• Journal for History of Mathematics
• /
• v.32 no.3
• /
• pp.135-155
• /
• 2019

One of the reasons students have difficulty in studying probability is that they do not understand the meaning of mathematical terms precisely. One such term is a continuous random variable. Students tend not to think of the accurate definition of continuous random variables but to understand the definition of continuity of functions and the meaning of continuity in probability as equal. In this study, we try to explore the degree of pre-service teachers' understanding on the concept of continuation of functions and continuous random variables. To do this, the questionnaire items related to continuous random variables and continuity of functions were developed by experts and examined by pre-service teachers. Based on this, we make suggestions on implications for teaching and learning about continuous random variables.

• Journal of Educational Research in Mathematics
• /
• v.20 no.2
• /
• pp.163-183
• /
• 2010

It has long been of controversy what the meanings of probability is. And a century has past after the mathematical probability has been at the center of the school curriculum of it. Recently statistical meaning of probability becomes important for various reasons. However the simple modification of its definition is not enough. The computational reasoning of the probability and its practical application needs didactical changes and new instructional transformations along with the modification of it. Most of the current text books introduce probability as a limit of the relative frequencies, a statistical probability. But when the probability computation of the union of two events, or of the simultaneous events is faced on, they use mathematical probability for explanation and practices. Accordingly there is a gap for students in understanding those. Probability is an intuitive concept as far as it belongs to the domain of the experiential frequency. And frequency distribution must be the instructional bases for the (statistical) probability novices. This is what we mean by the probability in accordance with the distribution concepts. First of all, in order to explain the probability of the complementary event we should explain the empirical relative frequency of it first. These are the case for the union of two events and for the simultaneous events. Moreover we need to provide a logic of probabilistic guesses, inferences and decision, which we introduce with the name “the likelihood principle”, the most famous statistical principle. We emphasized this be done through the problems of practical decision making.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.24 no.68
• /
• pp.1-7
• /
• 2001

A probabilistic model for fatigue life of a structural component is derived when the component is in a variable-amplitude loading environment. The physical mechanism which governs fatigue failure is used to model the fatigue life. Especially, the judgement of rotational symmetry in the-stress-intensity-factors results in the probability distribution for fatigue life. The probability distribution is related to the familiar truncated Gaussian distribution, which has a single parameter with a direct physical meaning.

• School Mathematics
• /
• v.4 no.4
• /
• pp.677-688
• /
• 2002

The context and intuitive understanding is very important in Statistics Education. Especially, there is a need to mitigate student's difficulty in studying probability density function. One of teaching method this concept is to using relative frequency histogram. But, as using this method, we should know several problems included in that. This study investigate problems in the method for teaching probability density function as gradual meaning of histogram. Also, as alternative approach, this thesis introduce the density curve concept. The application of four methods to teach the concept of the probability density function and analysis of the survey result is done in this research.

• Journal of Korea Society of Industrial Information Systems
• /
• v.17 no.1
• /
• pp.21-29
• /
• 2012

In this paper, we propose a new method to select colors representing the meaning of text contents based on the cognitive relation between words and colors, Our method is designed on the previous study revealing the existence of crucial words to estimate the colors associated with the meaning of text contents, Using the associative probability of each color with a given word and the strength of color association of the word, we estimate the probability of colors associated with a given text. The goal of this study is to propose a system to recommend the cognitively plausible colors for the meaning of the input text. To build a versatile and efficient database used by our system, two psychological experiments were conducted by using news site articles. In experiment 1, we collected 498 words which were chosen by the participants as having the strong association with color. Subsequently, we investigated which color was associated with each word in experiment 2. In addition to those data, we employed the estimated values of the strength of color association and the colors associated with the words included in a very large corpus of newspapers (approximately 130,000 words) based on the similarity between the words obtained by Latent Semantic Analysis (LSA). Therefore our method allows us to select colors for a large variety of words or sentences. Finally, we verified that our system cognitively succeeded in proposing the colors associated with the meaning of the input text, comparing the correct colors answered by participants with the estimated colors by our method. Our system is expected to be of use in various types of situations such as the data visualization, the information retrieval, the art or web pages design, and so on.

• The Mathematical Education
• /
• v.59 no.1
• /
• pp.47-62
• /
• 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 the Korean School Mathematics Society
• /
• v.1 no.1
• /
• pp.59-67
• /
• 1998

Probability and statistics is an important section in mathematics which is deeply related to everyday living, natural science and social science. In spite of its importance, many students will throw away it because it becomes very harder as its step(stage) deepens and probability and statistics' relative importance is very small in Korea-SAT(the test of college entrance in Korea). Therefore, by analyzing the involvement carefully between the curriculum in the elementary, middle, high school and the text book, by studying the problem and improvement direction, it is necessary to investigate an effective teaching method. This study intends to give the students the confidence, interests, and accomplishment motive about probability and statistics field and to make a rational and creative decision-making through mathematical speculation by proposing an effective teaching method through analyzing an existing facts in school's probability and statistics field. The contents of this study are composed of four chapters. Chapter three looks into the mathematical curriculum in the elementary, middle, high school and its teaching meaning, the outline of contents, some tips on teaching and problems and presents an effective and concrete teaching method on the basis of the theoretical background in the chapter two. Chapter four is a conclusive part and gives the general improvement and intentional direction in educating the probability and statistics.

• Journal of Gifted/Talented Education
• /
• v.20 no.1
• /
• pp.151-173
• /
• 2010

Several researches have been done on the meaning of probabilistic thinking level and its pedagogical implication. However, there is lack of trials of using topics in probability to educate mathematically gifted students. As a result, we don't have sound understanding on gifted students' probabilistic thinking level and how to facilitate it through educational program. This study examines the meaning of probabilistic thinking level, develops and applies tasks in probability for gifted education. Having the analysis of the student responses, this study tries to investigate how teachers who participate in an in-service teacher education program interpret the developed tasks and student responses. In conclusion, this study shows the possible approach of gifted education using probability tasks to facilitate gifted students' probabilistic thinking level and its potential in identification of giftedness through observation.

• Korean Institute of Interior Design Journal
• /
• v.23 no.4
• /
• pp.94-102
• /
• 2014

Nowadays when the social and cultural paradigm is changing, the incomplete space is becoming a matter of controversy. In order to figure out the solutions to it, are being held a variety of spatial discourses for spatial essence and meaning to be cleared. Accordingly, this study has tried to seek for any probability to interpret the ontology shown at any traditional space on the ground of Heidegger's Ontological Thinking Structure which has a considerable impact on Modern Space, whose conclusions are the followings. First, Heidegger's ontological space theory, which provided a foundation of Placeness concept, includes not only the character of interdisciplinary learning among philosophy, arts and any related studies but also that of mutual oriental and occidental cultures. Second, between the thoughts of Heidegger and Lao-tzu are considerable similarities from the methodical viewpoint that materializes the meaning of existence as an essence. Third, for a convenient interpretation, the ontological spatial concept of Lao-tzu's philosophy shown at traditional spaces have been categorized into Typology-Incident, Morphology-situation and Topology-meaning generation with Schultz's Existential Spatial Concept based on Heidegger's Ontology as a medium. In particular, the meaning generation which materializes the placeness has the trait of being clarified as the product of interactions between incidents and situations.

• Journal of Korean Society for Quality Management
• /
• v.46 no.1
• /
• pp.95-112
• /
• 2018

Purpose: To find out the appropriate probability distribution of credit card usage behavior by considering the relationship among income, expenditure and credit card usage amount. Such relationship is enabled by Korea's especially high penetration of credit card. Method: Goodness-of-fit test and effect size statistic W were used to identify the distribution of income and credit card usage amount. A simulation model is introduced to generate the credit card transactions on individual user level. Result: The three data sets for testing had either passed the chi-square test or showed low W values, meaning they follow the exponential distribution. And the exponential distribution turned out to fit the data sets well. The r values were very high. Conclusion: The credit card usage behavior, denoted as the counts of users by usage amount band, follows the exponential distribution. This distribution is easy to manipulate, has a variety of applications and generates important business implications.