may help students enhance the verbal, visual representation, and gestates symbol representation. Also, the class using manipulative materials may give positive influence in some part of mathematical behavioral characteristic. Therefore, if we use manipulative materials properly in the class, we have more positive effects on the students cognitive perspect and behavioral cteristics.
A Study on the effects of small group cooperative learning on strategies for estimating measurement - focused on 5th graders -
Kim, Myuog-Ok ; Kwoo, Sung-Yoog ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 329~352
The purpose of this study was to investigate the effects of small group cooperative communicative activities on the strategies for estimating measurement. To do this, two research questions were set as follow: First, are there any differences between strategies employed by students in the experimental group and the control group before and after the estimating measurement activities? Second, are there any differences between strategies employed by students in different ability levels(upper, middle, lower) of pre-estimating measurement test in the experimental group? The research results were drawn from the investigation as below: First, the strategical change of before and after the estimating measurement tasks in the experimental group was quite noticeable. Unlike the small strategical change in the control group, small group cooperative communicative learning resulted in a decrease of simple memorization and guessing strategies and an increase of refined strategies such as the standard strategy, clustering, unit load and so on. Second, mathematical communicative activities in a small group cooperative learning showed that the students in the upper level of pre-estimating measurement test used more refined strategies and the students in the lower level used simple memorization and guessing strategy more frequently. And through interaction in small group, students could have chances to recognize error of strategies and to modify and learn strategies. In conclusion, small group cooperative activities allowed students to have chances to communicate mathematically and it is a efficient way of helping students learn estimating measurement strategies.
Semantic analysis of the independency concepts in the probability
Yoo, Yoon-Jae ;
The Mathematical Education, volume 48, issue 3, 2009, Pages 353~358
The article discusses the independence concept occurring in the learning of probability. The author does not distinguishes the independence in the events from the independence in the trials. Instead, the author suggests the physico-empirical independence and the logico-mathematical independence to distinguish between the two concepts.