• The Mathematical Education
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• 제61권1호
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• pp.109-126
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• 2022

The purpose of this study is to explore how well teachers anticipate students to understand and solve equations. For this purpose, a questionnaire of the equal sign was developed, and 20 fourth-grade classes were selected as research participants. Teachers in each class were asked to predict various strategies on how their own students would respond to the questionnaire, and a total of 450 students from the 20 classes solved the questionnaire. As a result of the analysis, the teachers could predict students' computational strategies and relational strategies easily but did not fully understand that some students used both strategies or employed incorrect computational or relational strategies. The students tended to use relational strategies better than the teachers expected. They also employed operational strategies more often than the teachers expected. The teachers predicted that students' strategies would be influenced by the types of the problems such as equation-structure items and equation-solving items, whereas the students were more influenced by the forms of equations in the problems. Based on these results, several implications for the knowledge to which teachers needed to attend were discussed so that elementary school students could enhance the relational understanding of the equal sign.

• Journal of the Korean School Mathematics Society
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• 제8권2호
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• pp.273-289
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• 2005

This research was implemented to know how mathematics education is performed both in a school and in the private institute based on Skemp' Theory that strongly takes an emphasis on understanding of mathematics principle. On this study, I compare the method of a teacher in a school with in a private institute accompanying the analysis of textbook in teaching. The results are the followings: First, textbooks used in a school and an institute are not helpful for relational understanding of students, and the textbook used in school was more suitable for students than that in institute. Second, in the case of teaching methods, school teacher has focused more relational schema with the students than an private institute institutor, As we said, in school mathematics education is implemented focusing on the understanding of mathematics. According to this, students should to trust public education more than private institute in constructing schema in mathematics learning.

• Communications of Mathematical Education
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• 제29권2호
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• pp.215-239
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• 2015

A goal of this study is figuring out how fraction learning centered on various representation activities influences the fraction comprehension and mathematical attitudes. The study focused on 33 4th-grade students of B elementary school in Seoul. In the study, 15 fraction learning classes comprising enactive, iconic, and symbolic representations took place over 6 weeks. After the classes, the ratio of the students who achieved relational understanding increased and the students averagely recorded 90 pt or more on the fraction comprehension test I, II and III. Two-dependent samples t-test was conducted to analyze a significant difference in mathematical attitudes between pre-test and post-test. On the test result, there was the meaningful difference with 0.01 level of significance. To conclude, the fraction learning centered on various representation activities improves students' relational understanding and fraction understanding. In addition, the fraction learning centered on various representation activities gives positive influences on mathematical attitudes since it increases learning orientation, self-control, interests, value cognition, and self-confidence of the students and decreases fears of the students.

• School Mathematics
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• 제14권3호
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• pp.297-313
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• 2012

The purpose of this paper is to discuss the potential and to examine the effect of narrative, as an alternative approach to teach formal proof in more easier and comprehensible way. Identifying the key elements of narrative in proof, we constructed a narrative that derives the equation of function translation. We examined the effect of teaching through the narrative, in comparison with teaching the corresponding proof, on low-achieving students' instrumental understanding and relational understanding of function translation. Since we found no statistically significant differences between the experimental and the comparison group, this study could not conclude that teaching through the narrative was more effective than teaching the corresponding proof. But there were some qualitative differences in the relational understanding responses and the evaluation of the teaching between two groups. These findings suggested some potential of narratives that complement the formal proof.

• Journal of the Korean School Mathematics Society
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• 제15권4호
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• pp.643-671
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• 2012

The purpose of this study was to examine How the exploratory activities using Excel and GSP which are exploratory software, in learning analytic geometry affected on the underachievers' analytic geometry concept development process. The subjects of 5 students who received the 8th~9th grades from their examination of the last semester, participated in a total of 7 units based on Skemp's intelligent learning model. The results of the study showed that there were two important cases found to nearly achieve the category $R_2$. One was reflective thinking could happen through exploratory software in category $R_1$. The other was the exploratory activities which could have the same effectiveness as the relational understanding in category $I_2$, as Skemp mentioned that there is a room to be achieved in the elementary level when such relational understanding is achieved.

• Research in Mathematical Education
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• 제18권4호
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• pp.237-256
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• 2014

This paper reports findings from a written assessment which was designed to investigate Chinese primary school students' understanding of the equal sign and equation structure. The investigation included a sample of 110 Grade 3, 112 Grade 4, and 110 Grade 5 students from four schools in China. Significant differences were identified among the three grades and no gender differences were found. The majority of Grades 3 and 4 students were found to view the equal sign as a place indicator meaning "write the answer here" or "do something like computation", that is, holding an operational view of the equal sign. A part of Grade 5 students were found to be able to interpret the equal sign as meaning "the same as", that is, holding a relational view of the equal sign. In addition, even though it was difficult for Grade 3 students to recognize the underlying structure in arithmetic equation, quite a number of Grades 4 and 5 students were able to recognize the underlying structure on some tasks. Findings in this study suggest that Chinese primary school students demonstrate a relational understanding of the equal sign and a strong structural sense of equations in an earlier grade. Moreover, what found in the study support the argument that students' understanding of the equal sign is influenced by the context in which the equal sign is presented.

• Korean Journal of School Psychology
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• 제18권3호
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• pp.351-370
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• 2021

This study investigated the effect of parental psychological control on relational aggression among middle school students, the mediating effects of rejection sensitivity and friendship jealousy, and whether there were differences in these variables by the demographic characteristics of gender and family form. Data of 554 middle school students living in Daegu and Gyeongsangbuk-do were used for the final analysis. There were two major results. The first major result was what rejection sensitivity and friendship jealousy sequentially mediated the relationship between parental psychological control and relational aggression. The second major result was gender differences which was shown by a multi-group analysis to examine in the path from parental psychological control to rejection sensitivity, the path from parental psychological control to relational aggression, and the path from friendship jealousy to relational aggression. This study was meaningful in that it expanded the understanding of relational aggression and identified directions for therapeutic interventions.

• Journal of the Korean School Mathematics Society
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• 제18권4호
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• pp.353-370
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• 2015

This study was conducted as a qualitative case study that explored how gifted 3rd-grade elementary school children who had learned the primary concepts of division and fraction, when they studied contents about decimal, formed the transformed primary concept and transformed schema of decimal by the learning of accurate primary concepts and connecting the concepts. That is, this study investigated how the subjects attained relational understanding of decimal based on the primary concepts of division and fraction, and how they formed a transformed primary concept based on the primary concept of decimal and carried out vertical mathematizing. According to the findings of this study, transformed primary concepts formed through the learning of accurate primary concepts, and schemas and transformed schemas built through the connection of the concepts played as crucial factors for the children's relational understanding of decimal and their vertical mathematizing.

• Journal of Elementary Mathematics Education in Korea
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• 제21권4호
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• pp.643-662
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• 2017

The first appearance of the equations in elementary school mathematics is in the expression of the equal sign in the addition sentences without its definition. Most elementary school students have operational understanding of the equal sign in equations. Moreover, students' opportunities to have a clear concept of the properties of operations are limited because they are used implicitly in the textbooks. Based on this fact, it has been argued that it is necessary to introduce the properties of operations explicitly in terms of specific numbers and to deal with various types of equations for understanding a relational meaning of the equal sign. In this study, we use equations to represent the implicit properties of operations and the relational meaning of the equal sign in elementary school mathematics with respect to students' level of understanding. In addition, we give some explicit examples which show how to apply them to make efficient computations.

• Journal of Distribution Science
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• 제12권1호
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• pp.5-12
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• 2014

Purpose - The general objective of this study is to explain the governance mechanisms of relational exchanges by considering both economic and relational factors. As regards the relationship between opportunism and governance mechanisms, opportunism was hypothesized as being positively related to the use of the authority mechanism, and negatively related with use of the trust mechanism. Research design, data, and methodology - Purchasing relationships between original equipment manufacturers (OEMs) and their component suppliers were chosen as the empirical setting. Purchasing specialists in each company, who interact regularly with suppliers and have the major responsibility for managing the exchange relationships with suppliers, were used as the respondents for this study. A mail survey methodology was employed to collect data in the final field survey. Results - As predicted, opportunistic behavior is found to be negatively related to the use of the trust mechanism and positively related to the use of the authority mechanism. Therefore, the result supports the proposed hypotheses. Conclusions - By integrating research streams, this study contributes to the marketing discipline by improving our understanding of when and why different mixtures of governance mechanisms are used.