• 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.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• Journal of the Korean Chemical Society
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• v.47 no.2
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• pp.165-174
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• 2003

The purposes of this study were to investigate the correlation between the cognitive level and the probabilistic thinking level and to analyze the effects of the probability activities in Thinking Science (TS) program on the development of probabilistic thinking. The 219 7th grade students were sampled in the middle school and were divided into an experimental group and a control group. The probability activities in TS program were implemented to the experimental group, while only normal curriculum was conducted in the control group. The results of this study showed that most of 7th grade students were in the concrete operational stage and used both subjective and quantitative strategy simultaneously in probability problem solving. It was also found that the higher the cognitive level of the students, the higher the probabilistic thinking level of them. The sample space and the probability of an event in the constructs of probability were first developed as compared to the probability comparisons and the conditional probability. The probability activities encouraged the students to use quantitative strategy in probability problem solving and to recognize probability of an event. Especially, the effectiveness was relatively higher for the students in the mid concrete operational stage than those in any other stage.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.4
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• pp.354-358
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• 2001

This paper presents a fuzzy neural network model which solves the underutilization problem. This fuzzy neural network has both stability and flexibility because it uses the control structure similar to AHT(Adaptive Resonance Theory)-l neural network. And this fuzzy nenral network does not need to initialize weights and is less sensitive to noise than ART-l neural network is. The learning rule of this fuzzy neural network is the modified and fuzzified version of Kohonen learning rule and is based on the fuzzification of leaky competitive leaming and the fuzzification of conditional probability. The similarity measure of vigilance test, which is performed after selecting a winner among output neurons, is the relative distance. This relative distance considers Euclidean distance and the relative location between a datum and the prototypes of clusters. To compare the performance of the proposed fuzzy neural network with that of Kohonen Self-Organizing Feature Map the IRIS data and Gaussian-distributed data are used.