• Journal of The Korean Association of Information Education
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• v.23 no.3
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• pp.219-227
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• 2019

The educational method of physical computing, where students can experience software programming principles and practices while making concrete objects beyond outputs residing just inside of computer monitors, are drawing attentions. This current research sought an instructional method for pre-service teachers that they can experience 3D printing and modeling and at the same time they can understand programming principles in the 3D modeling processes. To achieve this aim, the TinkerCAD $Codeblocks^{(R)}$ was analyzed based on the computational thinking framework and a course utilizing the $Codeblocks^{(R)}$ to 3D modeling was devised. The designed class was applied to pre-service teachers and the students' perceptions of the class were collected by using a semi-structured survey. This study provides implications to software education for pre-service teachers as an instructional case that 3D printing is used to connecting computational thinking skills.

• Journal of the Korean Geographical Society
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• v.46 no.4
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• pp.534-553
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• 2011

Analogical thinking is a problem-solving strategy to use a familiar problem (or base analog) to solve a novel problem of the same type (the target problem). The purpose of this study is to provide new insight into geography teaching and learning by connecting cognitive science research on analogical thinking with issues of geography education and suggest that teaching with analogies can be a productive instructional strategy for geography. In this study, using the various examples of analogical thinking used in geography we defined analogical thinking, addressed the theoretical models on analogical transfer, and discussed conditions that make an effective analogical transfer. The major research findings include the following: a) the spatial analogy, indicating skills to find places that may be far apart but have similar locations, and therefore have other similar conditions and/or connections, can provide a useful way to design contents for place learning; b) representational transfer, specifying a common representation for two problems, can play a key role in solving geographic problems requiring data visualization and spatialization processes; and c) either asking learners to compare/analyze similar examples sharing common structure or providing them examples bridging the gap between concrete, real-life phenomena and the ideas and models can contribute to learning in geographic concepts and skills. The spatial analogy requiring both geographic content knowledge and visual/spatial thinking has the potential to become a content-specific problem-solving strategy. We ended with recommendations for future research on analogy that is important in geography education.

• Journal of Korean Elementary Science Education
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• v.25 no.4
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• pp.363-373
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• 2006

The purposes of this study were to analyze the within-group verbal interactions in Thinking Science activities and compare the characteristics of verbal interactions shown by the pupils as well as the differences in help by e teacher in Korea with those in the UK. For the purposes of this study, 16 pupils from comparable groups by cognitive level were selected from both countries. Verbal interactions and teacher help during group discussions were audio/ video taped and the types of students' interactions were classified into interactions related to problem solving, management of classroom loaming and others. The results of this study showed that the verbal interactions in Korean groups were more activated than those in the UK groups. However, the percentages of high level interactions such as metacognitive questions, elaborative suggestions and logical argumentations were higher in the UK groups than those in the Korean groups. Observation of the within-group activities revealed that the pupils of both countries shared some common ground in the following ways; neither recognized the need to formulate the hypothesis in the process of inquiry and that the procedures of discussion were dominated by the pupils of higher cognitive level as the discussion proceeded. It was also observed that the pupils in the UK were considerate in response to the questions posed by both their peers or the teacher, while the pupils in Korea were influenced by their prior knowledge in the subject. Analysis of the teacher help during the inquiry activities showed that the tendency fur the teacher to emphasize the process rather than the product in the procedures of discussion and the extent he/she allowed the pupils to think and consider were closely related to the characteristics of the teacher himself/herself and was found to be a point of commonality in both countries. However, the teachers in the UK revealed the tendency of trying to propose the task to the pupils in concrete and systematic ways and guide the discussion based on the thinking of the pupils, while those in Korea tried to use strategies designed to draw out active verbal interactions among the pupils.

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.117-145
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• 2006

Mathematically gifted children have creative curiosity about novel tasks deriving from their natural mathematical talents, aptitudes, intellectual abilities and creativities. More effect in nurturing the creative thinking found in brilliant children, letting them approach problem solving in various ways and make strategic attempts is needed. Given this perspective, it is desirable to select open-ended and atypical problems as a task for educational program for gifted children. In this paper, various types of open-ended problems were framed and based on these, teaming activities were adapted into gifted children's class. Then in the problem solving process, the characteristic of bright children's mathematical thinking ability and examples of problem solving strategies were analyzed so that suggestions about classes for bright children utilizing open-ended tasks at elementary schools could be achieved. For this, an open-ended task made of 24 inquiries was structured, the teaching procedure was made of three steps properly transforming Renzulli's Enrichment Triad Model, and 24 periods of classes were progressed according to the teaching plan. One period of class for each subcategories of mathematical thinking ability; ability of intuitional insight, systematizing information, space formation/visualization, mathematical abstraction, mathematical reasoning, and reflective thinking were chosen and analyzed regarding teaching, teaming process and products. Problem solving examples that could be anticipated through teaching and teaming process and products analysis, and creative problem solving examples were suggested, and suggestions about teaching bright children using open-ended tasks were deduced based on the analysis of the characteristic of tasks, role of the teacher, impartiality and probability of approaching through reflecting the classes. Through the case study of a mathematics class for bright children making use of open-ended tasks proved to satisfy the curiosity of the students, and was proved to be effective for providing and forming a habit of various mathematical thinking experiences by establishing atypical mathematical problem solving strategies. This study is meaningful in that it provided mathematically gifted children's problem solving procedures about open-ended problems and it made an attempt at concrete and practical case study about classes fur gifted children while most of studies on education for gifted children in this country focus on the studies on basic theories or quantitative studies.

• Journal of Educational Research in Mathematics
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• v.17 no.2
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• pp.163-177
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• 2007

Studies on mathematically gifted students have been conducted following Krutetskii. There still exists a necessity for a more detailed research on how these students' mathematical competence is actually displayed during the problem solving process. In this study, it was attempted to analyse the algebraic thinking process in the problem solving a peg puzzle in which 4 mathematically gifted students, who belong to the upper 0.01% group in their grade of elementary school in Korea. They solved and generalized the straight line peg puzzle. Mathematically gifted elementary school students had the tendency to find a general structure using generic examples rather than find inductive rules. They did not have difficulty in expressing their thoughts in letter expressions and in expressing their answers in written language; and though they could estimate general patterns while performing generalization of two factors, it was revealed that not all of them can solve the general formula of two factors. In addition, in the process of discovering a general pattern, it was confirmed that they prefer using diagrams to manipulating concrete objects or using tables. But as to whether or not they verify their generalization results using generalized concrete cases, individual difference was found. From this fact it was confirmed that repeated experiments, on the relationship between a child's generalization ability and his/her behavioral pattern that verifies his/her generalization result through application to a concrete case, are necessary.

• Journal of The Korean Association For Science Education
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• v.11 no.2
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• pp.23-30
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• 1991

The purpose of this study is to investigate the interrelationships on integrated science process skills and Piagetian cognitive modes for high school students according to the different cognitive reasoning levels. About 509 high school students were randomly selected for the samples of this study. They were identified as concrete, transitional and formal operational stage with the scores of GALT(Group Assessment of Logical Thinking) developed by Roadrangka, Yeaney and Padilla(1982), and TIPS II(Test of Integrated Process Skills) developed by Burns, Wise and Okey(1983). The result of this study were showed that about 11.8% of the samples were in the concrete operational stage and about 24.4% of the samples were in the transitional stage, while about 63.8% of them were in the formal operational stage. It was also found that the achivement scores of the science process skills increase in accordance with the cognitive reasoning levels. The value of the correlation coefficient between science process skills and cognitive reasoning abilities was 0.49, which was significant at the 0.05 level. This finding seems to support previous research that the student's cognitive reasoning abilities appeared to have influenced student's scores of the science process skills No differences to the logical reasoning ability between male and female students according to each cognitive level were found except formal operational stage.

• Education of Primary School Mathematics
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• v.8 no.2 s.16
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• pp.97-113
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• 2004

The purpose of this study is to develop instructional methods for the formalized algorithm through informal knowledge in teaching division of fractions. The following results have been drawn from this study: First, before students learn formal knowledge about division of fractions, they knowledge or strategies to solve problems such as direct modeling strategies, languages to reason mathematically, and using operational expressions. Second, students could solve problems using informal knowledge which is based on partitioning. But they could not solve problems as the numbers involved in problems became complex. In the beginning, they could not reinvent invert-and-multiply rule only by concrete models. However, with the researcher's guidance, they can understand the meaning of a reciprocal number by using concrete models. Moreover, they had an ability to apply the pattern of solving problems when dividend is 1 into division problems of fractions when dividend is fraction. Third, instructional activities were developed by using the results of the teaching experiment performed in the second research step. They consist of student's worksheets and teachers' guides. In conclusion, formalizing students' informal knowledge can make students understand formal knowledge meaningfully and it has a potential that promote mathematical thinking. The teaching-learning activities developed in this study can be an example to help teachers formalize students' informal knowledge.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.405-423
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• 1998

This study aims to reflect the origin and the meaning of open education and to derive pedagogical principles for open mathematics education. Open education originates from Socrates who was the founder of discovery learning and has been developed by Locke, Rousseau, Froebel, Montessori, Dewey, Piaget, and so on. Thus open education is based on Humanism and Piaget's psychology. The aim of open education consists in developing potentials of children. The characteristics of open education can be summarized as follows: open curriculum, individualized instruction, diverse group organization and various instruction models, rich educational environment, and cooperative interaction based on open human relations. After considering the aims and the characteristics of open education, this study tries to suggest the aims and the directions for open mathematics education according to the philosophy of open education. The aim of open mathematics education is to develop mathematical potentials of children and to foster their mathematical appreciative view. In order to realize the aim, this study suggests five pedagogical principles. Firstly, the mathematical knowledge of children should be integrated by structurizing. Secondly, exploration activities for all kinds of real and concrete situations should be starting points of mathematics learning for the children. Thirdly, open-ended problem approach can facilitate children's diverse ways of thinking. Fourthly, the mathematics educators should emphasize the social interaction through small-group cooperation. Finally, rich educational environment should be provided by offering concrete and diverse material. In order to make open mathematics education effective, some considerations are required in terms of open mathematics curriculum, integrated construction of textbooks, autonomy of teachers and inquiry into children's mathematical capability.

• Journal of The Korean Association For Science Education
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• v.22 no.4
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• pp.837-850
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• 2002

In an attempt to accelerate the development of formal reasoning ability of students, 'Thinking Science' activities developed by the Cognitive Acceleration through Science Education(CASE) project were implemented to 841 students in 7th grade aged 12+ in six middle schools over a period of two years. Homogeneity between the CASE group and control group was tested with SRT II, while the improvement of formal reasoning ability of the students was tested with SRT VII. The results were analyzed by treatment, gender, and cognitive levels of the students. Statistically significant gains were shown in the CASE group compared with those in the control group. Cognitive level of girls in the CASE group significantly increased as compared with the control group, while there was moderate effect in boys. These results implied that the thinking science activities were effective in cognitive acceleration of girls aged 12+. It was shown that much more CASE students in pre or concrete operational level shifted to formal operational level as compared with the control group while there were significant effects in all levels (ES=0.31${\sim}$1.10) without showing any tendency.

• Journal of Korean Elementary Science Education
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• v.22 no.1
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• pp.1-14
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• 2003

This study investigated the effects of the cognitive acceleration program devised for accelerating the development of formal reasoning ability of students. ‘Thinking Science’ activities developed by the Cognitive Acceleration through Science Education(CASE) project were implemented to 420 students in 5th grade aged 10+ in four elementary schools over a period of two yea. Homogeneity between the experimental group and control group was tested with SRT II, and the improvement of formal reasoning ability of the students was tested with SRT III. The results were analyzed by treatment, gender, and cognitive levels of the students. Statistically significant gains were shown in the CASE group compared with those in the control group. Cognitive level of girls in the CASE group increased as compared with the control group, while there was moderate effect in boys for the primary school. These results implied that the thinking science activities were effective in cognitive acceleration of girls aged 10+. It was shown that much more CASE students in concrete operational level shifted to formal operational level as compared with the control group while there were no significant effects in the other levels for primary school.