• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.21-58
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• 2015

The aim of this study is to look into the didactical background for teaching proportional reasoning in elementary school mathematics and offer suggestions to improve teaching proportional reasoning in the future. In order to attain these purposes, this study extracted and examined key ideas with respect to the didactical background on teaching proportional reasoning through a theoretical consideration regarding various studies on proportional reasoning. Based on such examination, this study compared and analyzed textbooks used in the United States, the United Kingdom, and South Korea. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: giving much weight on proportional reasoning, emphasizing multiplicative comparison and discerning between additive comparison and multiplicative comparison, underlining the ratio concept as an equivalent relation, balancing between comparisons tasks and missing value tasks inclusive of quantitative and qualitative, algebraic and geometrical aspects, emphasizing informal strategies of students before teaching cross-product method, and utilizing informal and pre-formal models actively.

• Journal of the Korean School Mathematics Society
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• v.11 no.4
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• pp.609-627
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• 2008

The purpose of this research was to investigate the relationship between the students' strategy types and the recognition for proportional situations. The students' strategy types which were based on the results of ratio and proportion tests were divided into an additive type, a multiplicative type, and a formal type. This research analyzed the students' activities of categorization when were given the proportional problems and nonproportional problems to the students. And it also explored how to develop students' recognizing for the discrimination between the proportional situations and nonproportional situations. The results was the following. First, the students didn't discriminate the proportional situations and the nonproportional situations in the initial state but they came to discriminate little by little. Secondly, the students didn't discriminate the direct proportions and the inverse proportions until the last stage. Third, the multiplicative type was outperformed more than the formal type in solving the ratio and proportion problems but the formal type was outperformed more than the multiplicative type in discriminating between proportional situations and nonproportional situations. These results are interpreted as showing that solving ratio and proportion tasks and recognizing proportional situations are different aspects of proportional reasoning and it is necessary to understand multiplicative strategy with formal strategy in recognizing proportional situations.

• School Mathematics
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• v.18 no.4
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• pp.819-838
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• 2016

This research analyzed proportional reasoning abilities of the 5th grade students who learned only the basis of ratio and rate and 6th grade students who also learned proportion and cross product strategy. Data were collected through the proportional reasoning tests and the interviews, and then the achievement of the students and their proportional reasoning strategies were analyzed. In the light of such analytical results, the conclusions are as follows. Firstly, there is not much difference between 5th and 6th grade students in the achievement scores. Secondly, both 5th and 6th graders are less familiar with the geometric, qualitative and comparisons tasks than the other tasks. Thirdly, not only 5th graders but also 6th graders used informal strategies much more than the formal strategy. Fourthly, some students can't come up with other strategies than the cross product strategy. Finally, many students have difficulties in discerning proportional situation and non-proportional situations. This study provided suggestions for improving teaching proportional reasoning in elementary schools in Korea as follows: focusing on letting students use their informal strategies fluently in geometric, qualitative, and comparisons tasks as well as algebraic, quantitative, and missing value tasks focusing on the concept of ratio and proportion instead of enforcing the formal strategy.

• Journal of Elementary Mathematics Education in Korea
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• v.21 no.2
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• pp.309-341
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• 2017

This study aims to investigate an approach to teach percentages in elementary mathematics class by analyzing calculating strategies with percentage the students use to solve the percentage tasks and their percentages of correct answers, as well as types of errors with percentages the students make. For this research 182 sixth graders were examined. The instrument test consists of various task types in reference to the previous study; the percentages tasks are divided into algebraic-geometric, part whole-comparison-change and find part-find whole-find percentage tasks. According to the analysis of this study, percentages of correct answers of students with percentage tasks were lower than we expected, approximately 50%. Comparing the percentages of correct answers according to the task types, the part-whole tasks are higher than the comparison and change tasks, the geometric tasks are approximately equal to the algebraic tasks, and the find percentage tasks are higher than the find whole and find part tasks. As to the strategies that students employed, the percentage of using the formal strategy is not much higher than that of using the informal strategy, even after learning the formal strategy. As an insightful approach for teaching percentages, based on the study results, it is suggested to reinforce the meaning of percentage, include various types of the comparison and change tasks, emphasize the informal strategy explicitly using models prior to the formal strategy, and understand the relations among part, whole and percentage throughly in various percentage situations before calculating.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.157-177
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• 2006

The concepts of ratio and proportion do not develop in isolation. Rather, they are part of the individual's multiplicative conceptual field, which includes other concepts such as multiplication, division, and rational numbers. The current study attempted to clarify the beginning of this development process. One fourth student, Kyungsu, was encourage to schematize his trial-and-error-based method, which was effective in solving so-called missing-value tasks. This study describes several advancements Kyungsu made during the teaching experiment and analyzes the challenges Kyungsu faced in attempting to schematize his method. Finally, the mathematical knowledge Kyungsu needed to further develop his ratio and proportion concepts is identified. The findings provide additional support for the view that the development of ratio and proportion concepts is embedded within the development of the multiplicative conceptual field.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.275-292
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• 2010

In this study, we discussed the way to teach algebra earlier through investigating to research trends of Early Algebra and researching about nature of subject involving algebra. There is a strong view that arithmetic and algebra have analogous forms and that algebra is on extension to arithmetic. Nevertheless, it is also possible to present a perspective that the fundamental goal and role of symbols and letters are difference between arithmetic and algebra. And, we could recognize that geometry was starting point of algebra trough historical perspectives. To consider these, we extracted some of possible directions to approaches to teach algebra earlier. To access to teaching algebra earlier, following ways are possible. (1) To consider informal strategy of young children. (2) Arithmetic reasoning considered of the algebraic relation. (3) Starting to algebraic reasoning in the context of geometrical problem situation. (4) To present young students to tool of letters and formular.

• Journal of The Korean Association For Science Education
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• v.24 no.5
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• pp.977-986
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• 2004

The purpose of this study was to investigate the general transfer effects of Thinking Science program on the problem solving with compensational reasoning of the elementary school students. For this study, 156 5th grade and 138 6th grade students were selected from four elementary schools. The students were tested with SRT(Science Reasoning Task) and compensational reasoning task. Statistically significant gains on the development of compensational reasoning were shown by the experimental group implemented with Thinking Science activities compared to the group implemented with compensation activity only. The achievement of the experimental group was higher than that of the compensation activity group in solving problem with compensational reasoning, specially for the boys and students in both the mature concrete and the concrete generalization stage. The results of this study implied that implementation of Thinking Science program related to several formal reasoning were effective for the development of reasoning ability as a general-transfer.

• Journal of Digital Convergence
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• v.10 no.10
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• pp.107-118
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• 2012

This study examined the analysis of the present condition, structure of fundraising activities, the effect of resource development and strategy for nonprofit social service organizations. This study investigated the fundraising and resource development activities of 356 non-profit organizations and community welfare centers nationwide. The results showed that a period of foundation of non-profit organization and community welfare center in Korea, was 10~14 years and organized with 13~19 workers. The community welfare centers were well prepared for the internal environment for resource development system such as workers, department, management for sponsors and computer program, while others were not prepared. Their recognition for the importance of fundraising activities was higher than the satisfaction of actual condition. The non-profit organization needs management sponsors, planning, public relations, fundraising skills and preparation proposal as the theme of education for fundraising activities. Their plans of the fundraising activity were events, proposal application, fundraising focus on companies, cause-related marketing. The non-profit organization complained of the difficulty about insufficiency manpower and skills of fundraising, external resource development and a budgetary deficit.

• Proceedings of the Korean Association of Geographic Inforamtion Studies Conference
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• 2004.03a
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• pp.415-421
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• 2004

막대한 예산을 투입하여 추진하고 있는 지자체 GIS사업은 기술의 발전에 비해 제도, 교육, 사용자의 마인드, 유지관리 활동, 향후 사업 구상 등에서 상대적인 빈곤을 경험하고 있는 것이 사실이다. 이렇듯 신기술이 도입됨에 따라 다양한 제반 여건들이 동반적으로 성숙하지 못함으로 인해 발생하는 현상을 과도기적 현상1)으로 진단하고 있다. 이미 다양한 분야에서 GIS를 도입한 지자체에서는 이러한 과도기적 현상을 극복하기 위해 상당한 어려움을 겪고 있으며, 새롭게 GIS를 도입하고자 하는 지자체에서도 타 지자체에서 모니터링을 통해 간접적으로 과도기적 현상을 경험함으로 인해 효과적인 사업 추진을 구상하는데 상당한 어려움을 겪고 있는 것이 현실이다. 또한 지자체의 경우 중앙정부에서 추진하고 있는 다양한 사업에 영향을 받을 수밖에 없고, 현재의 GIS 사업의 추세가 단순한 공간정보 중심의 사업이 아닌 다양한 속성정보와의 연계를 모색하고 있다는 점에서 지자체 GIS정보화의 방향은 예전과는 사뭇 다른 양상을 간파해 야 하는 현실에 놓여 있다. 이와 같은 지자체 GIS의 과도기적 현상을 극복하기 위해서는 정보기술의 빠른 변화속도와 외부환경의 극심한 환경변화의 상황에서 ‘보이는 것과 보이지 않는 것’의 관계를 진단하고, 변화에 대한 예측과 대비, 중요한 일과 급한 일을 구분한 총체적인 밑그림의 마련과 실행계획의 수립이 우선시 되어야 한다. 지자체 GIS의 문제 해결의 노력이 단숨에 바로 해결되는 것이 아니고, 또한 현재 추진된 사업을 기반으로 중복투자의 방지와 시너지 효과 극대화를 위한 투자의 노력이 장기간의 시간적 개념속에서 진행되어야 한다는 점에서 이를 이끌어줄 가이드가 필요한 것이다. 이러한 총체적인 지자체 GIS의 계획마련을 위해 건설교통부에서는 ‘국가지리정보구축 및 활용등에 관한 법률’상에 계획 수립의 항목을 명문화하고, 나아가 GIS정보화 전략계획 수립에 관한 지침작성을 위한 노력을 진행 중에 있다. 이러한 일련의 현실을 감안하여 지자체 GIS정보화 전략계획 수립을 체계적이고 실질적으로 수립할 수 있는 ‘지자체 GIS정보화 전략계획 수립모델’은 반드시 선행되어야 할 사항임에 분명하다. 지자체 GIS정보화 전략계획 수립 모델은 지자체 GIS정보화 전략계획 수립의 효과로 하고 있으며, 형식적 측면에서는 GIS특성을 반영한 전략계획 수립의 방법론적 측면을 중심으로 구성된다. 이러한 과정을 거처 실제 지자체 GIS정보화 전략계획을 수립하는데 필요한 9단계를 설정하고 각각의 단계에 대한 중심활동을 바탕으로 지자체에서 실제 전략계획 수립에 필요한 지침을 작성하는 것으로 구성되어 있다.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.155-171
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• 2007

One second grader, Junsu, was observed 4 times before and after formal multiplication lesson in Grade 2. This study describes how solution strategies in multiplication problems develop over time and investigates awareness of the relation between situation and computation in simple measurement and partitive division problems as informally experienced. It was found that Junsu used additive calculation for small-number multiplication problems but could not solve large-number multiplication problems and that he did not have concept of mathematical terms at first interview stage. After formal teaching, Junsu learned a variety of multiplication solution strategies and transferred from additive calculation to multiplicative calculation. The cognitive processing load of each strategy was gradually reduced. Junsu experienced measurement division as a dealing strategy and partitive division as a estimate-adjust strategy dealing more than one object in the first round.