• The Mathematical Education
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• v.49 no.2
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• pp.267-279
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• 2010

Mathematics is the subject which is distinctive in logical hierarchy, so the dificiency of prior learning or lack of understanding can result in learning disabilities of follow-up study. To minimize the learning disabilities, we should percieve student's problems and correct them through "Error Analysis" so that they can make up meaningful learning. Especially, in the case of division, its meaning is various, and the interpretation of the quotient and the remainder is the difference according to the caculation results, so students are likely to make errors often. Therefore, in this study, I presented the measures of how to instruct them under the circumstances in which division is applied by analyzing examples of incorrect answers.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.373-391
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• 2022

The distribution of observations in most econometric studies with spatial heterogeneity is skewed. Usually, a single transformation of the data is used to approximate normality and to model the transformed data with a normal assumption. This assumption is however not always appropriate due to the fact that panel data often exhibit non-normal characteristics. In this work, the normality assumption is relaxed in spatial mixed models, allowing for spatial heterogeneity. An inference procedure based on Bayesian mixed modeling is carried out with a multivariate skew-elliptical distribution, which includes the skew-t, skew-normal, student-t, and normal distributions as special cases. The methodology is illustrated through a simulation study and according to the empirical literature, we fit our models to non-life insurance consumption observed between 1998 and 2002 across a spatial panel of 103 Italian provinces in order to determine its determinants. Analyzing the posterior distribution of some parameters and comparing various model comparison criteria indicate the proposed model to be superior to conventional ones.

• Research in Mathematical Education
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• v.26 no.4
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• pp.271-289
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• 2023

This research investigates the development of elementary students' concepts of line segments, straight lines, and rays, employing metaphor analysis as a research methodology. By analyzing metaphorical expressions, the research aims to explore how elementary students form these geometric concepts line segments, straight lines, and lays and evolve their understanding of them across different grades. Surveys were conducted with elementary school students in grades three to six, focusing on metaphorical expressions and corresponding their reasons associated with line segments, straight lines, and rays. The data were analyzed through coding and categorization to identify the types in students' metaphorical expressions. The analysis of metaphorical expressions identified five types: straightness, infinity or direction, connections of another geometric concepts, shape and symbols, and terminology.

• Communications of Mathematical Education
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• v.20 no.2 s.26
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• pp.295-326
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• 2006

Despite the importance of mathematics education, many students in high school have lost their interests and felt difficulties and they don't have 'mathematical' experience with meanings attached because of the entrance examination. This paper attempted to resolve these problems and find the teaching-method with which students can study by themselves with more confidence. Nowadays students' use of Internet is very popular. After develop 'the development of mathematical power' program based on mathematics history, history, science, the application of problems in real world, and self-evaluation, I made students repeat them after making teaching lessons in classroom as moving pictures. Through this processes, I attempted to develop the Self-Directed Learning' ability by making public education substantial. First of all I analyzed the actual conditions on 'Self-Directed Learning' ability in mathematics subject, the conditions of seeing and hearing in Internet learning program, and students' and their parents' interests in Internet education. By analyzing the records, I observed the significance of the introducing mathematics history in mathematics subject in early stager, cooperative-learning, leveled-learning, self-directed learning, and Internet learning. Actually in aspect of applying 'the development of mathematical power' program, at first I made up the educational conditions to fix the program, collected the teaching materials, established the system of teaching-learning model, developed materials for the learning applying Internet mail and instruments of classroom, and carried out instruction to establish and practice mathematics learning plan. Then I applied the teaching-learning model of leveled cooperation and presentation loaming and at the same time constructed and used the leveled learning materials of complementary, average, and advanced process and instructed to watch teaching moving pictures through Internet mail and in the classroom. After that I observed how effective this program was through the interest arid attitude toward mathematics subject, learning accomplishment, and the change of self-directed learning. Finally, I wrote the conclusion and suggestion on the preparation of conditions fur the students' voluntary participation in mathematics learning and the project and application on 'the development of mathematical power' program and repeated learning with the materials of moving pictures in classroom.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.189-204
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• 2016

As compared with the gender differences in the achievement of mathematics of the PISA 2009, the results of this study on the PISA 2012 show that the achievement of male students sharply increased, while that of female students maintained the status quo. Based on the premise that this result is derived from the ratio differences between male and female students of high level, this study analyzed the educational context variable effects on the achievements of gender differences observed between male and female students of high level. In particular, this study inquired into the factors which influence the gender difference, by analyzing the identical variables regarding Singapore and Finland of which the achievement of female students registers high among other top high-ranking countries of the PISA 2012. Hence, the binominal logistic multi-level analysis was conducted in order to consider the characteristics of hierarchical structure of PISA, and to compare the features of the educational context variable effects between the high level (above level 5) by country and the highest level (above level 6) by group. The analysis results are as follows: in terms of after-school learning time realized either in private lessons and private institutes, no significant effects were shown in any of the students of these three countries. In terms of after-school homework time, the students of Korea and Singapore gave significant influences on the probability which would be included in the group of high level or the highest level. In particular, regarding the variables which influence the probability of inclusion of Korean female students in the group of high level or the highest level, they correspond to "Homework set by teacher", "Attitude toward school: learning activities", "ESCS of School" and "Teacher-student relations". And "Cultural possessions at home" gave main influences on the probability of inclusion of the female students of Korea, Singapore and Finland in the group of the highest level.

• School Mathematics
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• v.4 no.3
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• pp.375-399
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• 2002

When a curriculum change is being an issue, the editorships and the promotive directions reflect to supplement the social requests. However it is often criticized that such changes in the textbook itself are not satisfactory enough as to coherent to the editoships. And we set the following research questions; (1) One of the most important changes in the new 7th curriculum is to encourage the students' activities. We checked if it is well suited in the new textbooks. (2) Often textbook itself is not important In class, while instructor or students want something else other than the one suggested in the textbook. We asked 187 teachers how they use the textbooks in class. To answer (1), we checked up the introductory - activity - contents with 7 categories, which are ${\circled1}$ of real life sources ${\circled2}$ in use of concrete manipulative ${\circled3}$ in use of computers or calculators ${\circled4}$ in use of historical resources ${\circled5}$ stimulating to recall a relevant previous knowledges ${\circled6}$ of coherence between the activity and the exploratory contexts. ${\circled2}$ were increased, rewarding to the decrease of ${\circled5}$, in the new textbooks, while changes in ${\circled3}$ and ${\circled4}$ were not enough to talk about increments. Especially slight decrease in ${\circled6}$ were detected and it seemed to attribute to the unmatchable use of ${\circled1}$ and ${\circled2}$ with the explanation of mathematical subjects, which also implies how difficult to match ${\circled1}$ and ${\circled2}$ with ${\circled6}$. Analyzing the reponses of (2), about 70% of the teachers used the introductory activities in the textbook, which led better attention of sudents, while 30% of teachers do not use it because they felt that its inroductory activities had not been adequate for their purposes. Teachers counted inadequacy reasons for not being helpful in class, lack of time or lack of support of students, etc. Those teachers use introductory activities invented of their own for classes. As some results of the study, we suggest firstly that authors of textbooks have to get more informations to provide ways to entcourage students' interest in mathematics classes. The ways must be practical and brain storming as well as More use of computers and calculators and mathematical history are expected. Secondly, we are emphasizing the feedbacks between the textbook authors and the users(teachers and students) through internet. Which, we anticipate, will get better communications between them and be a good foundations of continuous modifications of textbooks.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• Journal of the Korean School Mathematics Society
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• v.19 no.2
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• pp.153-176
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• 2016

The purpose of this study is to suggest ways to promote student engagement by analyzing how a teacher's student engagement strategies and questioning strategies affect class participation and problem solving in a peer mentoring teaching method. As for the purpose, after recording 7th grader's classroom using a peer mentoring and transcribing classroom discourse, we analyzed student engagement strategies for class participation and questioning strategies for helping mathematical concepts and problem solving, and compared mathematics achievements in mid-term and final exams. As results, in learning environments based on comfortable atmosphere, diverse student engagement strategies and appropriate questioning strategies with effectiveness of peer mentoring encouraged students to participate in class by motivating them, helped them to develop mathematical concepts and deepen understanding of problem solving through effective social interactions, and improved student achievement in mathematics. The results can practically help to develop class design considering both student engagement strategy and questioning strategy by specifically presenting a teaching method for promoting student engagement and teacher's contributions to it.

• School Mathematics
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• v.13 no.1
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• pp.127-153
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• 2011

The purpose of this study was to investigate the effect of peer tutoring on mathematical inclination and mathematical communication ability of peer tutor. For the purpose of this study, research questions were established as follows: 1. How does peer tutoring affect to the mathematical inclination of peer tutors? 2. How does peer tutoring affect to the mathematical communication ability of peer tutors? To answer the research questions, four 5th grade peer tutors were selected for qualitative case study in an elementary school located in Goyang-si, Gyeonggi-do. Before and after 11 weeks of peer tutoring in their mathematics classes, mathematical inclination, mathematical communication ability of peer tutors were examined. For qualitative analysis, peer tutors were asked to complete worksheets, self-evaluation, journal for their peer tutoring in daily basis during the experiment. By comparing the scores in mathematical inclination test and mathematical communication test before and after the treatment and analyzing the data gathered for qualitative analysis, the conclusions were drawn as follows: First, Peer tutoring has positive effects on the mathematical inclination of peer tutors. Scores for mathematical inclination of peer tutors after the treatment increased and qualitative analysis showed positive change in their attitude toward mathematics. Second, Peer tutoring has positive effects on the mathematical communication ability of peer tutors. Scores in the performance assessment for mathematical communication ability of peer tutors after the treatment increased. Also qualitative analysis showed that peer tutors tried to develop various ways to solve a problem and explained them to their peer tutee sophisticatedly.

• Journal of Elementary Mathematics Education in Korea
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• v.19 no.4
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• pp.457-484
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• 2015

This study aims to investigate an approach to teach proportional reasoning in elementary mathematics class by analyzing the proportional strategies the students use to solve the proportional reasoning tasks and their percentages of correct answers. For this research 174 sixth graders are examined. The instrument test consists of various questions types in reference to the previous study; the proportional reasoning tasks are divided into algebraic-geometric, quantitative-qualitative and missing value-comparisons tasks. Comparing the percentages of correct answers according to the task types, the algebraic tasks are higher than the geometric tasks, quantitative tasks are higher than the qualitative tasks, and missing value tasks are higher than the comparisons tasks. As to the strategies that students employed, the percentage of using the informal strategy such as factor strategy and unit rate strategy is relatively higher than that of using the formal strategy, even after learning the cross product strategy. As an insightful approach for teaching proportional reasoning, based on the study results, it is suggested to teach the informal strategy explicitly instead of the informal strategy, reinforce the qualitative reasoning while combining the qualitative with the quantitative reasoning, and balance the various task types in the mathematics classroom.