• The Mathematical Education
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• v.55 no.1
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• pp.41-71
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• 2016

The purpose of this study is to investigate elementary students' communication in process of applying mathematical modeling. For this study, 22 fifth graders in an elementary school were observed by applying mathematical modeling process (presentation of problem ${\rightarrow}$ model inducement activity ${\rightarrow}$ model exploration activity ${\rightarrow}$ model application activity). And the level of their communication with their activity sheets and outputs, observation records and interviews were also analyzed. Additionally, by analyzing the activity cases of and , this study researched that what is a positive influence on students' communication skills. Whereas showed significant advance in the level of communication, who communicated actively on speaking area but not on every areas showed insensible changes. To improve communication abilities, cognitive tension and debate situation are needed. This means, mathematical education should continuously provide students with mathematical communication learning, and a class which contains mathematical communication experiences (such as mathematical modeling) will be needed.

• The Mathematical Education
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• v.41 no.2
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• pp.157-172
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• 2002

The purpose of this study is to improve middle students'mathematical communication ability. We designed the mathematics instruction model based on Vygotsky's ZPD to develop the mathematical communication ability, and applied to 2nd grade students in Middle School. And we investigated the significant differences between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation in aspects of learning achievement, mathematical disposition, and mathematical communication abilities. The results of the study are as follows : 1. There is no significant difference in learning achievement within significance level .05 between the group which was instructed with mathematical communication and the group which was instructed with teacher's traditional explanation by t-test. 2. There is a significant difference in reflection within significance level .01 and in self-confidence within significance level .10 by MANCOVA. 3. There is a significant difference in mathematical communication ability within significance level .01 between two groups by covariance analysis. In particular, there is a significant difference in reading within significance level .01 and in speaking within significance level .05 by t-test.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.135-145
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• 2011

When mathematicians solve the new problems, they present the solutions to their colleagues for getting the approval. If the solution is accepted, it will be theorems. This phenomenon also happens to classrooms in elementary and secondary school. That is main reason to emphasize mathematical communication activities in mathematics education. This study is aimed to develop teaching and learning model for the improvement of mathematical communication ability, applicate the teaching and learning model to two groups and analyze for mathematical thoughts. This study is a case study of 3rd grader's activities. Eight students, four are group applied the teaching and learning model and four are traditional group. The results have been drawn as follows: First, students in the teaching and learning model group induced richer interactions for student's understanding and investigation when we compare to those of traditional group. Second, students in the teaching and learning model group have the chance to explain their thoughts. And we can observe students to clear on their thought through speaking and discussing. This model makes students to enhance organizing, forming and clearing in their mathematical thoughts and is effective to estimate of students thought for teacher.

• ETRI Journal
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• v.43 no.3
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• pp.524-537
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• 2021

High-performance Linpack (HPL) is among the most popular benchmarks for evaluating the capabilities of computing systems and has been used as a standard to compare the performance of computing systems since the early 1980s. In the initial system-design stage, it is critical to estimate the capabilities of a system quickly and accurately. However, the original HPL mathematical model based on a single core and single communication layer yields varying accuracy for modern processors and accelerators comprising large numbers of cores. To reduce the performance-estimation gap between the HPL model and an actual system, we propose a mathematical model for multi-communication layered HPL. The effectiveness of the proposed model is evaluated by applying it to a GPU cluster and well-known systems. The results reveal performance differences of 1.1% on a single GPU. The GPU cluster and well-known large system show 5.5% and 4.1% differences on average, respectively. Compared to the original HPL model, the proposed multi-communication layered HPL model provides performance estimates within a few seconds and a smaller error range from the processor/accelerator level to the large system level.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.141-168
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• 2010

Mathematical communication is necessary to exchange mathematical idea among participants in teaching-learning process. The promotion of mathematical communication competence is clearly stated in many parts of the 2007 revised curriculum. As a result, mathematical communication tasks are contained in 'high school Mathematics' textbook. At this point of time when increasing importance of mathematical communication is realized, we will check over mathematical communication and analyze communicative tasks corner in 'high school Mathematics' textbook in this paper And thereby we hope this study help prepare for practical communicative tasks corner suggesting a way for invigoration of mathematical communication.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.463-485
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• 2011

This study was to investigate the effects of mathematical history-based mathematics teaching on mathematical communication and attitudes of elementary students, through selecting mathematical history content to apply to elementary mathematics and devising an instruction model to use effectively. For this purpose, while the experimental group received instruction using mathematical history and the comparative group lecture-based instruction using the common textbook, both quantitative and qualitative methods were employed to analyze gathered data. To conclusion, first, instructions using mathematical history were helpful for increasing the student's participation in communication, and secondly helped the students justify their opinions to others with mathematical logic.

• The Mathematical Education
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• v.55 no.2
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• pp.209-232
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• 2016

This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.

• Journal of Elementary Mathematics Education in Korea
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• v.12 no.2
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• pp.165-183
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• 2008

This study is to help to understand the influence of exchange writing activity in the elementary mathematics on students' mathematical communication skill. Various technical activities had been implemented during the classes and the ideas from those activities had been interpreted into writings in the final stage of the classes. Those writings, then, were distributed to other students or teachers in order to devise a teaching model for exchange writing, which is to be applied to the 3rd grade classes and to identify the influence on the in mathematical communication skill. From this study, we could get such conclusions as follows: First, there was considerable difference between experimental group practicing exchange writing and control group engaging in normal learning activities in the progress of their mathematical communication skill (group discussion), writing skill and expressivity when examining their average communication skill using t-method. Similar trend had been witnessed when self-evaluating their mathematical communication skill. Second, when it comes to the mathematical tendency, experimental group showed a higher tendency in positiveness compared to the control group. Therefore, we might conclude that the exchange writing has a positive influence on the students' mathematical tendency, especially on their curiosity or interest in teaming, willingness to study and their comprehension of its importance.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.305-321
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• 2019

Rapid demographic changes such as international marriages and immigration have led to the transition of Korea to a multicultural society, thereby causing the need for education for multicultural students. In particular, there is a growing need to support Korean Language Learners (KLLs) who learn in Korean in their classrooms and whose native language is a foreign language. This study aims to adapt some teaching strategies of the SIOP model developed in the U.S. for English Language Learners(ELLs) to fit classroom situations in Korea and apply them to the Korean language learners to analyze the features of mathematical communication and to examine the possibility of a change in mathematical errors. Specifically, three KLLs in 5th grade participated in seven geometry lessons adapting some characteristics of SIOP model and then, their mathematical communication and mathematical errors were analyzed. The results of this study are expected to provide didactical implications for identifying characteristics of KLLs and for setting direction for teaching them mathematics.

• The Mathematical Education
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• v.49 no.2
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• pp.223-246
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• 2010

Goos(2004) introduced educational researchers' demand for change on the way that mathematics is taught in schools and the series of curriculum documents produced by the National council of Teachers of Mathematics. The documents have placed emphasis on the processes of problem solving, reasoning, and communication. In Korea, the national curriculum documents have also placed increased emphasis on mathematical activities such as reasoning and communication(1997, 2007).The purpose of this study is to analyze the impact of inquiry-oriented instruction with guided reinvention on students' mathematical activities containing communication and reasoning for science high school students. In this paper, we introduce an inquiry-oriented instruction containing Polya's plausible reasoning, Freudenthal's guided reinvention, Forman's sociocultural approach of learning, and Vygotsky's zone of proximal development. We analyze the impact of mathematical findings from inquiry-oriented instruction on students' mathematical activities containing communication and reasoning.