• The Mathematical Education
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• v.47 no.2
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• pp.169-180
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• 2008

The purpose of this study was to analyze the elementary students' mathematical thinking, which is found during mathematical problem solving processes based on mathematical knowledge, heuristics, control, and mathematical disposition. The participants were 8 fifth grade elementary students in Seoul. A qualitative case study was used for investigating the students' mathematical thinking. The data were coded according to the four components of the students' mathematical thinking. The results of the analyses concerning mathematical thinking of the elementary students were as follows: First, in terms of mathematical knowledge, the elementary students frequently used conceptual knowledge, procedural knowledge and informal knowledge during problem solving processes. Second, students tended not to find new heuristics or apply new one, but they only used the heuristics acquired from the experiences of the class and prior experiences. Third, control was found while students were solving problems. Last, mathematical disposition influenced on the mathematical problem solving processes. Teachers need to in-depth observations on the problem solving processes of students, which leads to teachers'effective assistance on facilitating students' problem solving skills.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.545-562
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• 2009

This study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using "Protocol Analysis Method"and "Problem Behavior Graph" which is suggested by Newell and Simon as a qualitative analysis. In this study, four middle school students with high achievement in math were selected as subjects-two students for mathematical gifted group and the other two for control group also with high scores in math. The thinking characteristics of the four subjects, shown in the course of solving problems, were elicited, analyzed and compared, through the use of the creative test questionnaires which were supposed to clearly reveal the characteristics of mathematical gifted students' thinking processes. The results showed that there were several differences between the two groups-the mathematical gifted student group and their control group in their mathematical talents. From these case studies, we could say that it is significant to find out the characteristics of mathematical thinking processes of the mathematical gifted students in a more scientific way, in the sense that this result can be very useful to provide them with the chances to get more proper education by making clear the nature of thinking processes of the mathematical gifted students.

• Journal of Practical Engineering Education
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• v.10 no.1
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• pp.35-39
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• 2018

More and more universities are enforcing SW education for non-major undergraduates. However, they are experiencing difficulties in educating non-major students to understand computational thinking processes. In this paper, we did not use the mathematical operation problem to solve this problem. And we proposed a basic problem-solving process teaching method based on computational thinking using simple physical devices. In the proposed educational method, we teach a LED circuit using an Arduino board as an example. And it explains the problem-solving process with computational thinking. Through this, students learn core computational thinking processes such as abstraction, problem decomposition, pattern recognition and algorithms. By applying the proposed methodology, students can gain the concept and necessity of computational thinking processes without difficulty in understanding and analyzing the given problem.

• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.565-584
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• 2009

This study is aimed at providing the theoretical framework of characteristics of mathematical thinking processes and structuring the thinking process patterns of the mathematical gifted students through the analysis of their cognitive thinking processes. For this purpose, this study is trying to analyze characteristics of mathematical thinking processes of the mathematical gifted students in an objective and a systematic way, by using think-aloud method. For comparative study, the analysis framework with the use of the thinking characteristic code as a content-oriented method and the problem-solving processes code as a process-oriented method was developed, and the differences of thinking characteristics between the two groups chosen by the coding system which represented the subjects' thinking processes in the form of the language protocol through thinking-aloud method were compared and analyzed.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.87-101
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• 2005

The purpose of this paper is to propose a teaching method which is focused on the mathematical thinking skills such as the use of induction, counter example, analogy, and so on mathematicians use when they explore their research fields. Many have indicated that students have learned mathematics exploring to use very different methods mathematicians have done and suggested students explore as they do. In the first part of the paper, the plausible whole processes from the beginning time they get a rough idea to a refined mathematical truth. In the second part, an example with Euler characteristic of 1. In the third, explaining the same processes with ${\pi}$, a model modified from the processes is designed. It is hoped that the suggested model, focused on a variety of mathematical thinking, helps students learn mathematics with understanding and with the association of exploring entertainment.

• Journal of The Korean Association For Science Education
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• v.13 no.1
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• pp.31-47
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• 1993

This study was intended to find the characteristics of the middle school students' thinking processes and problem spaces when they solved the physics problems. Ten ninth grade students in Chon-Buk Do, Korea were participated in this study. The researcher investigated their thinking processes in solving 5 physics problems on electric circuit. "Thinking aloud" method was used as a research method. The students' thinking processes were recorded using an audio tape recorder and transfered into protocols. The protocols were analyzed by problem solving process coding system which was developed by Lee(1987) on the basis of Larkin's problem solving process model. The results are as follows : (1) On the average 2.85 items were solved among 5 test items, and only one person could solve all of the items correctly. (2) Problems were solved in sequence of understanding the problem, planning, carrying out the plan, and evaluating steps regardless of the problem difficulty. (3) In regard to the thinking process steps, there was no difference between the good solvers and the poor ones. But in the detail performance of problem solving, the former was different from the latter in respect with using the design of general solving procedure. (4) The basic problem spaces by the item analysis were divided into two classes. One was the problem space by using Qualitative approach in problem solving, and the other was one by using Quantitative approach. As novices in physics problem solving, most of the students used the problem space by using the Quantitative approach.

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.35-53
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• 2005

The purpose of this study is to analyze and confirm the effectiveness of two teacher-centered instruction methods in the context of linear functions: one with emphasis on mathematical thinking processes as an alternative to the more traditional method without such emphasis. The level of achievement of students under the teacher-centered instruction with explicit emphasis on mathematical thinking processes is consistently higher than that of students receiving the more traditional teacher-centered instruction. The alternative instruction method in the current study is expected to encourage and prompt students to better grasp and understand mathematical concepts, principles, as well as problem solving strategies. In contrast to other alternatives, the method offers the advantage of being readily incorporated into the actual teaching practices in the classroom, as the traditional frame of teacher-centered pedagogy familiar to teachers remains in tact.

• 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 the Korean Chemical Society
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• v.55 no.5
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• pp.846-856
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• 2011

In this study, we analyzed the characteristics of imagery thinking in the processes of generating analogy of seventh grade science-gifted students in terms of the information-processing of imagery. The analyses of the results revealed that science-gifted students' information-processing of imagery in the processes of generating analogy consisted of image generation, image operation, and image representation. The types of imagery used by science-gifted students were classified into perception imagery, memory imagery, and imagination imagery, and there were some differences in the patterns of information-processing of imagery. In the bases of these results, we suggested the information-processing model of imagery by the types of imagery used in generating analogy. The results of this study may provide useful implication to develop effective methods for a strategy of generating analogy emphasizing the interaction between analogy thinking and imagery thinking which promotes imagery thinking of science-gifted students.

• The Mathematical Education
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• v.42 no.5
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• pp.647-672
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• 2003

This study sought to determine the impact of the graphing calculator on prospective math-teachers' mathematical thinking while they engaged in the exploratory tasks. To understand students' thinking processes, two groups of three students enrolled in the college of education program participated in the study and their performances were audio-taped and described in the observers' notebooks. The results indicated that the prospective teachers got the clues in recalling the prior memory, adapting the algebraic knowledge to given problems, and finding the patterns related to data, to solve the tasks based on inductive, deductive, and creative thinking. The graphing calculator amplified the speed and accuracy of problem-solving strategies and resulted partly in students' progress to the creative thinking by their concept development.