• Journal of Educational Research in Mathematics
• /
• v.19 no.2
• /
• pp.233-256
• /
• 2009

The notions of conditional probability and independence are fundamental to all aspects of probabilistic reasoning. Several previous studies identified some misconceptions in students' thinking in conditional probability. However, they have not analyzed enough the nature of conditional probability. The purpose of this study was to analyze conditional probability and students' knowledge on conditional probability. First, we analyzed the conditional probability from mathematical, historico-genetic, psychological, epistemological points of view, and identified the essential aspects of the conditional probability. Second, we investigated the high school students' and undergraduate students' thinking m conditional probability and independence. The results showed that the students have some misconceptions and difficulties to solve some tasks with regard to conditional probability. Based on these analysis, the characteristics of reasoning about conditional probability are investigated and some suggestions are elicited.

• Journal of Educational Research in Mathematics
• /
• v.20 no.1
• /
• pp.1-20
• /
• 2010

Conditional probability may look simple but it raises various misconceptions. Preceding studies are mostly about such misconceptions. However, instead of focusing on those misconceptions, this paper focused on what the mathematical essence of conditional probability which can be applied to various situations and how good teachers' understanding on that is. In view of this purpose, this paper classified conditional probability which have different ways of defining into two-relative conditional probability which can be get by relative ratio and if-conditional probability which can be get by the inference of the situation change of conditional event. Yet, this is just a superficial classification of resolving ways of conditional probability. The purpose of this paper is in finding the mathematical essence implied in those, and by doing that, tried to find out how well teachers understand about conditional probability which is one integrated concept.

• Journal of Environmental Science International
• /
• v.22 no.8
• /
• pp.965-977
• /
• 2013

Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota's method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota's method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota's method and logistic regression analysis except for winter season data.

• Korean Journal of Child Studies
• /
• v.29 no.5
• /
• pp.243-269
• /
• 2008

The role of domain-specific causal mechanism information and domain-general conditional probability in young children's causal reasoning on physics and psychology was investigated with the participation of 121 3-year-olds and 121 4-year-olds recruited from seven child care centers in Seoul, Kyonggi Province, and Busan. Children watched moving pictures on physical and psychological phenomena, and were asked to choose an appropriate cause and justify their choice. Results showed that young children's causal reasoning differed depending on domain-specific mechanism. In addition, their causal reasoning on physics and psychology differed by the developmental level of causal mechanism. The interaction of domain-specific mechanism and domain-general conditional probability influenced children's causal reasoning : evident conditional probability between domain-appropriate cause and effect helped children make more inferences based on domain-specific causal mechanism.

• Journal of the Korean Mathematical Society
• /
• v.36 no.4
• /
• pp.699-705
• /
• 1999

Given a probability space and a subsigma algebra A, each measure equivalent to the probability measure generates a different conditional expectation operator. We characterize those which act boundedly on the original $L^2$ space, and show there are sufficiently many such conditional expectations to generate the commutant of $L^{\infty}$ (A).

• Korean Journal of Logic
• /
• v.8 no.2
• /
• pp.59-84
• /
• 2005

Adams' Thesis, or the so-called equation Pr$(A{\rightarrow}C)$ = Pr(C|A) seems to express a correct relationship between the probabilities of conditionals and conditional probabilities. But D. K. Lewis has proved the remarkable fact that probabilities of conditionals are not conditional probabilities. In this paper 1 present a version of Lewis' triviality results and give an explanation why probabilities of conditionals are not conditional probabilities. A conditional probability of C given A has a peculiar properly in that its probability is insulated from not-A facts: the only thing relevant is the proportion of ways in which A is true which are also ways for C to be true. This peculiarity of conditional probability seems to put the great obstacle in the way of attempting to find a proposition such that its probability of being true systematically coincides with conditional probability of something else.

• Journal of Families and Better Life
• /
• v.26 no.5
• /
• pp.333-354
• /
• 2008

This study aimed to investigate the role of domain-specific causal mechanism information and domain-general conditional probability in young children's causal reasoning on psychology and biology. Participants were 121 3-year-olds and 121 4-year-olds recruited from seven childcare centers in Seoul, Kyonggi Province, and Busan. After participants watched moving pictures on psychological and biological phenomena, they were asked to choose appropriate cause and justify their choices. Results of this study were as follows: First, young children made different inferences according to domain-specific causal mechanisms. Second, the developmental level of causal mechanisms has a gap between psychology and biology, and biological knowledge was proved to be separate from psychological knowledge during the preschool period. Third, young children's causal reasoning was different depending on the interaction effect of domain-specific mechanisms and domain-general conditional probability: children could make more inferences based on domain-specific causal mechanisms if conditional probability between domain-appropriate cause and effect was evident. To conclude, it can be inferred that the role of domain-specific causal mechanisms and domain-general conditional probability is not competitive but complementary in young children's causal reasoning.

• Journal for History of Mathematics
• /
• v.15 no.1
• /
• pp.135-146
• /
• 2002

In this paper, we demonstrate that one can teach conditional probability in a manner consistent with many features of the statistics education reform movement. Presenting a variety of applications of conditional probability to realistic problems, we propose that interactive activities and the use of technology make conditional probability understandable, interactive, and interesting for students at a wide range of levels of mathematical ability. Along with specific examples, we provide guidelines for implementation of the activities in the classroom and instructional cues for promoting curiosity and discussion among students.

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

• The Mathematical Education
• /
• v.58 no.3
• /
• pp.347-365
• /
• 2019

It is important to pay attention to how teachers recognize and use curriculum materials in order to link written curriculum and enacted curriculum. In this study, 90 preservice mathematics teachers were surveyed to identify their perspective and reading of curriculum materials. Especially, we focused on the curriculum documents, textbooks, and teachers' guidebooks containing the concept of conditional probability which is addressed in highschool mathematics curriculum. The various misconceptions of conditional probability were reported in the many researches, and there are multiple methods to introduce conditional probability in mathematics classes. As a result, curriculum materials have some limits to be used as they are and considered to be reconstructable by participants, but their curriculum reading were mainly classified to be descriptive and evaluative, not to be interpretive. However, unlike curriculum documents, textbooks and teachers' guidebooks were partially interpreted by participants using their knowledge of conditional probability. The purpose of this study is to investigate the profession of mathematics teachers in terms of curriculum implementation. We expect that this study will provide a basic framework for analyzing mathematics teachers' works and suggest some implications for the professional development of mathematics teachers.