• School Mathematics
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• v.18 no.2
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• pp.257-275
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• 2016

The purpose of this study was to investigate the impact of multiple representations on students' understanding of fractions, decimals, and percent. The instructional approach integrating multiple representations was compared to traditional algorithmic instruction, a form of direct instruction. To examine and compare the impact of multiple representations instruction with traditional algorithmic instruction, pre and post tests consisting of five similar items were administered with 87 middle school students. Students' scores in these two tests and their problem solving processes were analyzed quantitatively and qualitatively. The quantitative results indicated that students taught by traditional algorithmic instruction showed higher scores on the post-test than students in the multiple representations group. Furthermore, findings suggest that instruction using multiple representations does not guarantee a positive impact on students' understanding of mathematical concepts. Qualitative results suggest that the limited use of multiple representations during a class may have hindered students from applying their use in novel problem situations. Therefore, when using multiple representations, teachers should employ more diverse examples and practice with multiple representations to help students to use them without error.

• Communications of Mathematical Education
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• v.31 no.1
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• pp.103-123
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• 2017

Mathematical tasks in general introduce and deal with real-life situations, and they derive to students' thinking fluently in solving the given tasks. The tasks might be considered as an important and significant factor to lead a successful mathematical teaching and learning situation. MiC Textbook is a representative one showing such good examples and tasks. This study explores concretely and in detail the cognitive demand level of mathematical tasks, by the subject of MiC Textbook. To accomplish this, this study is to reconstruct more elaborately the analysis framework developed by Hwang and Park in 2013. The framework basically was set up utilizing 'the cognitive demand level' suggested by Stein, et, al. The cognitive demand level is divided into two levels such as low level and high level. The low level is comprized of two elements such as Memorization Tasks(MT), Procedures Without Connections Tasks(PNCT), and high level is Procedures With Connections Tasks(PWCT), and Doing Mathematics Tasks(DMT). This study deals with the tasks on the area of 'data analysis and statistics' in MiC 1, 2, 3 level Textbook. As a result, mathematical tasks of MiC Textbook led learners to deal with and understand mathematical content for themselves, and furthermore to do leading roles for checking and reinforcing the content. Also, mathematical tasks of MiC Textbook are comprized of the tasks suitable to enhance mathematical thinking ability through communication. In addition, mathematical tasks of MiC Textbook tend to offer more learning opportunity to learners' themselves while the level of MiC Textbook is going up.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.319-343
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• 2006

The purpose of this study is to investigate how fifth and sixth graders recognize average and to find out suggestions for teaching/learning methods of average by examining which difference there is depending on the way of the word problem presentation. For the this purpose, was conducted experiment study with the way of the world problem presentation set up as experimental treatment. The conclusions drawn from the results obtained in the this study were as follows : First, since students who did not learn the regular course of average had various informal concepts already, it is needed to consider handling more various concepts of average in order to enable students to expand flexible thoughts. Second, compared with fifth and sixth graders showed a wide difference in informal concepts of average depending on the way of the word problem presentation. In expect data with given average, concepts of mean as algorithm, balance point, and mode indicated similar percentage, while in estimate average with given data, the percentage of students who showed the concept of mean was very high at 67.6%. That may be because problems related to mean in the current textbooks are items of 'estimate average with given data', so in types of 'estimate average with given data', students solve questions with mean as algorithm without considering situations of problems. This result suggests that it is necessary to diversify the way of the word problem presentation even in textbooks. Third, as a result of analyzing informal concepts of average, there was significant difference in grades. In addition, the results suggested that there would be difference in the concepts of average depending on gender or attributes of discrete quantity and continuous quantity.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.69-79
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• 2011

The purpose of this study is to analyze 3rd, 4th and 5th graders' probability understanding and raise issues concerning instructional methods and search for the possibility of learning probability. For the purpose, a descriptive study through pencil-and-paper test regarding fairness, sample space, probability of event, probability comparison, independence and conditional probability was conducted. The following conclusions were drawn from the results obtained in this study. First, the 3rd, 4th, and 5th grade students scored the highest in the sample space questions. In descending order of skill, the students scored the highest in sample space following probability of events, fairness and probability comparison. Second, however, the level of independence understanding was low. There was no meaningful differences between grades and the conditional probability was the least understood. The independence is difficult to develop naturally according to cognitive development. The conditional probability recognizing the probability of an event changes in non-replacement situations was very difficult for these students. Third, there were significant differences between the 5th graders and the 3rd and 4th graders in the probability comparison questions. It shows that 5th graders understand the concept of proportion when they compare equal ratio probability of an event. The 3rd graers could do different ratio probability of an event more easily than equal ratio probability of an event after they were instructed on probability comparison.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.3
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• pp.101-111
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• 2020

Companies struggle to make their best products with high quality and service at a competitive price in global markets. However, customer needs and requirements keep changing with a variety of situations. Companies that face the changes can not stay the same and make an effort to adapt themselves to new circumstances. They would probably review the overall management system that is currently implementing to improve management efficiency. Among other things, quality might be considered to be a crucial element if they are manufacturing industries to be sustained in global markets. KSA (Korean Standards Association) is a government-affiliated organization under the Ministry of Trade, Infrastructure, and Energy. It is a Korean standards provider for quality and service industry. KSA confers national commendations for organizations, quality circles, artisans, QCEC (Quality Competitive Excellent Company), and the most honorable KNQA (Korean National Quality Award) every year. KSA established KNQA on the basis of Malcom Baldrige National Quality Award, Deming Prize, and European Quality Award. Research on quality awards shows that there are many similarities in the framework. Although KSA summarizes two factors for 13 evaluation indicators in the quality competitive excellent model of QCEC, the categorization is ambiguous to explain them according to earlier studies. We performed a deep analysis of foreign quality awards and background for KNQA and QCEC. We conducted a content analysis of KNQA and QCEC and matched evaluation items that were closely related. We proposed a quality competitiveness model with three factors, Technology, System, and Tools, summarizing 13 evaluation indicators in QCEC. Based on audit data for six years from 2012 to 2017 we carried out a confirmatory factor analysis for the proposed model by examining the model validity and fitness.

• The Mathematical Education
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• v.61 no.3
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• pp.441-456
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• 2022

The purpose of the current study is to report a part of our larger project whose focus is to understand a relationship between students' units coordination and K-12 school mathematics. In particular, in this paper we report how students who exhibit distinct levels of units coordinations used their knowledge of proportion to solve quadratic function problems of the form y = ax². To this end, three 7th grade students all of whom assimiliated whole number problem situations with three levels of units but showed different levels for fraction problems were chosen. We carried out clinical interviews not only to understand their ability to coordinate units but to understand their problem solving process of proportion and the quadratic function problems. The analysis suggest that their abilities to coordinate units influenced their ways to solving proportion problems, and in turn influenced their ways to solve the specific form of quadratic functions. We have finalized our study by discussing how students' ability to construct and coordinate units, their proportion knowledge, and their knowledge associated with expressing the specific type of quadractic functions could be related.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.257-276
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• 2023

Mathematical modeling can be described as a series of processes in which real-world problem situations are understood, interpreted using mathematical methods, and solved based on mathematical models. The effectiveness of mathematics instruction using mathematical modeling has been demonstrated through prior research. This study aims to explore insights for mathematical modeling instruction by analyzing the metacognitive characteristics shown in the mathematical modeling cycle, according to the mathematical thinking styles of elementary math gifted students. To achieve this, a mathematical thinking style assessment was conducted with 39 elementary math gifted students from University-affiliated Science Gifted Education Center, and based on the assessment results, they were classified into visual, analytical, and mixed groups. The metacognition manifested during the process of mathematical modeling for each group was analyzed. The analysis results revealed that metacognitive elements varied depending on the phases of modeling cycle and their mathematical thinking styles. Based on these findings, didactical implications for mathematical modeling instruction were derived.

• Journal of the Korea Society of Computer and Information
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• v.28 no.7
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• pp.77-84
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• 2023

This research originated from the need to enhance the security of secure multiparty computation by ensuring that participants involved in multiparty computations provide truthful inputs that have not been manipulated. While malicious participants can be involved, which goes beyond the traditional security models, malicious behaviors through input manipulation often occur in real-world scenarios, leading to privacy infringements or situations where the accuracy of multiparty computation results cannot be guaranteed. Therefore, in this study, we propose a signature scheme applicable to secure multiparty technologies, combining it with secret sharing to strengthen the accuracy of inputs using authentication techniques. We also investigate methods to enhance the efficiency of authentication through the use of batch authentication techniques. To this end, a scheme capable of input certification was designed by applying a commitment scheme and zero-knowledge proof of knowledge to the CL signature scheme, which is a lightweight signature scheme, and batch verification was applied to improve efficiency during authentication.

• The Mathematical Education
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• v.62 no.4
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• pp.457-471
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• 2023

Measurement is an imperative content area of early elementary mathematics, but it is reported that students' understanding of units in measurement situations is insufficient despite its importance. Therefore, this study examined lower-grade elementary students' quantitative reasoning of units in length measurement by identifying the levels of reasoning of units. For this purpose, we collected and analyzed the responses of second-grade elementary school students who engaged in a set of length measurement tasks using an open number line in terms of unitizing, iterating, and partitioning. As a result of the study, we categorized students' quantitative reasoning of unit levels into four levels: Iterating unit one, Iterating a given unit, Relating units, and Transforming units. The most prevalent level was Relating units, which is the level of recognizing relationships between units to measure length. Each level was illustrated with distinct features and examples of unit reasoning. Based on the results of this study, a personalized plan to the level of unit reasoning of students is required, and the need for additional guidance or the use of customized interventions for students with incomplete unit reasoning skills is necessary.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.735-760
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• 2009

Most of every teachers' life is occupied with his or her instruction, and a classroom is a laboratory for mutual development between teacher and students also. Namely, a teacher's professionalism can be enhanced by circulations of continual reflection, experiment, verification in the laboratory. Professional development is pursued primarily through teachers' reflective practices, especially instruction practices which is grounded on $Sch\ddot{o}n's$ epistemology of practices. And a thorough penetration about situations or realities and an exact understanding about students that are now being faced are foundations of reflective practices. In this study, at first, we explored the implications of earlier studies for discussing a teacher's practice. We could found two essential consequences through reviewing existing studies about classroom and instructions. One is a calling upon transition of perspectives about instruction, and the other is a suggestion of necessity of a teachers' reflective practices. Subsequently, we will talking about an instance of a middle school mathematics teacher's practices. We observed her instructions for a year. She has created her own practical knowledges through circulation of reflection and practices over the years. In her classroom, there were three mutual interaction structures included in a rich expressive environments. The first one is students' thinking and justifying in their seats. The second is a student's explaining at his or her feet. The last is a student's coming out to solve and explain problem. The main substances of her practical know ledges are creating of interaction structures and facilitating students' spontaneous changes. And the endeavor and experiment for diagnosing trouble and finding alternative when she came across an obstacles are also main elements of her practical knowledges Now, we can interpret her process of creating practical knowledge as a process of self-directed professional development when the fact that reflection and practices are the kernel of a teacher's professional development is taken into account.