• Education of Primary School Mathematics
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• v.16 no.1
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• pp.21-33
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• 2013

In this study, We analyzed the mathematical thinking of sixth grade students showed mathematics lessons through the application of Lakatos' methodology and search for the role of their teachers in this lessons. We supposed to find the solution to the way of teaching-learning regarding the Lakatos' methodology for the elementary school level. According to the stages of presenting a problem situation, suggesting an initial conjecture, examining the conjecture, and improving the conjecture, we had lessons 8 times that are applied to Lakato's methodology. We gathered and analyzed data from lessons and interviews recording videotapes, documents for this study. The participants showed a lot of mathematical thinking. They understood the problem situation with the skill of fundamental thinking and suggested the initial conjecture by the skill of developmental thinking and they found a counter-example to be able to rebut the initial conjecture by critical thinking. Correcting the conjecture not to have counter-example, they drew developmental thinking and made their thinking generalize.

• Journal of Science Education
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• v.42 no.3
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• pp.322-333
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• 2018

The purpose of this study is to identify the types and characteristics of the integrative thinking that learners with diverse learning backgrounds use in solving earth science problems. Four students in middle school were surveyed using questionnaires to know students' science learning background and test items with integrated content. A total of 200 items, 40 integrated items and 160 general items, were administered ten times. The students did not show a consistent relationship in terms of correct answer percentage in general items and that of in integrated items. In order to understand the type of integrative thinking of each student, after students solve an item, we analyzed the percentage of correct answers by types and interviewed them and analyzed the contents to identify the characteristics of the thinking used in solving each item. As a result, the types of integrative thinking used in problem solving were classified into three types, knowledge-based, real life-based, and integrated inquiry-based types. It is necessary to study various ways to improve the integrative thinking ability considering the characteristics of students in science teaching and learning.

• Journal of the Korean earth science society
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• v.39 no.1
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• pp.103-116
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• 2018

The purpose of this study was to explore $6^{th}$ graders learning progression for lunar phase change focusing astronomical systems thinking. By analyzing the results of previous studies, we developed the constructed-response items, set up the hypothetical learning progressions, and developed the item analysis framework based on the hypothetical learning progressions. Before and after the instruction on the lunar phase change, we collected test data using the constructed-response items. The results of the assessment were used to validate the hypothetical learning progression. Through this, we were able to explore the learning progression of the earth-moon system in a bottom-up. As a result of the study, elementary students seemed to have difficulty in the transformation between the earth-based perspective and the space-based perspective. In addition, based on the elementary school students' learning progression on lunar phase change, we concluded that the concept of the lunar phase change was a bit difficult for elementary students to learn in elementary science curriculum.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.63-86
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• 2013

This study aimed to explore how middle school students perceive constructed-response items and how they solve those items and the patterns of the processes. For this purpose, data were collected from middle school students through survey, written responses on those items that were developed for this particular purpose, and interviews. The survey data were analyzed by using Excel and the written responses and interview data qualitatively. The findings about the students' perceptions about the constructed-response items suggested that the middle school students perceive the items primarily as involving writing solutions logically(17%) and being capable of explaining while solving them(7%). The most difficulties they encounter when solving the items were understanding(26%), applying(12%), mathematical writing(25%), computing(23%), and reasoning(14%). The findings about the students' mathematical proficiencies showed that they made an error most in reasoning (35%), then in understanding(31%), in applying(9%), and least in computing(3%).

• Journal of Gifted/Talented Education
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• v.13 no.3
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• pp.69-85
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• 2003

This study verified the differences of thinking styles between science highschool students and general students in reference to academic achievement. The subjects of this study are 211 high school students, who were composed of 122 science school students and 93 general school students. The significant results of this study are as follows: First, science highschool students showed more distinguishable differences in thinking style than general highschool students. Second, the former rather than the latter is revealed to be more variable in thinking styles explaining academic achievement. Next, in case of science highschool students, thinking style which is affected by intelligence is turned out to be an indirect factor influencing academic achievement. Finally, I verified the importance of distinction of science highschool students and the usefulness of thinking styles, gave suggestions on the reformation and direction of current school education of science-gifted students.

• Journal of Gifted/Talented Education
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• v.18 no.1
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• pp.53-77
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• 2008

This study was conducted with the focus on the process of constructing 3 definition and produced definitions as well as gifted students' conceptions of a mathematical definition In the study, the students made five types of regular polyhedrons (section1), observed them and stated their characteristics (section2) and then constructed a definition of regular polyhedrons based on their observations (section3). We divided students into two groups by analyzing students' definitions. One group made definitions that were consist with a mathematical definition of regular polyhedrons, the other one made definitions that were not. We checked if they fulfilled requirements for a mathematical definition. Researchers sought to gain various suggestions through the analysis of the observations and definition laid down by the students and through the characteristics shown by the students in the process of defining the concept.

• Journal of Science Education
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• v.36 no.2
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• pp.216-234
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• 2012

This study examined the characteristics of verbal interactions presented in TS activities with different tasks' openness levels by the cognitive levels of students through the implementation of TS program to 14 fifth graders in gifted class. Results of this study revealed that the open-type TS activities showed higher percentages of verbal interactions than the guiding-type TS activities showed and that the higher the open level of tasks was, the more high-level verbal interactions occurred. These results were showed in almost all subcomponents of verbal interactions. The results according to the students' cognitive levels showed that the higher the cognitive level of students was, higher frequency of interactions, high-level verbal interactions and a variety of verbal interactions occurred. The influence of both cognitive level of students and the task's openness on verbal interactions among students seemed to be interactive, however. In guiding-type activities, the percentage of high-level verbal interactions was not high although the cognitive level of students was high. And students in low level of cognition showed far lower frequency of interactions and their percentage of high-level verbal interactions was low even though the openness of the tasks was high. The results of this study meant that although open-type activities drew higher level verbal interactions by stimulating students' thought, the effects would be limited owing to their low cognitive level. Based on these findings, an implication was suggested that it is important to design instructional strategies and adjust openness level of TS activities to students' cognitive level so as to stimulate the thinking of students in lower cognitive level and to highten their engagement in activities.

• School Mathematics
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• v.11 no.1
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• pp.147-164
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• 2009

This study investigated the development of geometrical thinking levels of the under achievers at mathematics through supplementary classes according to van Hiele's learning process by stages using mathematical journal writing. We selected five under achievers at mathematics among the fourth graders. We examined their geometrical thinking levels in advance and interviewed them to collect basic data related to their family backgrounds and their attitude toward mathematics and their characteristics. Supplementary classes for the under achievers were conducted a couple of times a week during 12 weeks. Each class was conducted through five learning stages of van Hiele and journal writing was applied to the last consolidating stage. After 12th class had been finished, posttest on geometrical thinking levels was conducted and the journals written by the pupils were analyzed to find out changes in their geometrical thinking levels. The result is that three out of five under achievers showed one or two level-up in their geometrical thinking levels, though the other two pupils remained at the same level as the results by the pretest. Moreover we found that mathematical journal writing could provide the pupils with opportunities to restructure the content which they study through their class.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.101-115
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• 2012

Analogy, a plausible reasoning on the basis of similarity, is one of the thinking strategy for concept formation, problem solving, and new discovery in many disciplines. Statistics educators argue that analogy can be used as an useful thinking strategy in statistics as well. This study investigated the characteristics of students' analogical thinking in statistics. The mathematically gifted were asked to construct similar problems to a base problem which is a statistical problem having a statistical context. From the analysis of the problems, students' new problems were classified into five types on the basis of the preservation of the statistical context and that of the basic structure of the base problem. From the result, researchers provide some implications. In statistics, the problems, which failed to preserve the statistical context of base problem, have no meaning in statistics. However, the problems which preserved the statistical context can give possibilities for reconceptualization of the statistical concept even though the basic structure of the problem were changed.

• Journal of Gifted/Talented Education
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• v.26 no.1
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• pp.211-230
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• 2016

The study aimed to investigate the characteristics of algebraic thinking of the mathematically gifted students and search for how to teach algebraic thinking. Research subjects in this study included 93 students who applied for a science gifted education center affiliated with a university in 2015 and previously experienced gifted education. Students' responses on an algebraic item of a creative thinking test in mathematics, which was given as screening process for admission were collected as data. A framework of algebraic thinking factors were extracted from literature review and utilized for data analysis. It was found that students showed difficulty in quantitative reasoning between two quantities and tendency to find solutions regarding equations as problem solving tools. In this process, students tended to concentrate variables on unknown place holders and to had difficulty understanding various meanings of variables. Some of students generated errors about algebraic concepts. In conclusions, it is recommended that functional thinking including such as generalizing and reasoning the relation among changing quantities is extended, procedural as well as structural aspects of algebraic expressions are emphasized, various situations to learn variables are given, and activities constructing variables on their own are strengthened for improving gifted students' learning and teaching algebra.