• 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.20 no.4
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• pp.493-509
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• 2010

Researchers have suggested that educators have to focus their attention on variability and reasoning about variation as means of developing students' statistical thinking in school mathematics. This paper investigated knowledge for the teaching of variability and reasoning about variation; what are sources of variability, how to cope with variability, what are types of variability, how to recognize variability, and the relationship between statistical problem solving and variability. The results involve: discussion on the sources of variability and how to cope with variability promotes students' awareness of different types of variability and students' motivation in the following steps in the statistical activity; emphasis on reasoning about variation in teaching representation of data accords with objectives of statistics education; reexamination of curriculum for statistics education is needed, which has a content-oriented arrangement.

• Journal of The Korean Association For Science Education
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• v.29 no.8
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• pp.990-1010
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• 2009

To derive brain-based evolutionary educational principles, this study examined the studies on the structural and functional characteristics of human brain, the biological evolution occurring between- and within-organism, and the evolutionary attributes embedded in science itself and individual scientist's scientific activities. On the basis of the core characteristics of human brain and the framework of universal Darwinism or universal selectionism consisted of generation-test-retention (g-t-r) processes, a Model of Brain-based Evolutionary Scientific Teaching for Learning (BEST-L) was developed. The model consists of three components, three steps, and assessment part. The three components are the affective (A), behavioral (B), and cognitive (C) components. Each component consists of three steps of Diversifying $\rightarrow$ Emulating (Executing, Estimating, Evaluating) $\rightarrow$ Furthering (ABC-DEF). The model is 'brain-based' in the aspect of consecutive incorporation of the affective component which is based on limbic system of human brain associated with emotions, the behavioral component which is associated with the occipital lobes performing visual processing, temporal lobes performing functions of language generation and understanding, and parietal lobes, which receive and process sensory information and execute motor activities of the body, and the cognitive component which is based on the prefrontal lobes involved in thinking, planning, judging, and problem solving. On the other hand, the model is 'evolutionary' in the aspect of proceeding according to the processes of the diversifying step to generate variants in each component, the emulating step to test and select useful or valuable things among the variants, and the furthering step to extend or apply the selected things. For three components of ABC, to reflect the importance of emotional factors as a starting point in scientific activity as well as the dominant role of limbic system relative to cortex of brain, the model emphasizes the DARWIN (Driving Affective Realm for Whole Intellectual Network) approach.