• International Journal of Internet, Broadcasting and Communication
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• v.11 no.3
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• pp.49-58
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• 2019

Efficient evidential reasoning is an important issue in the development of advanced knowledge based systems. Efficiency is closely related to the design of problems solving methods adopted in the system. The explicit modeling of problem-solving structures is suggested for efficient and effective reasoning. It is pointed out that the problem-solving method framework is often too coarse-grained and too abstract to specify the detailed design and implementation of a reasoning system. Therefore, as a key step in developing a new reasoning scheme based on properties of the problem, the problem-solving method framework is expanded by introducing finer grained problem-solving primitives and defining an overall control structure in terms of these primitives. Once the individual components of the control structure are defined in terms of problem solving primitives, the overall control algorithm for the reasoning system can be represented in terms of a finite state diagram.

• Education of Primary School Mathematics
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• v.2 no.2
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• pp.113-131
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• 1998

The purpose of this study is to investigate the relationships among affective characteristics, mathematical problem-solving abilities, and reasoning abilities of the 6th graders for mathematics, and to analyze whether the relationships have any differences according to the regions, which the subjects live. The results are as follows： First, self-awareness is the most important factor which is related mathematical problem-solving abilities and reasoning abilities, and learning habit and deductive reasoning ability have the most strong relationships. Second, for the relationships between problem-solving abilities and reasoning abilities, inductive reasoning ability is more related to problem-solving ability than deductive reasoning ability Third, for the regions, there is a significant difference between mathematical abilities and deductive reasoning abilities of the subjects.

• International Journal of Advanced Culture Technology
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• v.7 no.3
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• pp.158-165
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• 2019

Knowledge based system includes tools for constructing, testing, validating and refining the system along with user interfaces. An important issue in the design of a complete knowledge based system is the ability to produce explanations. Explanations are not just a series of rules involved in reasoning track. More detailed and explicit form of explanations is required not only for reliable reasoning but also for maintainability of the knowledge based system. This requires the explanation mechanisms to extend from knowledge oriented analysis to task oriented explanations. The explicit modeling of problem solving structures is suggested for explanation generation as well as for efficient and effective reasoning. Unlike other explanation scheme such as feedback explanation, the detailed, smaller and explicit representation of problem solving constructs can provide the system with capability of quality explanation. As a key step to development for explanation scheme, the problem solving methods are broken down into a finer grained problem solving primitives. The system records all the steps with problem solving primitives and knowledge involved in the reasoning. These are used to validate the conclusion of the consultation through explanations. The system provides user interfaces and uses specific templates for generating explanation text.

• Journal of Korean Elementary Science Education
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• v.25 no.spc5
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• pp.567-581
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• 2007

This study examined patterns of reasoning of both the scientifically-gifted and children of average ability as witnessed in their science problem solving skills. Science problem solving skills are one of the significant characteristics of scientifically gifted children, and by using methods such as individual interviews, inductive reasoning, abductive reasoning, and deductive reasoning, the characteristics of these children can be to be further explored and categorized. The study also compared the findings with those of average children. This study sought to determine efficient guidelines fur teaching the scientifically-gifted, to come up with basic materials for developing relevant programs, and to find suggestions for identifying such students. The results of the study are as follows: Firstly, the creative science problem solving skills of the scientifically-gifted were better than that of the average students. Secondly, all of the three reasoning patterns used revealed in creative science solving processes were different between the gifted and the average, especially in terms of abductive reasoning, which was proved to reveal the greatest distinction between the two groups.

• East Asian mathematical journal
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• v.31 no.2
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• pp.145-165
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• 2015

The purpose of this study is to suggest how to go about teaching and learning secondary school algebra by analyzing problem-solving ability and problem-solving process through algebraic reasoning. In doing this, 393 students' data were thoroughly analyzed after setting up the exam questions and analytic standards. As with the test conducted with technical school students, the students scored low achievement in the algebraic reasoning test and even worse the majority tried to answer the questions by substituting arbitrary numbers. The students with high problem-solving abilities tended to utilize conceptual strategies as well as procedural strategies, whereas those with low problem-solving abilities were more keen on utilizing procedural strategies. All the subject groups mentioned above frequently utilized equations in solving the questions, and when that utilization failed they were left with the unanswered questions. When solving algebraic reasoning questions, students need to be guided to utilize both strategies based on the questions.

• The Mathematical Education
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• v.60 no.2
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• pp.133-157
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• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• The Mathematical Education
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• v.51 no.2
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• pp.95-114
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• 2012

This study examines the use of ill-structured problem to help the 4th graders' problem solving and reasoning. It appears that children with good understanding of problem situation tend to accept the situation as itself rather than just as texts and produce various results with extraction of meaningful variables from situation. In addition, children with better understanding of problem situation show AR (algorithmic reasoning) and CR (creative reasoning) while children with poor understanding of problem situation show just AR (algorithmic reasoning) on their reasoning type.

• 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.

• School Mathematics
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• v.19 no.1
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• pp.153-170
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• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

• 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.