• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• Korean Journal of Culture and Social Issue
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• v.14 no.1
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• pp.101-123
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• 2008

We investigated the implicit representations of success/failure associated with mother in male and female college students. In study 1, participants were presented 'mother' or 'basket' as a context prime and 'success' or 'failure' related words as second primes for 100ms, and were asked to make lexical decisions about 'accept' or 'reject' related words and non-words after 150 ms (SOA 250ms). Results revealed that lexical decision times on the mother condition were more rapid than the ones on the basket condition, and lexical decision times on the acceptance condition were more rapid than the ones on the rejection condition, and female participants showed shorter times than male students did. In study 2, we divided participants into four groups by gender and attachment style, Results showed that the interaction between success/failure and acceptance/rejection was statistically significant, that is, quickest lexical decision times on the success-acceptance condition, and slowed times on failure-acceptance, failure-rejection, and success-rejection condition in order. On the other hand, no significant differences between high and low attachment group were found in males, but significant three-way interactions were found in females. In highly attached females, lexical decision times in success-acceptance condition were not differed from ones in success-rejection condition, and slowed times in failure-rejection condition. Low attached females showed very rapid times in success-acceptance condition, but very slow times in success-rejection condition. The results were discussed in terms of self-positivity and success/failure scheme depending on gender and attachment styles.

• Journal of the Korean earth science society
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• v.22 no.5
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• pp.339-349
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• 2001

The aim of this study is to explore effective teaching strategies through an investigation of the problem-solving abilities and reasons for the unsuccessful problem solving of pre-service teachers. The participants of the study were 60 pre-service teachers who were expected to teach earth science in elementary school (40) and secondary school (20). The participants had taken a course in astronomy before they took part in the present study. The instruments for the study were a paper-and-pencil test and interviews. The results demonstrated that the pre-service teachers' abilities to solve problems were low. The pre-service teachers of the elementary school were inferior to those of the secondary school in their problem solving abilities. The causes for the unsuccessful problem solving were identified as follows: (1) lack of prerequisite knowledge to understand the motions of the moon and the planets, (2) failure to represent problems based on solution principles, (3) failure to apply the knowledge acquired in one setting to another, different setting, (4) frames of reference the frameworks for everyday life situation and for earth science problem situation, and (5) rote-memorization of facts rather than understanding the cause-and-effect relationships. The above causes for unsuccessful problem solving seemed to be related to the characteristics of novice problem solvers in general and of the tasks about the motions of the moon and the planets. Suggestions are made to enhance pre-service teachers' problem solving abilities based on the result of the study.

• Journal of Gifted/Talented Education
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• v.25 no.4
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• pp.581-605
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• 2015

The purpose of this study is to build an instruction method focused on the mathematical process and apply it to 12, 5-year-olds from Kindergarten located in Seoul with a view to explore the changes in their mathematical thinking. In addition, surveys with parents and teachers, as well as those conducted in the field of early childhood education, were conducted to analyze the current situation. The effects focused on the five mathematical processes, namely problem solving, reasoning and proof, connecting, representing and communication was found to help the interactions between teacher-child and child-child stimulate the mathematical thinking of the children and induce changes. The mathematical process-focused instruction aimed to advance mathematical thinking internalized mathematical knowledge, presented an integrated problematic situation, and empathized the mathematical process, which enabled the children to solve the problem by working together with peers. As such, the mathematical thinking of the children was integrated and developed within the process of a positive change in the mathematical attitude in which mathematical knowledge is internalized through mathematical process.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.635-662
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• 2016

Combinatorics, the basis of probabilistic thinking, is an important area of mathematics and closely linked with other subjects such as informatics and STEAM areas. But combinatorics is one of the most difficult units in school mathematics for leaning and teaching. This study, using the designed combinatorial models and executable expression, aims to analyzes the eye movement of graduate students when they translate the written combinatorial problems to the corresponding executable expression, and examines not only the understanding process of the written combinatorial sentences but also the degree of difficulties depending on the combinatorial semantic structures. The result of the study shows that there are two types of solving process the participants take when they solve the problems : one is to choose the right executable expression by comparing the sentence and the executable expression frequently. The other approach is to find the corresponding executable expression after they derive the suitable mental model by translating the combinatorial sentence. We found the cognitive processing patterns of the participants how they pay attention to words and numbers related to the essential informations hidden in the sentence. Also we found that the student's eyes rest upon the essential combinatorial sentences and executable expressions longer and they perform the complicated cognitive handling process such as comparing the written sentence with executable expressions when they try the problems whose meaning structure is rarely used in the school mathematics. The data of eye movement provide meaningful information for analyzing the cognitive process related to the solving process of the participants.

• The Mathematical Education
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• v.42 no.5
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• pp.637-646
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• 2003

Visual representation is very important topic in Mathematics Education since it fosters understanding of Mathematical concepts, principles and rules and helps to solve the problem. So, the purpose of this paper is to analyze and clarify the various meaning and roles about the visual representation. For this purpose, I examine the status of the visual representation. Since the visual representation has the roles of creatively mathematical activity, we emphasize the using of the visual representation in teaching and learning. Next, I examine the errors in relation to the visual representation which come from limitation of the visual representation. It suggests that students have to know conceptual meaning of the visual representation when they use the visual representation. Finally, I suggest some examples of problem solving via the visual representation. This examples clarify that the visual representation gives the clues and solution of problem solving. Students can apprehend intuitively and easily the mathematical concepts, principles and rules using the visual representation because of its properties of finiteness and concreteness. So, mathematics teachers create the various visual representations and show students them. Moreover, mathematics teachers ask students to design the visual representation and teach students to understand the conceptual meaning of the visual representation.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.595-605
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• 2014

Infinite decimals have an infinite number of digits, chosen arbitrary and independently, to the right side of the decimal point. Since infinite decimals are ambiguous numbers impossible to write them down completely, the infinite decimal representation accompanies unavoidable opaqueness. This article focused the transparent aspect of infinite decimal representation with respect to the completeness axiom of real numbers. Long before the formalization of real number concept in $19^{th}$ century, many mathematicians were able to deal with real numbers relying on this transparency of infinite decimal representations. This analysis will contribute to overcome the double discontinuity caused by the different conceptualizations of real numbers in school and academic mathematics.

• Korean Journal of Cognitive Science
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• v.2 no.2
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• pp.221-259
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• 1990

Four experiments explored how the size ratio of two letter patterns affects jundgment times in a same-different matching task.Size, continuity of strokes,positions of the two vowel letters were systematically varied in order to test predictions,derved from the following hypotheses:Analogue transformation,position,use of diagnostic information,and decision sriteria.Size ratio influenced only reaction times for same responses and,more importantly,changes in the length of a horizintal line in a letter affected same responses more than the other feature.Taken together,the present experiments provide support for the diagnostic information hypothesis, while casting in doubt the other hypotheses on the nature of size transformations.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06c
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• pp.210-213
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• 2011

기억 인출 단서는 학습을 통해 장기기억 공간에 저장된 정보를 인출하는 과정에서 중요하며, 서로 다른 종류의 기억 인출 단서에 따른 기억 인출 결과 및 이에 대한 인지 학습적 특성 규명은 교육, 범죄 수사, 그리고 인간의 뇌 기능을 모방한 기계학습 연구 등에서 중요하게 다루어져야 할 문제이다. 본 논문에서는 비디오 데이터를 이용하여 학습한 내용을 인출하는 과정에서 텍스트와 이미지가 각각 인출 단서로서 기억인출 결과에 미치는 영향을 분석하고, 기억 정보 및 시각 정보 처리와 관련된 뇌 영역에서의 뇌전도 분석을 이용하여 이를 해석하였다. 실험 결과를 통해 기억 인출을 위해 이미지-텍스트를 제시할 경우 전전두엽의 기억인출 관련 부위와 시각 피질이 위치한 후두엽의 인터랙션이 높게 이루어지면서 암묵적인 시각적기억 표상의 인출이 발생하는 것을 알 수 있었다.

• Journal of Digital Convergence
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• v.14 no.8
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• pp.555-564
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• 2016

Space perception is generally treated as a problem relevant to the ability to recognize objects. Alternatively, the data from shape perception studies contributes to discussions about the geometry of visual space. This geometry is generally acknowledged not to be Euclidian, but instead, elliptical, hyperbolic or affine, which is to say, something that admits the distortions found in so many shape perception studies. The purpose of this review article is to understand perceived shape and the geometry of visual space in the context of visually guided action. Thus, two prominent approaches that explain the relation between perception and action were compared. It is important to understand the fundamental information of how human perceive visual space and perform visually guided action for the convergence on embodied cognition, and further on artificial intelligence researches.