• 한국수학교육학회지시리즈D:수학교육연구
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• 제25권4호
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• pp.285-309
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• 2022

A large body of previous studies investigated mathematical tasks by analyzing the design process prior to lessons or textbooks. While researchers have revealed the significant roles of mathematical tasks within written curricular, there has been a call for studies about how mathematical tasks are implemented or what is experienced and learned by students as enacted curriculum. This article proposes a mathematical task analytic framework based on a holistic definition of tasks encompassing both written tasks and the process of task enactment. We synthesized the features of the mathematical tasks and developed a task analytic framework with multiple dimensions: breadth, depth, bridging, openness, and interaction. We also applied the scoring rubric to analyze three multiplication tasks to illustrate the framework by its five dimensions. We illustrate how a series of tasks are analyzed through the framework when students are engaged in multiplicative thinking. The framework can provide important information about the qualities of planned tasks for mathematics instruction (proactive) and the qualities of implemented tasks during instruction (reactive). This framework will be beneficial for curriculum designers to design rich tasks with more careful consideration of how each feature of the tasks would be attained and for teachers to transform mathematical tasks with the provision of meaningful learning activities into implementation.

• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.467-486
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• 2007

이 논문은 스프레드시트를 활용한 수학적 모델링에서 스프레드시트 환경이 수학적 모델의 정교화과정에 어떤 영향을 미치는 지를 고찰한 것이다. 좀 더 자세히 살피면 수학적 모델링에서 스프레드시트 모델의 활용은 학생이 분석 불가능한 수학적모델도 분석할 수 있도록 해줌으로써 모델을 단순화하지 않고, 대신 모델을 정교화 할 수 있는 기회를 제공하고 수학적 개념을 확장해 나갈 수 있음을 보였다. 또한 수학적 모델을 스프레드시트 모델로 변환하여, 수학적 모델로부터 수학적 결론을 얻는 단계를 거치지 않고도 실세계 상황을 해석하고 설명할 수 있는 기회를 제공할 수 있음을 보였다.

• 대한수학회보
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• 제23권2호
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• pp.202-202
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• 1986

• 대한수학교육학회지:학교수학
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• 제1권1호
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• pp.123-133
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• 1999

For an appropriate assessment in mathematics, students should play an active role in their learning by becoming aware of what they have learned in mathematics and by being able to assess their attainment of mathematical knowledge. The process of actively examining and monitoring students' own progress in learning and understanding of their mathematical knowledge, process, and attitude is called self-assessment, Researchers in mathematics education have found some important facts about the meta-cognitive process which is related to self-assessment : i. e. meta-cognition progress is composed of being aware of ones' own personal thinking of content knowledge and cognitive process(self-awareness) and engagement in self-evaluation. Tipical method for self-assessment in mathematics developed upon above finding about meta-cognitive progress is describing about students' knowledge and their problem solving strategies. In the beginning of the description in mathematics about themselves, students are required to answer which part they know and which part they don't know. Self-assessment of students' attitudes and dispositions can be just as important as assessment of their specific mathematical abilities. To make the self-assessment method a success, teachers should let students' have confidence and earn their cooperation by let them overcoming fear to be known the their ability to other students. In conclusion, self-assessment encourages students to assume an active role in development of mathematical power. For teachers, student self-assessment activities can provide a prism through which the development of students' mathematical power can be viewed.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권3호
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• pp.217-231
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• 2004

The purpose of this paper is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process (MPSP). The proposed research question is as follows: Can the MPSP activate metacognitive abilities of high school students in the pencil-and-paper environment using guidance material for metacognitive activities\ulcorner To solve this question, two case studies have been carried out. Two students for the study were selected via informal interview. They voluntarily took part in 13 experimental lectures. The activating paths of their metacognitive abilities in the MPSP were chronically described and analyzed. All the activating processes of the students focusing on the aspects of metacognitive behaviors were analyzed by means of interview, observation, self-report, and activity data. The two high school students participating in the MPSP voluntarily recognized and reflected their deficiencies in metacognitive abilities, and therefore maximized their own performance. They made quite significant progress in the course of activating their metacognitive abilities through voluntary participation and gained greater confidence in the MPSP. Hence they have become good problem solvers. They expressed not only the factors influencing their behavior but also their self-awareness during the metacognitive activities. In the long run, this experiment will increase possibilities for the internalization of the metacognitive process.

• 대한수학회지
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• 제42권6호
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• pp.1215-1230
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• 2005

In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.

• 대한수학회지
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• 제35권1호
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• pp.207-224
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• 1998

After the review of known results on the connections between selfsimilar processes with independent increments (processes of class L) and selfdecomposable distributions and between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions, dichotomy of those processes into transient and recurrent is discussed. Due to the lack of stationarity of the increments, transience and recurrence are not expressed by finiteness and infiniteness of mean sojourn times on bound sets. Comparison in transience-recurrence of the Levy process and the process of class L associated with a common distribution of class L is made.

• 한국시뮬레이션학회논문지
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• 제11권4호
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• pp.69-80
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• 2002

This study deals with the productivity improvement on a flow production system with the consideration of line-balancing. In a flow production system, similar product models are produced on a same assembly line, the predefined process order and the limitation of total worker number. The system can be increased the work-in -process(WIP) inventory and the worker's idle time. In this study, the worker assignment model is developed to assign evenly workload of process to each product model in such a manner that each process has the different number of worker. This worker assignment model is the mathematical model that determines worker number in each process such that the idle time of processes is reduced and the utilization of worker is improved. We use a simulation technique to simulate the production line proposed by the mathematical model and apply real production line. With the result of simulation, this study analyzes the propriety of production line and proposes the alternatives of new production line

• Fibers and Polymers
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• 제5권4호
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• pp.309-315
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• 2004

In this paper, a comparison between a mathematical and an experimental method for the evaluation. of some process components of polyester microfibre dyeing is presented. In the experimental part, a dyeing procedure was chosen, K/S values of the dyed samples were measured and the coefficients of the mathematical formula presented in the mathematical part were obtained. K/S values of different dyeing procedures were also measured. In the mathematical part, predicted K/S values were calculated by a novel formula. The results of the two methods were then compared. According to the results obtained, the mathematical formula presented in this study can be used for calculating the predicted K/S values at lower dye concentrations.

• 한국수학교육학회지시리즈A:수학교육
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• 제56권3호
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• pp.257-280
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• 2017

The purpose of this study is to analyze middle school students' learning characteristics they showed on the inquiry-based learning process of circumcenter using various teaching tools, and then to identify the effects of using teaching tools in the middle school students' learning process of circumcenter. For this purpose, we developed teaching materials for inquiry-based learning of circumcenter using textbook, origami, ruler and compass, GeoGebra and sand experiment. Then we applied them on the learning process of circumcenter for five groups of middle school students. From the analyzing of audio/video materials and documents which are collected from the process of participants' inquiry-based learning of circumcenter, we identified the following results. First, inquiry-based learning of circumcenter using various teaching tools promoted mathematical discourses among participants of this study. For example, they conjectured mathematical properties or justified their opinions after manipulated teaching tools in the process of learning circumcenter. Second, inquiry-based learning of circumcenter using various teaching tools promoted participants' divergent thinking. They tried many inquiry methods to find new mathematical properties relate to circumcenter. For example, they tried many inquiry methods to know whether there is unique circle containing four vertices of given quadrangles. Third, we found several didactic implications relate to inquiry-based learning of circumcenter using various teaching tools which are due to characteristics of teaching tools themselves. Participants showed several misconceptions about mathematical properties during they participated inquiry-based activity for learning of circumcenter using various teaching tools. We identified their misconceptions were not due to any other variables containing their learning characteristics but to characteristics of teaching tools.