• Journal of Educational Research in Mathematics
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• v.21 no.4
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• pp.327-344
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• 2011

This study is the first step for us toward improving high school students' capability of statistical inferences, such as obtaining and interpreting the confidence interval on the population mean that is currently learned in high school. We suggest 5 underlying concepts of 'discretion of contingency and inevitability', 'discretion of induction and deduction', 'likelihood principle', 'variability of a statistic' and 'statistical model', those are necessary to appreciate statistical inferences as a reliable arguing tools in spite of its occasional erroneous conclusions. We assume those 5 concepts above are to be gradually developing in their school periods and Korean mathematics textbooks of grades 1-12 were analyzed. Followings were found. For the right choice of solving methodology of the given problem, no elementary textbook but a few high school textbooks describe its difference between the contingent circumstance and the inevitable one. Formal definitions of population and sample are not introduced until high school grades, so that the developments of critical thoughts on the reliability of inductive reasoning could not be observed. On the contrary of it, strong emphasis lies on the calculation stuff of the sample data without any inference on the population prospective based upon the sample. Instead of the representative properties of a random sample, more emphasis lies on how to get a random sample. As a result of it, the fact that 'the random variability of the value of a statistic which is calculated from the sample ought to be inherited from the randomness of the sample' could neither be noticed nor be explained as well. No comparative descriptions on the statistical inferences against the mathematical(deductive) reasoning were found. Few explanations on the likelihood principle and its probabilistic applications in accordance with students' cognitive developmental growth were found. It was hard to find the explanation of a random variability of statistics and on the existence of its sampling distribution. It is worthwhile to explain it because, nevertheless obtaining the sampling distribution of a particular statistic, like a sample mean, is a very difficult job, mere noticing its existence may cause a drastic change of understanding in a statistical inference.

• Journal of The Korean Association For Science Education
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• v.27 no.9
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• pp.930-943
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• 2007

The purpose of this study was to investigate if students may actually experience scientific reasoning based on an epistemology of authentic science during authentic open inquiry. The samples were 86 10th graders in a science-high school in Seoul. The experimental group practiced authentic open inquiry and the control group practiced traditional school science inquiry in five weeks. Then, the questions students asked while performing inquiry tasks were analyzed. The frequency of the questions asked by students was almost same between two groups, however, the types of questions were different. The frequency of thinking questions in experimental group was higher than the control, and the difference was statistically significant (P<.01). Particularly, the frequency of expansive thinking questions and anomaly detection questions was much higher in experimental than the control group. Judging from the result, with the students from the experimental group asking questions reflecting on the epistemology of authentic science such as scientific methods, anomalous data, and uncertainty about reasoning, students may understand authentic science features during the activities of open authentic inquiry. The result from comparing questions according to the inquiry subject showed that more openness caused the higher frequency of anomaly detection questions and strategy questions, but that inductive thinking questions and analogical thinking questions were connected to inquiry subject rather than the openness of the inquiry.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.539-560
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• 2013

The purpose of this study was to investigate characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Eight mathematically gifted high school students, who already learned graphs of functions and inequalities necessary for design activities, were selected to work in pairs in our experiment. Results indicate that logical thinking and mathematical abstraction, intuitive and structural insights, flexible thinking, divergent thinking and originality, generalization and inductive reasoning emerged in the design activities. Nonetheless, fine-grained analysis of their mathematical activities also implies that teachers for gifted students need to emphasize both geometric and algebraic aspects of mathematical subjects, especially, algebraic expressions, and the tasks for the students are to be rich enough to provide a variety of ways to simplify the expressions.

• Journal of The Korean Association For Science Education
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• v.31 no.5
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• pp.770-787
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• 2011

The purpose of this study was to analyze science-gifted students' knowledge-generation processes by analyzing students' inquiry journal. As a result, first, science-gifted students showed various knowledge-generation processes, but they were limited to inductive thinking and abductive thinking, and their thinking processes were very simple. Second, most of the knowledge-generation processes of science gifted were simple, repetitive and diagrammatic processes because of observation and empirical situation of a limited scope. And a simple and repetitive diagram was generated by a simple variable selection and design, observation in limited scope, unbiased intervention by subjective thinking, and absence of exploration or finding errors. And they showed often a logical leap of reasoning.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.131-148
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• 2016

Mathematical formal justification may be seen as a bridge towards the proof. By requiring the mathematically gifted students to prove the generalized patterned task rather than the implementation of deductive justification, may present challenges for the students. So the research questions are as follow: (1) What are the difficulties the mathematically gifted elementary students may encounter when formal justification were to be shifted into a generalized form from the given patterned challenges? (2) How should the teacher guide the mathematically gifted elementary students' process of transition to formal justification? The conclusions are as follow: (1) In order to implement a formal justification, the recognition of and attitude to justifying took an imperative role. (2) The students will be able to recall previously learned deductive experiment and the procedural steps of that experiment, if the mathematically gifted students possess adequate amount of attitude previously mentioned as the 'mathematical attitude to justify'. In addition, we developed the process of questioning to guide the elementary gifted students to formal justification.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.417-435
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• 2011

Mathematical justification is essential to assert with reason and to communicate. Students learn mathematical justification in 8th grade in Korea. Recently, However, many researchers point out that justification be taught from young age. Lots of studies say that students can deduct and justify mathematically from in the lower grades in elementary school. I conduct questionnaire to know awareness and steps of elementary school students and middle school students. In the case of 9th grades, the rate of students to deduct is highest compared with the other grades. The rease is why 9th grades are taught how to deductive justification. In spite of, however, the other grades are also high of rate to do simple deductive justification. I want to focus on the 6th and 5th grades. They are also high of rate to deduct. It means we don't need to just focus on inducing in elementary school. Most of student needs lots of various experience to mathematical justification.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.185-205
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• 2011

In this paper, we investigated the mathematical output of a gifted student's independent study. We chose one student who was taking a mentorship course in mathematics at the Gifted Education Center in Chonnam National University, and analyzed the characters of the result which a student showed through the output of independent study and studied the psychological change of a student while he was making a presentation of the results of his study. We found following facts. First, a mentor-independent study improves a mathematical gifted student's inductive thinking and ability to generalize and apply to other cases. Second, presenting a mathematical gifted student's output for mentor-independent study improves his ability of mathematical communication in the abilities of creative problem solving. Finally, there is an increased change in his perception and self-efficacy of mathematics after the presentation.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• Journal of Korean Society of Transportation
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• v.28 no.4
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• pp.19-30
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• 2010

It has become important to have some proper guidelines of how to provide public transport information services in response to the rapid IT developments and the wide spread of public information services. The current study takes a contextual approach to the analysis of public transportation information use under a dynamic decision situation, complementing the conventional cross-sectional approaches. Using the CHAID of decision tree induction based on decision table formalism applied to the survey data of activity travel and information use, the study found that the information type and medium choices are strongly affected by the decision contexts in addition to the individuals' socio-demographic characteristics. The results suggest an important implication to the market segmentation of information services for public transportation.

• School Mathematics
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• v.11 no.4
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• pp.583-605
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• 2009

This research aims to examine the characteristics and main subjects of the mathematics class-criticism by elementary' teachers. In this aim, we analyzed the mathematics class-criticism by the 11 elementary teachers. As the results of this research, the elementary teachers criticized the mathematics class while understanding and describing the class as it is. And mathematics class-criticism by elementary teachers showed contextual and situational characteristics. Furthermore, the main subjects of mathematics class-criticism by elementary teachers were identified as mathematical communication, teacher's question to foster the students' mathematical thinking, appropriateness of task, motivation for students, concrete operational activity, appropriateness on teacher's mathematical behavior and teacher's use of mathematical term, experience of inductive reasoning. While, we identified the significance of mathematics class-criticism for elementary teachers. The elementary teachers pointed out the necessity and importance of the mathematics class-criticism on the mathematics class in usual context.