• The Mathematical Education
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• v.58 no.4
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• pp.531-543
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• 2019

Continuous probability distribution was one of the mathematics concept that students had difficulty. This study analyzed the definition and introduction of the continuous probability distribution under the 2009-revised curriculum and 2015-revised curriculum. In this study, the following subjects were studied. Firstly, definitions of continuous probability variable in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. Secondly, introductions of continuous probability distribution in 'Probability and Statistics' textbook developed under the 2009-revised curriculum and 2015-revised curriculum were analyzed. The results of this study were as follows. First, 8 textbooks under the 2009-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range or an interval. And 1 textbook under the 2009-revised curriculum defined the continuous probability variable as probability variable when the set of its value is uncountable. But all textbooks under the 2015-revised curriculum defined the continuous probability variable as probability variable with all the real values within a range. Second, 4 textbooks under the 2009-revised curriculum and 4 textbooks under 2015-revised curriculum introduced a continuous random distribution using an uniformly distribution. And 5 textbooks under the 2009-revised curriculum and 5 textbooks under the 2015-revised curriculum introduced a continuous random distribution using a relative frequency density.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.3
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• pp.475-492
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• 2014

The purpose of this study is to analyze the United States Elementary Mathematics textbooks "Everyday Mathematics", focused on area of the probability. The concept of probability as qualitative probability is taught from Kindergarten in EM curricula for progressive mathematising. EM have reflected both perspectives in probability which are a frequency perspective and a classical perspective. And EM includes abundant activities for remedying the misconceptions of probability. On the basis of the results from this analysis, we have five suggestions which are helpful for the revision of the Korean national curriculum.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.217-225
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• 2012

A generalized quadratic fuzzy set is a generalization of a quadratic fuzzy number. Zadeh defines the probability of the fuzzy event using the probability. We define the normal fuzzy probability on $\mathbb{R}$ using the normal distribution. And we calculate the normal fuzzy probability for generalized quadratic fuzzy sets.

• The Mathematical Education
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• v.25 no.1
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• pp.1-8
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• 1986

It is a common saying that markov-chain is a special case of probability course. That is to say, It means an unchangeable markov-chain process of the transition-probability of discontinuous time. There are two kinds of ways to show transition probability parade matrix theory. The first is the way by arrangement of a rightangled tetragon. The second part is a vertical measurement and direction sing by transition-circle. In this essay, I try to find out existence of procession for transition-probability applied markov-chain. And it is possible for me to know not only, what it is basic on a study of chain but also being applied to abnormal problems following a flow change and statistic facts expecting to use as a model of air expansion in physics.

• The Mathematical Education
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• v.59 no.1
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• pp.47-62
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• 2020

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.25-50
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• 2008

Several previous studies suggested that simulation could be a main didactic instrument in overcoming misconception and probability modeling. However, they have not described enough how to reorganize probability knowledge as knowledge to be taught in a curriculum using simulation. The purpose of this study is to identify the theoretical knowledge needed in developing a didactic transposition method of probability knowledge using simulation. The theoretical knowledge needed to develop this method was specified as follows : pseudo-contextualization/pseudo-personalization, and pseudo-decontextualization/pseudo-deper-sonalization according to the introductory purposes of simulation. As a result, this study developed a local instruction theory and an hypothetical learning trajectory for overcoming misconceptions and modeling situations respectively. This study summed up educational intention, which was designed to transform probability knowledge into didactic according to the introductory purposes of simulation, into curriculum, lesson plans, and experimental teaching materials to present didactic ideas for new probability education programs in the high school probability curriculum.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.53-65
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• 1997

There are many mistakes when we estimate probability of an event, for example, we often omit some likelihoods (of an event), sometimes give too large or too small possibility for a particular case, cannot relate current cases with which were concerned before, apply at another cases as soon as discuss about it insufficiently, etc. If we go into a history of probability and statistics, we shall ascertain that many scientists and mathmaticians made essentially same mistakes with us. In the paper, we will consider the theorization of probability and statistics as a process of modification of mistakes which were made during one's estimating possibility of an event. On that point of view, we shall look at historical background of probability and statistics.

• Smart Structures and Systems
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• v.25 no.5
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• pp.593-604
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• 2020

Temperature may have more significant influences on structural responses than operational loads or structural damage. Therefore, a comprehensive understanding of temperature distributions has great significance for proper design and maintenance of bridges. In this study, the temperature distribution of the steel box girder is systematically investigated based on the structural health monitoring system (SHMS) of the Sutong Cable-stayed Bridge. Specifically, the characteristics of the temperature and temperature difference between different measurement points are studied based on field temperature measurements. Accordingly, the probability density distributions of the temperature and temperature difference are calculated statistically, which are further described by the general formulas. The results indicate that: (1) the temperature and temperature difference exhibit distinct seasonal characteristics and strong periodicity, and the temperature and temperature difference among different measurement points are strongly correlated, respectively; (2) the probability density of the temperature difference distribution presents strong non-Gaussian characteristics; (3) the probability density function of temperature can be described by the weighted sum of four Normal distributions. Meanwhile, the temperature difference can be described by the weighted sum of Weibull distribution and Normal distribution.

• School Mathematics
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• v.9 no.3
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• pp.397-408
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• 2007

This research intends to look into how mathematically gifted 6th graders (age12) who have not learned conditional probability before solve conditional probability problems. In this research, 9 conditional probability problems were given to 3 gifted students, and their problem solving approaches were analysed through the observation of their problem solving processes and interviews. The approaches the gifted students made in solving conditional probability problems were categorized, and characteristics revealed in their approaches were analysed. As a result of this research, the gifted students' problem solving approaches were classified into three categories and it was confirmed that their approaches depend on the context included in the problem.

• Journal of Educational Research in Mathematics
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• v.16 no.2
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• pp.139-156
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• 2006

The concept of probability in current school mathematics has been dealt with in the classic viewpoint (mathematical probability) and part of the frequency viewpoint and axiomatic viewpoint have been introduced. However, since the exact understanding of the probability concepts is not possible only with the classic viewpoint, we need to research further on methods to complement classic viewpoint and emphasize various aspects of probability concepts (Lee, Kyung Hwa, 1996). Therefore, this study is to find out optimal computer simulation plans in teaching statistical probability. For the purpose, it examines how the nature of mathematical knowledge may be changed when statistical probability is taught with a use of computer simulation based on the Theory of Didactical Situation presented by Brousseau(1997). Next, it identifies how probability curriculum should be reconstituted for introducing statistical probability through computer simulation. Finally, it develops specific teaching materials that introduce statistical probability using computer simulation based on the results obtained.