• School Mathematics
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• v.14 no.4
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• pp.495-516
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• 2012

This study distinguished thinking related to statistical variability into six components - the noticing of variability, the explanation of variability, the control of variability, the modeling of variability, the understanding of samples, and the understanding of sampling distribution and investigated the relationships among the thinking components. This study found that this distinction of thinking components related to statistical variability is reasonable. The results showed that each correlation coefficient of the modeling of variability, the understanding of samples, and the understanding of sampling distribution with regard to the noticing of variability, the explanation of variability, and the control of variability is similar. Based on this results, new variable, the understanding of sampling, has been drawn. The results also showed that while the noticing of variability and the control of variability influence the understanding of sampling, the explanation of variability does not influence it.

• Journal of Educational Research in Mathematics
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• v.21 no.1
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• pp.17-32
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• 2011

This study investigated pre-service teachers' understanding of statistical sampling. The researchers categorized major topics related to sampling into representativeness of samples, sampling variability, and sampling distribution, and selected concepts connected to each topic. Findings on this study are as follows: Even though most of the pre-service teachers considered the random sampling bringing unbiased outcomes as a proper sampling method, only 64% of them recognized that sample is a quasi-proportional, small-scale version of population; Few pre-service teachers understood that more important is the size of sample, not the portion of sample to population, and half of them appreciated that the number of sampling has a powerful effect on drawing of reliable results than the size of sample; Few pre-service teachers understood that sampling distribute is irrelevant to the shape of population and has a symmetrical bell-shape.

• Journal of Gifted/Talented Education
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• v.22 no.3
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• pp.503-525
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• 2012

This study compared levels of mathematically talented students' statistical thinking with those of non-talented students in statistical modeling and sampling distribution understanding. t tests were conducted to test for statistically significant differences between mathematically gifted students and non-gifted students. In case of statistical modeling, for both of elementary and middle school graders, the t tests show that there is a statistically significant difference between mathematically gifted students and non-gifted students. Table of frequencies of each level, however, shows that levels of mathematically gifted students' thinking were not distributed at the high levels but were overlapped with those of non-gifted students. A similar tendency is also present in sampling distribution understanding. These results are thought-provoking results in statistics instruction for mathematically talented students.

• 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.

• School Mathematics
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• v.16 no.4
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• pp.727-743
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• 2014

The concepts of sample and sampling are central to the statistical thinking and foundations of the statistical literacy, so we need to be emphasized their importance in the statistics education. However, many researches which dealt with samples only analyze textbooks or students' responses. In this study, the concept of sample is addressed by a historical consideration which is one aspect of the didactical analysis. Moreover, developing concept of sample is analyzed from the preceding studies about the statistical literacy, considering the sample representativeness and the sampling variability. The results say that the historical process of developing the concept of sample can be divided into three step: understanding the sample representativeness; appearing the sample variance; recognizing the sampling variability. Above all, it is important to aware and control the sampling variability, but many related researches might not consider sample variability. Therefore, it implies that the awareness and control of sampling variability are needed to reflect to the teaching-learing of sample for developing the students' statistical literacy.

• The Journal of the Korea Contents Association
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• v.15 no.9
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• pp.307-316
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• 2015

The purpose of this study was to investigate the relationship between emotional intelligence, burnout and nursing productivity, to find the factors for nursing productivity need to the efficient management of nursing organization. 255 nurses were collected a structured questionnaire by convenience sampling with 300 beds, Nov. 12-Dec. 26 in 2013. Data were processed SPSS 17.0, using t-test, one way ANOVA, Scheffe test, Pearson's correlation coefficient, and enter multiple regression analysis. These results showed a significant negative correlation between emotional intelligence and burnout, a significant positive correlation between emotional intelligence. Emotional intelligence, total clinical experence, burnout and position had a significant influence on nursing productivity, Nursing productivity explained 43.4% of the variation. Therefore, it demanded that to build the infrastructure for the nursing organization of carrer management, to improve emotional intelligence, to design diverse intervention program for the nurses, to reduce burnout, and to increase work productivity.