• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.431-456
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• 2016

The purpose of this study is to investigate the appropriate time of introduction and the usage of the number line, in order to suggest the right point of learning the number concept to the elementary school students. For the efficient achievement of this purpose, we investigated the mathematical models for constructing the number concept such as number line, empty number line and double number line, counting and development of number concept. Then, we conducted case study on the time of introduction and the usage of the number line. Finally, we analyzed the result. First, there is need for adjustment to conduct the introduction of the number line from the second year of elementary school, so to help the students understand the continuing number concept through the understanding on the metaphorical concept of the number line. Second, there is the need of positive introduction and the use on the mathematical models; empty number line which helps to draw various thinking strategy visually through the process of operations such as addition and subtraction; the division into equal part and division by equal part in which multiplicative comparative situation or division takes place; the double number line which helps to understand the rate or proportional distribution. Finally, when adopting the number line, the empty number line, or the double number line, we suggested the necessity of learning about elaborate guidance and the usage in order to fully understand the metaphorical concept of the number line.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.95-120
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• 2011

Modern society is the age of the information. As new information is springing up every day and pace of change becomes faster, the importance of communication skills is growing. The recent mathematics education is recognized as not a fragmentary mathematical knowledge or results of the learning, but a procedure of mathematical thinking, and the effective expression skill of their mathematical ideas and the ability to forward it to others are regarded very serious. As the method of mathematics evaluation, mathematical essay is introduced to replace the existing multiple-choice written test. This method assess the ability which students have, that express the reorganized knowledge and information according to given situation by themselves. Ultimately, it is expected to help that students get the higher order thinking skills such as logical thinking and creativity. However, definition of elementary mathematical essay is unclear, and proper teaching methods is lacking for each stage of elementary school students. Thus, in this paper, I have defined the concept of elementary mathematical essay and made a foundation of elementary mathematical essay research, then researched about the effective utilization of elementary mathematical essay using school education. Also elementary mathematical essay teaching-learning materials is developed and applied to analyzed the students' responses. Using this program, in real elementary school education, the implications has deduced.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.361-383
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• 2011

This study is on teaching about the areas of plane figures through open instruction, which aims to discover the pedagogical meanings and implications in the application of open methods to math classes by running the Math A & B classes regarding the areas of parallelogram, triangle, trapezoid and rhombus for fifth graders of elementary school through open instruction method and analyzing the educational process. This study led to the following results. First, it is most important to choose proper open-end questions for classes on open instruction methods. Teachers should focus on the roles of educational assistants and mediators in the communication among students. Second, teachers need to make lists of anticipated responses from students to lead them to discuss and focus on more valuable methods. Third, it is efficient to provide more individual tutoring sessions for the students of low educational level as the classes on open instruction methods are carried on. Fourth, students sometimes figured out more advanced solutions by justifying their solutions with explanations through discussions in the group sessions and regular classes. Fifth, most of students were found out to be much interested in the process of thinking and figuring out solutions through presentations and questions in classes and find it difficult to describe their thoughts.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.345-363
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• 2010

The purpose of this study is to investigate and analyze informal knowledge of students who do not learn the conception of proportion and to identify how the informal knowledge can be used for teaching the conception of proportion in order to present an effective method of teaching the conception. For doing this, proportion was classified into direct and inverse proportion, and 'What are the informal knowledge of students?' were researched. The subjects of this study were 117 sixth-graders who did not have prior learning on direct and inverse proportion. A total eleven problems including seven for direct proportion and four for inverse proportion, all of them related to daily life. The result are as follows; Even though students didn't learn about proportion, they solve the problems of proportion using informal knowledge such as multiplicative reasoning, proportion reasoning, single-unit strategy etc. This result implies mathematics education emphasizes student's informal knowledge for improving their mathematical ability.

• School Mathematics
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• v.10 no.3
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• pp.443-461
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• 2008

The purpose of this study was to provide teachers with suggestions on how to teach the unit of finding the area of plane figure by analyzing students' different solution methods. The solution methods were analyzed according to how the original area of the given figure was kept: partition, transformation, and elimination. The partition method was most used. With regard to transformation, students seemed to find it easy to use the area of rectangle. With regard to elimination, students were successful using elimination to find the area of a given figure but had difficulty in producing a formula from the method. The teacher played a key role to encourage students to employ different solution methods, and gave them opportunities to compare and contrast various methods. A cautionary note is that, with too much emphasis on 'variety', the mathematical efficiency may be lost in the process. It suggests that a teacher should be careful to establish appropriate sociomathe- matical norms with students in order that they can make their own judgment on which solution method is mathematically worth and efficient.

• School Mathematics
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• v.11 no.2
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• pp.261-280
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• 2009

This study was motivated by recognizing the weakness of teaching and learning about the concepts of statements in high school mathematics curriculum. To report the reality of students' understanding about statements, this study investigated the 33 first-year undergraduate students' understanding about the concepts of statements by giving them 22 statement problems. The problems were selected based on the conceptual framework including five types of statement concepts which are considered as the key ideas for understanding mathematical reasoning and proof in college level mathematics. The analysis of the participants' responses to the statement problems found that their understanding about the concepts of prepositions are very limited and extremely based on the instrumental understanding applying an appropriate remembered rule to the solution of a preposition problem without knowing why the rule works. The results from this study will give the information for effective teaching and learning of statements in college level mathematics, and give the direction for the future reforming the unite of statements in high school mathematics curriculum as well.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.145-166
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• 2012

The objective of this study is to analyze the cases related to the lingual and non-lingual metaphors used in the math class at elementary school and consider the values of metaphors as a teaching method for the subject of mathematics. Throughout this study, teachers' gestures are analyzed as lingual and non-lingual metaphors shown between teachers and students in the class for the topic of the inverse proportion in quartic equations for direct and inverse proportions in Chapter 7 for the first semester of the 6th grade at elementary school in terms of the amended curriculum for the year of 2007. According to the results of the analysis, it can be concluded that there are mechanical and hypothetical movement metaphors in the mathematical metaphors observed in this study. Also, in terms of gestures, iconic, metaphoric and deixis gestures are found. Such metaphors seem to be evenly distributed throughout the math class and expressed in various forms. Based on the results of the analysis, the educational meaning given by the utilization of metaphors is considered for the math class.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.399-424
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• 2014

Although teacher preparation programs are important for prospective teachers to build a foundation of teaching expertise, there has been lack of research in this area. This paper analyzed in what ways prospective teachers' ability in describing and commenting on elementary mathematics instruction has been changed while they were taking in the course of teaching elementary school mathematics. The results of this study showed that in late description the teachers tended to notice the core flow of a lesson and the use of instructional strategies appropriate to the mathematical content to be taught. They also tended to comment on instructional strategies and mathematical discourse from the teacher's perspective and evaluated them without alternative approaches. A noticeable change occurred in late comments wherein prospective teachers considered both the teacher and students, supported their comments by theories they had learned through the course, and interpreted the classroom events they had noticed. Building on these results, this paper closes with implications of teacher education programs to enhance prospective teachers' ability to analyze elementary mathematics lessons.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.19-44
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• 2014

This study aims to develop strategies for improving the affective characteristics of Korean students based on results from international achievement tests. In pursuing the goal, different research methods are employed including a) analysis of the theories and literature regarding the affective domains included in PISA and TIMSS studies; b) analysis of the current situation and needs of Korean students with respect to the affective factors based on PISA and TIMSS results; c) case studies of best practices in relation to students' affective domains in Korea and abroad; and d) development of strategies for improving and supporting Korean students' affective characteristics. In this paper, first of all, relevant theories on affective characteristics in literature are introduced. In other words, the concepts of three affective domains in question - interest, self-efficacy, and value - are reviewed, and their definitions for the present study are made. Also, teaching strategies and support plans for improving students' affective factors are extracted from previous studies. Furthermore, this paper reviews recent trends in research on how the affective domains are related to mathematics education and how one can teach them effectively. The teaching guidelines for each affective domain are developed according to the instruction principles extracted through literature review in general for all subjects. Based on the results of the findings mentioned above, this paper establishes and suggests the guidelines on how to teach mathematics reflecting the affective characteristic.

• Journal of the Korean School Mathematics Society
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• v.24 no.1
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• pp.151-172
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• 2021

In this study, I investigated prospective mathematics teachers' perceptions of activities using Wax-paper, a hands-on material (manipulatives), and GeoGebra, a technological tool, in teaching quadratic curves. Twenty prospective mathematics teachers in the Mathematics Education Department of a local university participated in a survey on their perception of the use of hands-on materials and technological tools in teaching quadratic curves. According to the results of this study, prospective mathematics teachers generally preferred the use of technological tools for learning and teaching quadratic curves. Additionally, mathematics teachers thought that the tool helped students develop intuitive thinking through visualizing quadratic curves, enabling the exploration of various mathematical properties, assisting the comprehension of various concepts, and increasing students' interest levels. However, they were concerned about the immature use of technological tools by students or teachers, and recognized that the advantages and disadvantages of using hands-on material and technological tools were complementary. Based on these findings, it is suggested that hands-on material and technological tools should be used complementally in mathematics classes, and the development and dissemination of class materials that are not affected by students' or teachers' ability to use technological tools is important.