• Communications of Mathematical Education
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• v.23 no.3
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• pp.735-760
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• 2009

Most of every teachers' life is occupied with his or her instruction, and a classroom is a laboratory for mutual development between teacher and students also. Namely, a teacher's professionalism can be enhanced by circulations of continual reflection, experiment, verification in the laboratory. Professional development is pursued primarily through teachers' reflective practices, especially instruction practices which is grounded on $Sch\ddot{o}n's$ epistemology of practices. And a thorough penetration about situations or realities and an exact understanding about students that are now being faced are foundations of reflective practices. In this study, at first, we explored the implications of earlier studies for discussing a teacher's practice. We could found two essential consequences through reviewing existing studies about classroom and instructions. One is a calling upon transition of perspectives about instruction, and the other is a suggestion of necessity of a teachers' reflective practices. Subsequently, we will talking about an instance of a middle school mathematics teacher's practices. We observed her instructions for a year. She has created her own practical knowledges through circulation of reflection and practices over the years. In her classroom, there were three mutual interaction structures included in a rich expressive environments. The first one is students' thinking and justifying in their seats. The second is a student's explaining at his or her feet. The last is a student's coming out to solve and explain problem. The main substances of her practical know ledges are creating of interaction structures and facilitating students' spontaneous changes. And the endeavor and experiment for diagnosing trouble and finding alternative when she came across an obstacles are also main elements of her practical knowledges Now, we can interpret her process of creating practical knowledge as a process of self-directed professional development when the fact that reflection and practices are the kernel of a teacher's professional development is taken into account.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.181-199
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• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.407-434
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• 2008

This research is to analyze the descriptions in the statistic chapter of the grade 7's current textbooks. The analysis is based on the distribution concepts suggested by Nam(2007). Thus we assumed that the goal of this statistic chapter is to establish concepts on the distributions and to learn ways of communication and comparison through distributional presentations. What we learned and wanted to suggest through the study is the followings. 1) Students are to learn what the distribution is and what are not. 2) Every kinds of presentational form of distributions is to given its own right to learn so that students are more encouraged to learn them and use them more adequately. 3) Density histogram is to be introduced to extend student's experiences viewing an area as 3 relative frequency, which is later to be progressed into a probability density. 4) Comparison of two distributions, especially through frequency polygons, is to be an hot issue among educational stakeholder whether to include or not. It is very important when stochastic correlations be learned, because it is nothing but a comparison between conditional distributions. 5) Statistical literacy is also an important issue for student's daily life. Especially the process ahead of the data collection must be introduced so that students acknowledge the importance of accurate and object-oriented data.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.305-322
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• 2010

The epistemological obstacles in the area learning of plane figure can be categorized into two types that is closely related to an attribute of measurement and is strongly connected with unit square. First, reasons for the obstacle related to an attribute of measurement are that 'area' is in conflict. with 'length' and the definition of 'plane figure' is not accordance with that of 'measurement'. Second, the causes of epistemological obstacles related to unit square are that unit square is not a basic unit to students and students have little understanding of the conception of the two dimensions. Thus, To overcome the obstacle related to an attribute of measurement, students must be able to distinguish between 'area' and 'length' through a variety of measurement activities. And, the definition of area needs to be redefined with the conception of measurement. Also, the textbook should make it possible to help students to induce the formula with the conception of 'array' and facilitate the application of formula in an integrated way. Meanwhile, To overcome obstacles related to unit square, authentic subject matter of real life and the various shapes of area need to be introduced in order for students to practice sufficient activities of each measure stage. Furthermore, teachers should seek for the pedagogical ways such as concrete manipulable activities to help them to grasp the continuous feature of the conception of area. Finally, it must be study on epistemological obstacles for good understanding. As present the cause and the teaching implication of epistemological obstacles through the research of epistemological obstacles, it must be solved.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.103-121
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• 2008

The primary purpose of this study was to gather knowledge about $5^{th},\;6^{th},\;and\;7^{th}$ graders' proportional reasoning ability by investigating their reactions and use of strategies when encounting proportional or nonproportional problems, and then to raise issues concerning instructional methods related to proportion. A descriptive study through pencil-and-paper tests was conducted. The tests consisted of 12 questions, which included 8 proportional questions and 4 nonproportional questions. The following conclusions were drawn from the results obtained in this study. First, for a deeper understanding of the ratio, textbooks should treat numerical comparison problems and qualitative prediction and comparison problems together with missing-value problems. Second, when solving missing-value problems, students correctly answered direct-proportion questions but failed to correctly answer inverse-proportion questions. This result highlights the need for a more intensive curriculum to handle inverse-proportion. In particular, students need to experience inverse-relationships more often. Third, qualitative reasoning tends to be a more general norm than quantitative reasoning. Moreover, the former could be the cornerstone of proportional reasoning, and for this reason, qualitative reasoning should be emphasized before proportional reasoning. Forth, when dealing with nonproportional problems about 34% of students made proportional errors because they focused on numerical structure instead of comprehending the overall relationship. In order to overcome such errors, qualitative reasoning should be emphasized. Before solving proportional problems, students must be enriched by experiences that include dealing with direct and inverse proportion problems as well as nonproportional situational problems. This will result in the ability to accurately recognize a proportional situation.

• Journal of Educational Research in Mathematics
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• v.25 no.1
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• pp.95-111
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• 2015

The purpose of this study is to analyze cases on teaching solutions exploration of Wythoff's game through using the analogy for the gifted elementary students, to suggest useful teaching methods. Students recognized structural similarity among problems on the basis of relevance of conditions of problems. The discovery of structural similarity improves the ability to solve problems. Although 2 groups-NIM game with surface similarity is not helpful in solving Wythoff's game, Queen's move game with structural similarity makes it easier for students to solve Wythoff's game. Useful teaching methods to find solutions of Wythoff's game through using the analogy are as follow. Encoding process helps students make sense of the game. It is significant to help students realize how many stones are remained and how the location of Queen can be expressed by the ordered pair. Inferring process helps students find a solution of 2 groups-NIM game and Queen's move game. It is necessary to find a winning strategy through reversely solving method. Mapping process helps students discover surface similarity and structural similarity through identifying commonalities between the two games. It is crucial to recognize the relationship among the two games based on the teaching in the Encoding process. Application process encourages students to find a solution of Wythoff's game. It is more important to find a solution by using the structural similarity of the Queen's move game rather than reversely solving method.

• School Mathematics
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• v.12 no.4
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• pp.473-491
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• 2010

In the TIMSS assessment goal and open TIMSS 2007, Singapore recorded a lower overall achievement level compared with Korea; however, the excellent results shown by Singapore furnished an opportunity for various countries to research into the education in Singapore. This paper conducted a comparative analysis of the "Proportion, Proportional Expression, and Percentile" area out of the three topics involving "Fractions and Decimals", "Proportion, Proportional expression, and Percentile", and "Measurement", in all of which Singapore exhibited a higher percentage of correct answers than Korea. The paper was able to discover the following differences through a comparative analysis of how Korean and Singaporean textbooks deal with the open questions of TIMSS 2007 after looking into them according to four assessment goals. First, the Singaporean textbook introduced the concept of proportion one year ahead of the Korean textbook. Second, the Singaporean textbook repeatedly coped with the topic of "Proportion, Proportional Expression, and Percentile" in depth and by academic year, and its volume was larger than that of the Korean textbook. Third, there was a difference in the introduction and definition of the concept of proportion. Fourth, the way of introducing a proportional expression was also different, and the Singaporean textbook proposed many more questions that utilize this expression in ordinary life. Based on these differences, the paper suggested implications that could be applied to the Korean curriculum and textbook.

• Steel and Composite Structures
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• v.36 no.2
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• pp.213-228
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• 2020

Shape Memory Alloys (SMAs) are new materials used in various fields of science and engineering, one of which is civil engineering. Owing to their distinguished capabilities such as super elasticity, energy dissipation, and tolerating cyclic deformations, these materials have been of interest to engineers. On the other hand, the connections of a steel structure are of paramount importance because of their vulnerabilities during an earthquake. Therefore, it is indispensable to find approaches to augment the efficiency and safety of the connection. This research investigates the behavior of steel connections with extended end plates equipped hybridly with 8 rows of high strength bolts as well as Nitinol superelastic SMA bolts. The connections are studied using component method in dual form. In this method, the components affecting the connections behavior, such as beam flange, beam web, column web, extended end plate, and bolts are considered as parallel and series springs according to the Euro-Code3. Then, the nonlinear force- displacement response of the connection is presented in the form of moment-rotation curve. The results obtained from this survey demonstrate that the connection has ductility, in addition to its high strength, due to high ductility of SMA bolts.

• Journal of Gifted/Talented Education
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• v.20 no.1
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• pp.31-59
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• 2010

Previous studies reported that gifted students' capacity on mathematics had high correlations with results of the performance assessment. However, there have been few studies that develop recommending tools through the assessment that can be used to identify mathematically gifted students or analyse their applications. Then it is difficult to use them to identify mathematically gifted students practically. Therefore, this study developed the tasks and evaluation tables for the tools. And one of them was applied for four students in Grade 1 of a middle school to simulate the assessment and characteristics assessment teachers showed were analysed. As the results, the extensive and specific information on the giftedness of the students was obtained through using the tool. The gifted capacity grasped from the order, speed, and attitudes of problem-solving was identified as observing the process of solving the task.

• The Korean Journal of Elementary Counseling
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• v.4 no.1
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• pp.123-150
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• 2005

The purpose of this study was to examine the effects of self-regulated learning program on the underachiever's academic achievement and academic self-concept. To achieve the purpose of study the research hypotheses were as follows : Hypothesis 1 : There will be significant differences in the improvement of academic achievement between the experimental group and the control group. Hypothesis 2 : There will be significant differences in the improvement of academic self-concept between the experimental group and the control group. To verify these hypotheses, 32 underachievers were selected from sixth grade students of 'D' elementary school located in Seoul. 16 students were allocated to the experimental group and 16 students were allocated to the control group. The experimental group trained with self-regulated learning program for 10 times(The length of each section was 60 minutes). The self-regulated learning program in this study was based on program by Kim. Yong-Soo(1998), The measurement instruments of the study were mathematics achievement test paper and academic self-concept test. To find out the difference, Pretest-posttest control design was used. Mean and standard deviations obtained from these tests were analysed with t-test. The major findings obtained through this study are as follows : First, self-regulated learning program was effective in improvement of academic achievement (p<.05). Second, self-regulated learning Program was not effective in improvement of academic self-concept. However, the experimental group showed significant improvement(p<.01) at academic self-concept and sub academic self-concepts (ability, achievement) in the data of pre-post test. it can be suggested that this program had positive influence on underachievers. Although it has some limitations, self-regulated learning program is effective to academic achievement and academic self-concept of underachievers, even though not significant, it has a positive t.