• Journal of Educational Research in Mathematics
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• v.22 no.3
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• pp.401-427
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• 2012

The recent Korean mathematics curriculum stresses to teach mathematics focusing on mathematical process composed of problem solving, reasoning and communication. To be successful in applying the rationale of the process-focused mathematics education, the assessment practice in classrooms should be also centered on mathematical process. In this study we conducted a large-scale survey on teachers' perspectives about the process-focused mathematics assessment. First, we surveyed teachers' opinion on current assessment practices in school mathematics related to regular school exams and performance assessments. Second, we investigated teachers' perception on mathematical process components such as problem solving, reasoning, and communication regarding how they should be assessed. Finally, we examined the difference of teachers' opinion according to their teaching experience, city size, and the type of school. Based on the results, we discussed implications for mathematics assessment and process-focused mathematical assessment.

• School Mathematics
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• v.12 no.4
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• pp.507-530
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• 2010

The purpose of this study was to help teachers for their teaching practice by analyzing the excellent lesson videos. To analyze the lesson videos between teacher and students, the researchers classified excellent lesson classes into four types as 'Discourse type', 'Representation type', 'Operation type' and 'Complex type' by mathematical communication pattern and kept close watch each lesson videos. Mathematical communication of the best discourse type classroom was analyzed in terms of questioning, explaining, and the sources of mathematical ideas. As a result, the number of Discourse type classes was 6. Operation type classes were 16 owing to characteristic of elementary class. Representation type class was 1 and Complex type class was 1. The Classes excluding Operation type was more planned by teachers. Teachers need to know about mathematical communication accurately because they designed just 5 lesson plan considering mathematical communication of students and only one of the lessons has the intellectual purpose of communication. Furthermore teachers should reflect questioning for student-to-student in their lesson plan.

• Communications of Mathematical Education
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• v.21 no.3
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• pp.407-430
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• 2007

The extreme didactic phenomena that occur by ignoring or overemphasizing the process of personalization/contextualization, depersonalization/decontextualization of mathematical knowledge is always in our teaching practice and in fact, seems to be a kind of phenomena that suppress teachers psychologically or didactically. The study of the problems on error, misconception or obstacles revealed by students has been done continuously, but that of the extreme didactic phenomena revealed by teachers has not. In this study, I will explain four extreme didactic phenomena and help you understand them by giving various examples from several case studies and analyzing them. And also, I will discuss the way to overcome the extreme didactic phenomena in the mathematical class, based on this analysis. This thesis will become a standard of didactic phenomena that are proceeded extremely by having teachers reconsider their own classes and furthemore, will offer the research data for considering better didactic situation.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.477-493
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• 2018

The six core competencies included in the mathematics curriculum Revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the creativity and convergence competency is very important for students' enhancing much higher mathematical thinking. Based on the creativity and convergence competency, this study selected the five elements of the creativity and convergence competency such as productive thinking element, creative thinking element, the element of solving problems in diverse ways, and mathematical connection element, non-mathematical connection element. And also this study selected the content(chapter) of the graph in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the five elements of the creativity and convergence competency were shown in each textbook.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.653-674
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• 2023

The development of mathematical problem solving ability and the making(transforming) mathematical problems are consistently emphasized in the mathematics curriculum. However, research on the problem making methods or the analysis of the characteristics of problem making methods itself is not yet active in mathematics education in Korea. In this study, we concretize the method of deductive problem making(DPM) in a different direction from the what-if-not method proposed by Brown & Walter, and present the characteristics and phases of this method. Since in DPM the components of the problem solving process of the initial problem are changed and problems are made by going backwards from the phases of problem solving procedure, so the problem solving process precedes the formulating problem. The DPM is related to the verifying and expanding the results of problem solving in the reflection phase of problem solving. And when a teacher wants to transform or expand an initial problem for practice problems or tests, etc., DPM can be used.

• Communications of Mathematical Education
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• v.30 no.2
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• pp.161-178
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• 2016

Mathematics problem based learning(PBL), which has recently attracted much attention, is a teaching and learning method to increase mathematical ability and help learning mathematical concepts and principles through problem solving using students' mathematical prerequisite knowledge. In spite of such a quite attention, it is not easy to apply and practice PBL actually in school mathematics. Furthermore, the recent instructional situations or environments has focused on student's self construction of their learning and its process. Because of this reason, to whom is related to mathematics education including math teachers, investigation and recognition on the degree of students' acquisition of mathematical thinking skills and strategies(for example, inductive and deductive thinking, critical thinking, creative thinking) is an very important work. Thus, developing mathematical thinking skills is one of the most important goals of school mathematics. In particular, recently, connection or integration of one subject and the other subject in school is emphasized, and then mathematics might be one of the most important subjects to have a significant role to connect or integrate with other subjects. While considering the reason is that the ultimate goal of mathematics education is to pursue an enhancement of mathematical thinking ability through the enhancement of problem solving ability, this study aimed to implement basically what is the meaning of the integrated thinking ability in problem based learning theory in Mathematics. In addition, using historical materials, this study was to develop mathematical materials and a sample of a concrete instructional guideline for enhancing integrated thinking ability in problem based learning program.

• Education of Primary School Mathematics
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• v.20 no.4
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• pp.253-266
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• 2017

The purpose of the study was to investigate the perceptions of Elementary school teachers on mathematics instruction. To do this, 7 test items were developed to obtain data on teacher's perception of mathematics instruction and 73 teachers who take mathematical lesson analysis lectures were selected and conducted a survey. Since the data obtained are all qualitative data, they were analyzed through coding and similar responses were grouped into the same category. As a result of the survey, several facts were found as follow; First, When teachers thought about 'mathematics', the first words that come to mind were 'calculation', 'difficult', and 'logic'. It is necessary for the teacher to have positive thoughts on mathematics and mathematics learning, and this needs to be stressed enough in teacher education and teacher retraining. Second, the reason why mathematics is an important subject is 'because it is related to the real life', followed by 'because it gives rise to logical thinking ability' and 'because it gives rise to mathematical thinking ability'. These ideas are related to the cultivating mind value and the practical value of mathematics. In order for students to understand the various values of mathematics, teachers must understand the various values of mathematics. Third, the responses for reasons why elementary school students hate mathematics and are hard are because teachers demand 'thinking', 'because they repeat simple calculations', 'children hate complicated things', 'bother', 'Because mathematics itself is difficult', 'the level of curriculum and textbooks is high', and 'the amount of time and activity is too much'. These problems are likely to be improved by the implementation of revised 2015 national curriculum that emphasize core competence and process-based evaluation including mathematical processes. Fourth, the most common reason for failing elementary school mathematics instruction was 'because the process was difficult' and 'because of the results-based evaluation'. In addition, 'Results-oriented evaluation,' 'iterative calculation,' 'infused education,' 'failure to consider the level difference,' 'lack of conceptual and principle-centered education' were mentioned as a failure factor. Most of these factors can be changed by improving and changing teachers' teaching practice. Fifth, the responses for what does a desirable mathematics instruction look like are 'classroom related to real life', 'easy and fun mathematics lessons', 'class emphasizing understanding of principle', etc. Therefore, it is necessary to deeply deal with the related contents in the training courses for the improvement of the teachers' teaching practice, and it is necessary to support not only the one-time training but also the continuous professional development of teachers.

• School Mathematics
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• v.13 no.1
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• pp.37-63
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• 2011

This research had investigated the teaching practice in the mathematics classrooms with immigrant students to describe how effectively mathematics teachers create inclusive learning environment of mathematics. The analysis of the data from the elementary schools suggests that teaching practice in the class was consistent to the criteria for 'contextualization of students' lived experience' and 'mathematical conversation'. However, while the quantitative results suggested that the teachers showed high expectation to their students in their teaching, the qualitative analysis revealed the teacher's beliefs and attitudes against providing equitable educational opportunity for every student. In the middle school classrooms, it was found that the teaching practices were not compatible to the goals of multicultural mathematics education. The analysis of the survey data regarding teachers' multicultural competence suggests that the teachers possessed rather advan]ced understanding of multicultural mathematics education but they need materials and pedagogy for classroom teaching from multicultural perspectives.

• Journal of the Korean Society of Costume
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• v.51 no.2
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• pp.181-192
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• 2001

Men study the nature in two ways. Scientists and mathematicians inquire a branch of those two ways. Mathematical formulations are the tools and the expressions of their nature. Meanwhile, the other branch, the art, alms for different inquiry. Instead of formulating the nature, the artists create their masterpieces from their ultimate source, the Mother Nature. For thousands of years these two branches have grown together, influencing each others work. Some mathematicians find that formulation, are not enough to fully express the beauty of nature. It is believed that such a simple expression, formula, easily omits the careful details of nature. The nature is simply too chaotic to be shaped with a formula. Of those mathematicians, Mandelbrot, one of the first to realize this matter, introduced the world of fractal geometry. Fractals give new possibilities. It allows us not to limit ourselves to linear prospect, rather a whole new view of this chaotic beauty of the nature. A popular practice to understand fractals is in costume design. The artistic characteristic and organization mechanism is appalled to costumes. Meanwhile, another practice, rather aggressive, is using computer to create an image of fractals. This image is then used for motives to generate artistic expressions. Computer and paper ironing technique is used for fashion illustration in this research. The works were synthesized arid transformed from computer programs. To add more traditional painting touch to this work, Paper ironing technique was used. Since the of effect of this technique is so random, irregular, and unordered, it corresponds to fractal consideration. This thesis asserts an another prospect to fractal as a structural way of describing nature ailed fashion illustration, rather than restricting it to only mathematical theory.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.433-457
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• 2022

An effective teacher community helps the participating teachers improve their instructional quality. This study reports a teacher community consisting of 15 elementary school teachers and one teacher educator. This paper analyzed 15 mathematics lessons in which the teachers implemented the five practices for orchestrating productive mathematics discussions by Smith and Stein (2018) based on the grade-specific discussions as well as the whole community's discussions. The results of this study showed that the overall levels of each practice either increased gradually or maintained at the highest Level 4, as mathematics lessons had been implemented. Specifically, the following practices were quite successful: setting goals for a lesson, selecting an appropriate task, anticipating student responses, and selecting student solutions. However, both sequencing and connecting student solutions were implemented at various levels. Monitoring student work tended to remain at Level 2 which included incorrect implementation of the practice. This paper closes with implications related to the skillful implementation of the five practices through a teacher community.