• The Journal of the Korea Contents Association
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• v.17 no.4
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• pp.606-620
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• 2017

The purpose of this study was to develop and validate a Children's Play Disposition Scale(CPDS) which could be used to evaluate children's play patterns and preferences. The participants of this study were parents of 437 5-7-year-old children (age range from 51months to 106months). Preliminary items were developed through a review of relevant research, multiple intelligence theory and scales, confirmation of item adequacy and content validity. After the content validity was confirmed by experts, these items were edited down to a final list of 27 items representing 6 factors identified by exploratory factor analysis. The 6 factors of the scale consists of initiative, linguistic activity, logical-mathematical activity, art and craft, physical activity, and sensitivity respectively. Concurrent validity was established by using correlations between each factor of the CPDS and sub-factors and the total scores of Multiple Intelligence Checklist for preschoolers (Multiple Intelligence Institute Co., Ltd, 2008) and Multiple Intelligence Checklist for elementary schoolers (Multiple Intelligence Institute Co., Ltd, 2007). In addition, the reliability of each factor, as measured by Cronbach's ${\alpha}$, ranged from .53 to .79. The CPDS provides the developmental and educational information for strengthening children's developmental forte and for supporting children's developmental weakness. This scale can be used on developing children's play contents and guiding play methods in the future.

• The Transactions of the Korea Information Processing Society
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• v.7 no.8
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• pp.2484-2496
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• 2000

High speed switches have been developing to interconnect a large number of nodes. It is important to analyze the switch performance under various conditions to satisfy the requirements. Queueing analysis, in general, has the intrinsic problem of large state space dimension and complex computation. In fact, The petri net is a graphical and mathematical model. It is suitable for various applications, in particular, manufacturing systems. It can deal with parallelism, concurrence, deadlock avoidance, and asynchronism. Currently it has been applied to the performance of computer networks and protocol verifications. This paper presents a framework for modeling and analyzing ATM switch using stochastic activity networks (SANs). In this paper, we provide the ATM switch model using SANs to extend easily and an approximate analysis method to apply A TM switch models, which significantly reduce the complexity of the model solution. Cell arrival process in output-buffered Queueing A TM switch with finite buffer is modeled as Markov Modulated Poisson Process (MMPP), which is able to accurately represent real traffic and capture the characteristics of bursty traffic. We analyze the performance of the switch in terms of cell-loss ratio (CLR), mean Queue length and mean delay time. We show that the SAN model is very useful in A TM switch model in that the gates have the capability of implementing of scheduling algorithm.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.81-109
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• 1999

This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

• Education of Primary School Mathematics
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• v.25 no.1
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• pp.57-79
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• 2022

Current mathematics It is necessary to ensure that ratio and proportion concept is not distorted or broken while being treated as if they were easy to teach and learn in school. Therefore, the purpose of this study is to analyze the activities presented in the textbook. Based on prior work, this study reinterpreted the proportional reasoning task from the proportional perspective of Beckmann and Izsak(2015) to the multiplicative structure of Vergnaud(1996) in four ways. This compared how they interpreted the multiplicative structure and relationships between two measurement spaces of ratio and rate units and proportional expression and proportional distribution units presented in the revised textbooks of 2007, 2009, and 2015 curriculum. First, the study found that the proportional reasoning task presented in the ratio and rate section varied by increasing both the ratio structure type and the proportional reasoning activity during the 2009 curriculum, but simplified the content by decreasing both the percentage structure type and the proportional reasoning activity. In addition, during the 2015 curriculum, the content was simplified by decreasing both the type of multiplicative structure of ratio and rate and the type of proportional reasoning, but both the type of multiplicative structure of percentage and the content varied. Second, the study found that, the proportional reasoning task presented in the proportional expression and proportional distribute sections was similar to the previous one, as both the type of multiplicative structure and the type of proportional reasoning strategy increased during the 2009 curriculum. In addition, during the 2015 curriculum, both the type of multiplicative structure and the activity of proportional reasoning increased, but the proportional distribution were similar to the previous one as there was no significant change in the type of multiplicative structure and proportional reasoning. Therefore, teachers need to make efforts to analyze the multiplicative structure and proportional reasoning strategies of the activities presented in the textbook and reconstruct them according to the concepts to teach them so that students can experience proportional reasoning in various situations.

• Journal of Elementary Mathematics Education in Korea
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• v.10 no.1
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• pp.67-87
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• 2006

This study is to recognize a problem in the practice of performance assessment in elementary school, and to find out some suggestive points for improvement of teaching·learning method in elementary mathematics through assessment by reducing time restriction according to assessment through the practice of self-assessment, peer-assessment and observation, and then by reflecting the results of assessment on teaching learning plan. For that, the questions of study set up are as follows ; 1. How should self-assessment and peer-assessment be applied to in elementary mathematics assessment? 2. How should the time for 'let's play an interesting game' be managed for assessment of elementary mathematics? 3. How should the results of assessment be reflected on the Process of teaching and learning of mathematics? To solve these problems, a researcher of this thesis performed self-assessment, peer-assessment on 40 students of second grade under her charge as a class teacher, and applied observation in the time management process for 'let's play an interesting game' for a semester. self-assessment was made by mathematics journal, self-assessment chart, peer-assessment was by the analysis of conversation record among students in the situations of assessment, and observation was by observation of activity when playing with the results data of play analyzed. the concrete methods of application as follows ; First, mathematics journal was applied $1{\sim}2$ times by each unit with reconstruction into the level of second grade on the basis of the preceding-study models. Second, peer-assessment was applied to the unit-assessment time and the play-activities time by the method of recording·analyzing the contents of conversation among students in the process of assessment. Third, mathematical attitude & dispositions of students making use of the self- assessment table were examined referring to the teaching learning plan. Fourth, the time management for 'let's play an interesting game' was made through the prior recognition of play method and the joyful play-activities by use of the play-plate. Assessment depended on analysis of play-activities results of students making use of an observation form. Fifth, the results of self-assessment, peer-assessment, and observation were analyzed, and then they were made use of as self-observation data, of teacher her/his self, or teaching·learning improvement data. Students' self-assessment datum (mathematics diary, self-assessment sheets, conversation contents in the process of assessment) and observation materials (check lists, Play-activity result materials, conversation contents in the process of play) obtained in the process of application was analyzed as follows ; 1. From the practice of self-assessment in form of mathematics journal, I could obtain not only datum showing how much students was understanding the learning aims by unit time and to any degree they reached but also information about their response to learning datum and favorable type of learning. 2. Assessment by self-assessment chart was useful in planning the mathematics teaching learning process because it helps ascertain mathematical attitude & dispositions of students. 3. Through the application of peer-assessment, students had the opportunity of communicating with other students looking back on his/her explaining process, and teachers could obtain basic materials for assessment of students. 4, In case of time management for 'let's play an interesting game', there was natural extension of play made through time-security by prior looking into the method of play-activity, and then, for a remained time, by making children play a new game. 5, I could easily record the activities of students by use of the observation. form, and make use of it as basic data for descriptive assessment. 6, Each kinds of data obtained from the results of assessment was helpful for securing self-observation materials in the process of teaching learning and for their betterment in mathematics subject. However, because they were in the second grade of elementary school and there was an individual difference, some students could not make use of mathematics diary or self-assessment form properly. In case of these students, assessment data would be obtained through interview or observation. And for effective operation of play, its purpose & method and matters that demand special attention when play-acting should be clearly guided. Also, when applying an effective play in addition to play activities in textbook, to lessons, interesting mathematics lessons could be guided.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.99-118
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• 2011

For this case study of gifted education, two classrooms in two locations, show life in general of the gifted educational system. And for this case study the identity of teachers and the gifted, help to activate the mathematically gifted education for these research questions, which are as followed: Firstly, how is the gifted education classroom life? Secondly, what kind of identity do the teachers and gifted students bring to mathematics, mathematics teaching and mathematics learning? Being selected in the gifted children's education center solves the research problem of characteristic and approach. Backed by the condition and the permission possibility, 2 selected classes and 2 people, which are coming and going. Gifted education classroom life, the identity of teachers and gifted students in mathematics and mathematics teaching and mathematic learning. It will be for 3 months, with various recordings and vocal instruction between teacher and students. Collected observations and interviews will be analyzed over the course of instruction. The results analyzed include, social participation, structure, and the formation of the gifted education classroom life. The organization of classes were analyzed by the classes conscious levels to collect and retain data. The classes verification levels depended on the program's first class incentive, teaching and learning levels and understanding of gifted math. A performance assessment will be applied after the final lesson and a consultation with parents and students after the final class. The six kinds of social participation structure come out of the type of the most important roles in gifted education accounts, for these types of group discussions and interactions, students must have an interaction or individual activity that students can use, such as a work product through the real materials, which release teachers and other students for that type of questions to evaluate. In order for the development of meaningful mathematical concepts to formulate, mathematical principles require problem solving among all students, which will appear in the resolution or it will be impossible to map the meaning of the instruction from which it was formed. These results show the analysis of the mathematics, mathematics teaching, mathematics learning and about the identity of the teachers and gifted. Gifted education teachers are defined by gifted math, which is more difficult and requires more differentiated learning, suitable for gifted students. Gifted was defined when higher level math was created and challenged students to deeper thinking. Gifted students think that gifted math is creative learning and they are forward or passive to one-way according to the education atmosphere.

• The Mathematical Education
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• v.44 no.3 s.110
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• pp.457-475
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• 2005

We have inquired on what the statistical classes of the secondary schools had been aiming to, say the epistermlogical objects. And we now appreciate that the main obstacle to the systematic articulation is the lack of anticipation on what the statistical concepts are. This study focuses on the ingredients of the statistical concepts. Those are to be the ground of the systematic articulation of statistic courses, especially of the one for the school kids. Thus we required that those ingredients must satisfy the followings. i) directly related to the contents of statistics ii) psychologically developing iii) mutually exclusive each other as much as possible iv) exhaustive enough to cover all statistical concepts We examined what and how statisticians had been doing and the various previous views on these. After all we suggest the following three concepts are the core of conceptual developments of statistic, say the concept of distributions, the summarizing ability and the concept of samples. By the concepts of distributions we mean the frequency views on each random categories and that is developing from the count through the probability along ages. Summarizing ability is another important resources to embed his probe with the data set. It is not only viewed as a number but also to be anticipated as one reflecting a random phenomena. Inductive generalization is one of the most hazardous thing. Statistical induction is a scientific way of challenging this and this starts from distinguishing the chance with the inevitable consequences. One's inductive logic grows up along with one's deductive arguments, nevertheless they are different. The concept of samples reflects' one's view on the sample data and the way of compounding one's logic with the data within one's hypothesis. With these three in mind we observed Korean Statistic Curriculum from K to 12. Distributional concepts are dealt with throughout but not sequenced well. The way of summarization has been introduced in the 1 st, 5th, 7th and the 10th grade as a numerical value only. One activity on the concept of sample is given at the 6th grade. And it jumps into the statistical reasoning at the selective courses of ' Mathematics I ' or of ' Probability and Statistics ' in the grades of 11-12. We want to suggest further studies on the developing stages of these three conceptual features so as to obtain a firm basis of successive statistical articulation.

• 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.

• Journal of Educational Research in Mathematics
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• v.15 no.1
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• pp.75-105
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• 2005

This study explored a mathematical modeling flow and the effect of interactions among students and between a student and Excel on modeling in a small group modeling environment with Excel. This is a case study of three 8th graders' modeling activity using Excel during their extra lessons. The conclusions drawn from this study are as follows: First, small group modeling using Excel was formed by formulating 4∼10 modeling cycles in each task. Students mainly formed tables and graphs and refined and simplified these models. Second, students mainly formed tables, algebraic formulas and graphs and refined tables considering each variable in detail by obtaining new data with inserting rows. In tables, students mainly explored many expected cases by changing the values of the parameters. In Graphs, students mainly identified a solution or confirmed the solution founded in a table. Meanwhile, students sometimes constructed graphs without a purpose and explored the problem situations by graphs mainly as related with searching a solution, identifying solutions that are found in the tables. Thus, the teacher's intervention is needed to help students use diverse representations properly in problem situations and explore floatingly and interactively using multi-representations that are connected numerically, symbolically and graphically. Sometimes students also perform unnecessary activities in producing data by dragging, searching a solution by 'trial and error' and exploring 'what if' modeling. It is considered that these unnecessary activities were caused by over-reliance on the Excel environment. Thus, the teacher's intervention is needed to complement the Excel environment and the paper-and-pencil environment properly.