• Journal of the Korean School Mathematics Society
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• v.19 no.1
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• pp.103-122
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• 2016

The purpose of this study was to analyze the sentences related with mathematical modeling in the third and fourth grade mathematics textbooks in accordance with changing of Korean mathematics curricula. In the preliminary analysis, the researchers used the criteria that Kim(2010) had analyzed Mathematics in Context[MiC], and analyzed South Korean textbooks from the perspective of mathematical modeling. The researchers revised them for the analysis criteria among South Korean elementary mathematics textbooks and employed them as the analysis framework of the present study. From the mathematical modeling perspective, the study reached the following conclusions in accordance with the change of textbooks from the 7th curriculum to the 2009 revised curriculum. The contexts of real-world situations presented in the textbooks are increased in all areas except Probability and Statistics areas, the methods of expression of mathematical model are diversified in all areas except Patterns area, and the communication types are also diversified and frequencies increased in all areas except Patterns area. Based on this research, several suggestions were made for the development of future textbooks.

• Communications of Mathematical Education
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• v.37 no.3
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• pp.329-348
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• 2023

This study is necessary for the stable settlement of the 2022 revised mathematics curriculum 'data and possibility' area. This study was conducted centering on literature analysis. The purpose of this study is to realize statistics education in line with the 2022 revised mathematics curriculum. This purpose was achieved by examining the statistics learning contents of the 2022 revised curriculum, analyzing Chinese mathematics curriculum, and analyzing Chinese mathematics textbooks. In this study, the following studies were conducted. First, five elements were extracted through the analysis of the 'statistics and probability' area of the Chinese mathematics curriculum. The extracted elements are the 4th grade goals, synthesis and practice content areas, achievement standards for statistics and probability (6), (9), and (11). Second, examples presented in Chinese mathematics textbooks and Chinese curriculum appendices related to the extracted elements were analyzed. Regarding the 4th grade goal, the statistical problem-solving process of the 7th grade 2nd semester mathematics textbook was analyzed. Regarding the synthesis and practice content area, the data analysis unit of the 8th grade 2nd semester mathematics textbook was analyzed. In relation to the achievement standard (6), Example 85 of the curriculum appendix was analyzed, in relation to the achievement standard (9), Example 86 was analyzed, and in relation to the achievement standard (11), Example 87 was analyzed. Third, based on the analysis results, implications for the development of new curriculum and 'textbook development, teaching and learning methods' according to the 2022 revised middle school mathematics curriculum were derived. Through the results of this study, we expect the successful realization of the 2022 revised middle school mathematics and curriculum statistics education.

• School Mathematics
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• v.14 no.1
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• pp.151-163
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• 2012

In 2006 with the revised national curriculum, Elementary mathematics teaching and learning methods are presented in the following ways. Learners explore the way through the operational activities of the teachers and students with learning and learners' active learning activities, etc., and an active learning based on the principle of attention to learning how to maximize the effectiveness are required. In this study, from first grade through sixth grade elementary school mathematics textbooks for all learning activities presented in 10 different types were investigated This result of 5 contents area of number and operation, geometry, probability and statistics, measurement and patterns and problem solving and divided into low, middle, and hight three were intentional. In addition, teachers are looking forward to this result was compared with the type of activity.

• Journal of Educational Research in Mathematics
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• v.15 no.4
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• pp.445-459
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• 2005

Statistics education is considered within the mathematics curriculum and, thus, can be integrated into other areas of mathematics. However, statistical concepts and thinking skills have to be considered as very different from those of other areas. It is possible to make statistics more meaningful for the learner by making definitions or explanations of concepts in textbooks more clear and consistent. In 'Math I' and 'Probability & Statistics' of the 7th curriculum, the definitions of sample standard deviation are different, which might confuse students. In this study, firstly, some issues relevant to sample standard deviation concept are discussed through the analysis in terms of didactical situation and curriculum. Secondly, the characteristics of sample standard deviation concept as a scholarly knowledge are examined. Finally, the characteristics of didactic transposition of sample standard deviation concept in Japanese, American, and British textbooks are investigated and some suggestions are elicited.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.95-102
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• 2017

Gamma generalized linear models have received less attention than Poisson and binomial generalized linear models. Therefore, many old-established statistical techniques are still used in gamma generalized linear models. In particular, existing literature and textbooks still use approximate estimates for the dispersion parameter. In this paper we study the efficiency of various dispersion parameter estimators in gamma generalized linear models and perform numerical simulations. Numerical studies show that the maximum likelihood estimator and Cox-Reid adjusted maximum likelihood estimator are recommended and that approximate estimates should be avoided in practice.

• School Mathematics
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• v.15 no.2
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• pp.315-335
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• 2013

Probability has distinctive characteristics which are different from other areas of school mathematics. The critical change can be noticed in the domain, 'probability and statistics' of 2009 revised national curriculum for elementary school mathematics. This indicates that the concept of chance is supposed to be taught in the 5~6 grade band instead of the definition of probability which is moved to the middle school level. The purpose of this study is to seek desirable methods for teaching the concept of chance which reflect the achievement criteria and the attention point for teaching and learning of the curriculum at the point of time when textbooks haven't yet been developed. To do this, based on theoretical considerations and comparative analysis of the curricula in the longitudinal - latitudinal dimensions respectively, the validity of the latest curriculum change was confirmed and several learning activities were devised. And then two lessons were planned for applying these activities to eight fifth graders and were implemented along the plan. As a result, the relevance of the learning activities was examined and students' difficulties in learning the concept of chance with educational implications were discussed.

• The Mathematical Education
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• v.49 no.1
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• pp.67-83
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• 2010

The purpose of this study was to analyze the research trends of elementary mathematics education with regard to the topics, methods, subjects, and mathematical contents of such research. For this purpose, the papers published in domestic journals during the recent 5 years (2004-2009) were analyzed. A total of 383 papers from 8 professional journals were analyzed with the 4 criteria. First, the frequent research topics included instructional design and methods, learners' perspectives and abilities, and analysis of curriculum and textbooks in order. Second, qualitative research methodology was used twice as many as quantitative one. Whereas a survey was the most frequent quantitative research method, content analysis and case study were for qualitative methods. Third, research subjects included mainly typical students, specifically fifth and sixth graders. Papers dealing with lower graders or low-achievers as well as pre-service teachers were rare. Lastly, whereas the research on geometry as well as number and operations was active, that of measurement as well as probability and statistics was not. On the basis of these results, this paper includes several implications for the future research direction in elementary mathematics education.

• Journal of the Korean School Mathematics Society
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• v.23 no.4
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• pp.509-521
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• 2020

This study began with the discovery of the concept of frequency density in Singapore textbooks and in a set of subject contents of the UK's General Certificate of Secondary Education. To understand the mathematical meaning of frequency density, the mathematical connection of frequency density was considered in terms of mathematics internal connections and mathematics external connections. In addition, the teaching method of frequency density was introduced. In terms of mathematical internal connections, the connections among the probability density function, relative frequency density, and frequency density in high school statistics were examined. Regarding mathematical external connections, the connection with the density concept in middle school science was analyzed. Based on the mathematical connection, the study suggested the need to introduce the frequency density concept. For the teaching method of frequency density, the Singapore secondary mathematics textbook was introduced. The Singapore textbook introduces frequency density to correctly represent and accurately interpret data in histograms with unequal class intervals. Therefore, by introducing frequency density, Korea can consistently teach probability density function, relative frequency density, and frequency density, emphasizing the mathematical internal connections among them and considering the external connections with the science subject. Furthermore, as a teaching method of frequency density, we can consider the method provided in the Singapore textbook.

• Journal of Educational Research in Mathematics
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• v.18 no.3
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• pp.407-434
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• 2008

This research is to analyze the descriptions in the statistic chapter of the grade 7's current textbooks. The analysis is based on the distribution concepts suggested by Nam(2007). Thus we assumed that the goal of this statistic chapter is to establish concepts on the distributions and to learn ways of communication and comparison through distributional presentations. What we learned and wanted to suggest through the study is the followings. 1) Students are to learn what the distribution is and what are not. 2) Every kinds of presentational form of distributions is to given its own right to learn so that students are more encouraged to learn them and use them more adequately. 3) Density histogram is to be introduced to extend student's experiences viewing an area as 3 relative frequency, which is later to be progressed into a probability density. 4) Comparison of two distributions, especially through frequency polygons, is to be an hot issue among educational stakeholder whether to include or not. It is very important when stochastic correlations be learned, because it is nothing but a comparison between conditional distributions. 5) Statistical literacy is also an important issue for student's daily life. Especially the process ahead of the data collection must be introduced so that students acknowledge the importance of accurate and object-oriented data.

• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.