• 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 Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.317-332
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• 2011

The purpose of this study is to suggest an effective plan for teaching the definition of prism by integrating and analyzing the theories related to the instruction of definitions. The subjects in this study to realize these objectives were as follows. First, it looks to theoretical backgrounds regarding the instruction of the definition of solid by functions of definition in mathematics education. Second, it explores the instructional way to form the definition of solid through function of definition, by analyzing the unit of solid in the 6th grade. Third, after conducting the real practice with the 5th graders who before learn solid in 6th curriculum, according to plan of instruction, it examined student's response and testify its effectiveness, and then propose a teaching scheme which is designed to be useful based on the outcomes. In terms of theoretical background, it investigated the precedent research in relation to the instruction of the definition that mathematical definition is not given perfectly but the process of making knowledge that mathematization activity is necessary. It investigated the effects of the instruction of definitions, based on the effects of teaching and interviews with the 5th graders, and analysis of student's handout. The followings were the results of this study. First, 'Making Definitions' activities through remove counterexample process was possible to analytic thinking not intuitively thinking, and it effects the extend of awareness in definition that definition is not fixed but various. Second, it need the step of organize terms that is useful on solid's definition through activate of background knowledge. Third, it is effective that explore characters of the solids after construct the solids. Fourth, interactive discussion that students correct their mistakes each other through mathematical communication and they can think developmental is useful on making definition more than individual study.

• The Mathematical Education
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• v.56 no.3
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• pp.301-318
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• 2017

This paper explores students' question generation process and their study in small group discussion. The research is based on Anthropological Theory of the Didactic developed by Chevallard. He argues that the savior (knowledge) we are dealing with at school is based on a paradigm that we prevail over whether we 'learn' or 'study' socially. In other words, we haven't provided students with autonomous research and learning opportunities under 'the dominant paradigm of visiting works'. As an alternative, he suggests that we should move on to a new didactic paradigm for 'questioning the world a question', and proposes the Study and Research Courses (SRC) as its pedagogical structure. This study explores the SRC structure of small group activities in solving ill-structured problems. In order to explore the SRC structure generated in the small group discussion, one middle school teacher and 7 middle school students participated in this study. The students were divided into two groups with 4 students and 3 students. The teacher conducted the lesson with ill-structured problems provided by researchers. We collected students' presentation materials and classroom video records, and then analyzed based on SRC structure. As a result, we have identified that students were able to focus on the valuable information they needed to explore. We found that the nature of the questions generated by students focused on details more than the whole of the problem. In the SRC course, we also found pattern of a small group discussion. In other words, they generated questions relatively personally, but sought answer cooperatively. This study identified the possibility of SRC as a tool to provide a holistic learning mode of small group discussions in small class, which bring about future mathematics classrooms. This study is meaningful to investigate how students develop their own mathematical inquiry process through self-directed learning, learner-specific curriculum are emphasized and the paradigm shift is required.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.657-673
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• 2015

In this study, we are interested in the teachers' MCK about '$N{\div}0$' and MPCK in relation to the proper ways to teach it. Even though '$N{\div}0$' is not on the current curriculum and textbooks of elementary school mathematics, a few students sometimes ask a question about it because the division of the form '$a{\div}b$' is dealt in whole number including 0. Teacher's obvious understanding and appropriate guidance based on students' levels can avoid students' error and have positive effects on their subsequent learning. Therefore, we developed an interview form to investigate teachers' MCK about '$N{\div}0$' and MPCK of the proper ways to teach it and carried out individual interviews with 30 elementary school teachers. The results of the analysis of these interviews reveal that some teachers do not have proper MCK about '$N{\div}0$' and many of them have no idea on how to teach their students who are asking about '$N{\div}0$'. Based on our discussion of the results, we suggest some didactical implications.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.353-372
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• 2008

This study looks around the goals of teaching statistical graphs that are introduced in the seventh Korean Curriculum for Elementary School and in the Principles and Standards for School Mathematics(NCTM, 2000), and these are compared. We compare how to transpose statistical graphs didactically between the Korean and MiC textbooks. For it, it examines the types of statistical graphs, the methods defining them, and the making connections and comparing among them, which are content components in the chapters on statistical graphs. The results show that in contrast to the Korean textbooks, NCTM(2000) has allowed students to develop their own expression for data, to compare results analysed within different graphs, and to consider a graph as a whole in the goals of teaching statistical graphs. MiC textbooks have introduced the number-line plot and the box plot more than Korean. Although both of Korean and MiC textbooks usually use extensive methods for defining individual graphs, the former use extensive methods together with synonymic methods and the latter use extensive methods with the characteristics of graphs. Also, the number-line plot is defined using operative method in the MiC textbooks. MiC textbooks contain various activities for connecting and comparing graphs, but there are comparatively few comparing activities in the Korean textbooks.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.253-267
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• 2013

The newly revised mathematics curriculum of 2007 speaks of ultimate goal to develop ability to think and communicate mathematically, in order to develop ability to rationally deal with problems arising from the life around, which puts emphasize on mathematical communication. In this study, analysis on mathematical communication and analogical thinking process of group of students with similar level of academic achievement and that with different level, and thus analyzed if such communication has affected analogical thinking process in any way. This study contains following subjects: 1. Forms of mathematical communication took placed at the two groups based on achievement level were analyzed. 2. Analogical thinking process was observed through trapezoid's area obtaining activity and analyzed if communication within groups has affected such process anyhow. A framework to analyze analogical thinking process was developed with reference of problem solving procedure based on analogy, suggested by Rattermann(1997). 15 from 24 students of year 5 form of N elementary school at Gunpo Uiwang, Syeonggi-do, were selected and 3 groups (group A, B and C) of students sharing the same achievement level and 2 groups (group D and E) of different level were made. The students were led to obtain areas of parallelogram and trapezoid for twice, and communication process and analogical thinking process was observed, recorded and analyzed. The results of this study are as follow: 1. The more significant mathematical communication was observed at groups sharing medium and low level of achievement than other groups. 2. Despite of individual and group differences, there is overall improvement in students' analogical thinking: activities of obtaining areas of parallelogram and trapezoid showed that discussion within subgroups could induce analogical thinking thus expand students' analogical thinking stage.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.545-562
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• 2009

Calculus is used in various parts of human life and the basis of social science such as economics and public administration. Yet that is still considered important in the field of science and technology only, and there have been a lot of disputes on that phenomenon. Fortunately, calculus is going to be taught as part of the academic high school second-year mathematics curriculum in and after 2010. Students who face calculus for the first time should be helped not to lose interest in differentiation learning, not to be apprehensive of it nor to avoid it. The purpose of this study was to examine the types of errors made by students in the course of solving differentiation problems in an effort to lay the foundation for differentiation education. A pilot test was conducted after generalized differentiation problems to which students were usually exposed were selected, and experts were asked to review the pilot test. And then a finalized test was implemented to make an error analysis according to an error type analysis framework to serve the purpose.

• Journal of the Korean School Mathematics Society
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• v.8 no.4
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• pp.509-523
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• 2005

This study empirically examines motivations of entering college of education and academic problems that pre-service teachers encounter under the curricular activities. We analyze the phenomena of professional development under the four categories: motivation toward entering college of education, pedagogical content knowledge, subject matter knowledge and future vision. We conducted survey for the S university students first and interviewed 3 selected participants. Almost 50 students from college of education participated answering to the surveys. Using SPSS package, there was no significant difference between freshmen, sophomore and junior students in any category Male students responded more positively than female students in all the categories. To explore survey results deeply, we selected 3 students from sophomore and junior levels and 2 extra senior students to conduct interviews. The interpretation of the data described how their academic problems unfold partly because they seek another major and how their professional development take place carrying out practicum activities. Most of the interviewees felt that their academic lives were affected motivations of entering college of education and difficulties of studying subject matter knowledge. At the end, several suggestions are added for future research.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.1-29
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• 2013

The main goal of the research is to develop instructional consulting manual to help math teachers improve classroom teaching. Improving the quality of teaching in schools is stressed as a central focus of meaningful classroom instruction and high quality education. In this research, teaching consulting was defined as an activity that covers reflection process oriented towards formative assessment and continuing professional development. Within this context, subject-specific teaching consulting and teaching professionalism with focus on PCK was reviewed. Further, the questionnaire survey was conducted to investigate the current situation of teaching consulting and teachers' needs for consulting. And also, specific examples of subject-specific consulting based on our previous consulting experiences in math classes were shown. Alternative ways to improve subject teaching were derived through the conferences where consultants and consultees analyze video-taped lessons conducted by the consultees. By those results, a manual for invigorating teaching consulting was developed. The contents of the manual consists of setting conditions of teaching consulting and its implementation in the classroom teaching. The first part of the manual contains steps to establish teaching consulting system, the qualification and role of the consultant, system evaluation, etc. The second part of the manual presents the pre-preparation, prescription and implementation and follow-up management steps. Each part of the manual provides consultants with specific guidelines for each step. Finally, recommendations for making policy related to ways to invigorate teaching consulting was suggested. It is expected that specific examples and cases of subject-specific teaching consulting presented in this research will be used to narrow the gap between theory and practice of teaching consulting, and to help math, science and English teachers develop teaching professionalism.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.325-344
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• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.