• The Mathematical Education
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• v.62 no.4
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• pp.473-490
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• 2023

Previous studies from domestic and abroad are accumulating information on how to reason students' continuous changes through teaching experiments. These studies deal with scenes in which students who make 'smooth reasoning' and 'chunky reasoning' construct mathematical results together in teaching experiments. However, in order to analyze their results in more detail, it is necessary to check what kind of results a student reasoning in a specific way constructs for the tasks of previous studies. According to the need for these studies, the researcher conducted a total of 14 teaching experiments on one first-year high school student who was found to make 'chunky reasoning'. In this study, it was possible to observe a scene in which a student who makes 'chunky reasoning' constructs an output similar to 'a mathematical result constructed by students with various reasoning methods(smooth reasnoning or chunky reasoning) in previous studies.' In particular, the student who participated in this study observed a consistent construction method of constructing the function of 'time-speed' from the function of 'time-distance'. The researcher expected that information on this student's distinctive construction methods would be helpful for subsequent studies.

• Journal of The Korean Association For Science Education
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• v.29 no.2
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• pp.253-266
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• 2009

This study was focused on analyzing students' informal reasoning patterns and their considerations in decision-making on socioscientific issues. This study involved 20 undergraduate students (10 biology majors and 10 non-biology majors) and showed how the two groups responded on socioscientific issues. Semi-structured interviews were conducted twice respectively based on six scenarios of gene therapy and human cloning. The result showed 93% of the total number of participants' decisions were made by rationalistic reasoning, whereas emotional reasoning was 49%, and intuitive reasoning was 27%. Students usually used two or three informal reasoning patterns together. Most of the students took more consideration on social factors. Some perceived ethical and moral implications of the issues, but they did not consider them seriously. They made their decisions depending on their own values, etc. 65% of the participants got their information on socioscientific issues from the mass media. Biology majors hardly used intuitive reasoning compared to non-biology majors. The Biology major group took into deep considerations on socioscientific issues while the non-biology major group seemed to interpret the given scenarios simply. This implied that the content knowledge was a significant factor of their decision-making. Therefore, it is necessary to develop proper science courses for non-major students to improve their decision-making on socioscientific issues. So, when we develop educational materials or programs, we should consider students' reasoning patterns, their considerations in decision-making, and their content knowledge. And because the mass media has the potential to play a key role for an effective education, we need to make a plan to make a practical application.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.355-369
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• 2009

Though there is no agreement on the definition of analogical reasoning, there is no doubt that analogical reasoning is the means of mathematical knowledge construction. Mathematicians generally have a tendency or desire to find similarities between new and existing Ideas, and new and existing representations. They construct appropriate links to new ideas or new representations by focusing on common relational structures of mathematical situations rather than on superficial details. This focus is analogical reasoning at work in the construction of mathematical knowledge. Since analogical reasoning is the means by which mathematicians do mathematics and is close]y linked to measures of intelligence, it should be considered important in mathematics education. This study investigates how mathematicians used analogical reasoning, what role did it flay when they construct new concept or problem solving strategy.

• School Mathematics
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• v.15 no.4
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• pp.723-742
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• 2013

The purpose of this study was to analyze children's proportional reasoning process on an ill-structured "architectural drawing" problem solving and to investigate their level and characteristics of proportional reasoning. As results, they showed various perspective and several level of proportional reasoning such as illogical, additive, multiplicative, and functional approach. Furthermore, they showed their expanded proportional reasoning from the early stage of perception of various types of quantities and their proportional relation in the problem to application stage of their expanded and generalized relation. Students should be encouraged to develop proportional reasoning by experiencing various quantity in ration and proportion situations.

• The Transactions of the Korea Information Processing Society
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• v.5 no.1
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• pp.103-110
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• 1998

In case of traditional Rule-Based Reasoning(RBR) and Case-Based Reasoning(CBR), although knowledge is reasoned either by one of them or by the integration of RBR and CBR, there is a problem that much time should be consumed by numerous rules and cases. In order to improve this time-consuming problem, in this paper, a new type of reasoning technique, which is a kind of integration of reduced RB and CB, is to be introduced. Such a new type of reasoning uses Rough Set, by which we can represent multi-meaning and/or random knowledge easily. In Rough Set, solution is to be obtained by its own complementary rules, using the process of RB and CB into equivalence class by the classification and approximation of Rough Set. and then using reduced RB and CB through the integrated reasoning.

• The Mathematical Education
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• v.55 no.3
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• pp.251-279
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• 2016

There are many studies on 'how' students solve mathematical problems, but few of them sufficiently explained 'why' they have to solve the problems in their own different ways. As quantitative reasoning is the basis for algebraic reasoning, to scrutinize a student's way of dealing with quantities in a problem situation is critical for understanding why the student has to solve it in such a way. From our teaching experiments with two ninth-grade students, we found that emergences of a certain level of covariational reasoning were highly consistent across different types of problems within each participating student. They conceived the given problem situations at different levels of covariation and constructed their own quantity-structures. It led them to solve the problems with the resources accessible to their structures only, and never reconciled with the other's solving strategies even after having reflection and discussion on their solutions. It indicates that their own structure of quantities constrained the whole process of problem solving and they could not discard the structures. Based on the results, we argue that teachers, in order to provide practical supports for students' problem solving, need to focus on the students' way of covariational reasoning of problem situations.

• Research in Mathematical Education
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• v.18 no.3
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• pp.223-234
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• 2014

Research shows that formative assessment has a more powerful effect on student learning than summative assessment. This case study of an 8th grade algebra classroom focuses on how the implementation of Formative Assessment Lessons (FALs) and the participation in teacher learning communities related to FALs changed in the teacher's instructional practices, over the course of a year, to promote students' mathematical reasoning and justification. Two classroom observations are analyzed to identify how the teacher elicited and built on students' mathematical reasoning, and how the teacher prompted students to respond to and develop one another's mathematical ideas. Findings show that the teacher solicited students' reasoning more often as the academic year progressed, and students also began developing mathematical reasoning in meaningful ways, such as articulating their mathematical thinking, responding to other students' reasoning, and building on those ideas leading by the teacher. However, findings also show that teacher change in teaching practices is complicated and intertwined with various dimensions of teacher development. This study contributes to the understanding of changes in teaching practices, which has significant implications for teacher professional development and frameworks for investigating teacher learning.

• Journal of KIISE:Software and Applications
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• v.32 no.9
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• pp.927-935
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• 2005

The certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions appearing in the rules are represented by real values between zero and one. If it can allow the certainty factors of the fuzzy production rules and the certainty factors of fuzzy propositions can be represented by intervals, such as vague numbers between zero and one based on vague sets, then it can allow the reasoning of rule-based systems to perform fuzzy reasoning in more flexible manner[18]. we are also proposed an efficient algorithm to perform vague set reasoning automatically. This vague set reasoning algorithm allows the rule-based systems to perform reasoning in a more flexible and more efficient.

• School Mathematics
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• v.14 no.1
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• pp.85-107
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• 2012

Problem solving is important in school mathematics as the means and end of mathematics education. In elementary school, inductive reasoning is closely linked to problem solving. The purpose of this study was to examine ways of improving problem solving ability through analysis of inductive reasoning process. After the process of inductive reasoning in problem solving was analyzed, five different stages of inductive reasoning were selected. It's assumed that the flow of inductive reasoning would begin with stage 0 and then go on to the higher stages step by step, and diverse sorts of additional inductive reasoning flow were selected depending on what students would do in case of finding counter examples to a regulation found by them or to their inference. And then a case study was implemented after four elementary school students who were in their sixth grade were selected in order to check the appropriateness of the stages and flows of inductive reasoning selected in this study, and how to teach inductive reasoning and what to teach to improve problem solving ability in terms of questioning and advising, the creation of student-centered class culture and representation were discussed to map out lesson plans. The conclusion of the study and the implications of the conclusion were as follows: First, a change of teacher roles is required in problem-solving education. Teachers should provide students with a wide variety of problem-solving strategies, serve as facilitators of their thinking and give many chances for them ide splore the given problems on their own. And they should be careful entegieto take considerations on the level of each student's understanding, the changes of their thinking during problem-solving process and their response. Second, elementary schools also should provide more intensive education on justification, and one of the best teaching methods will be by taking generic examples. Third, a student-centered classroom should be created to further the class participation of students and encourage them to explore without any restrictions. Fourth, inductive reasoning should be viewed as a crucial means to boost mathematical creativity.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1998.10a
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• pp.224-227
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• 1998

This paper proposes inter-level causal reasoning to implement synergistic approach. We decompose KOSPI prediction model into economy and industry level. Two kinds of intra-level QCOM are combined in inter-level QCOM via Inter-level relations. Downward reasoning is achieved by propagating the disturbance in the higher level to lower level while upward reasoning is to analyze the reverse cases.