• Journal for History of Mathematics
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• v.22 no.3
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• pp.187-206
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• 2009

On this study, the historical flow of the notation was briefly examined and the direction of mathematical investigation activity of the content of notation by analogy was explored and teaching learning materials were developed. Diverse mathematical facts were investigated on the basis of decimal system and binary system which are learned in middle school. First, the way of progressing analytic activity with algebraic material was examined. Second, on the basis of the notation which are learned in the first grade of middle school, the definition of the scale of a -notation, -a -notation, $\frac{1}{a}$notation, $\sqrt{a}$-notation was extended by analogy. The result of this study will be expected to establish the curriculum of mathematics and provide teaching and learning with the meaningful current events.

• Proceedings of the Korean Society for Cognitive Science Conference
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• 2002.05a
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• pp.59-64
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• 2002

인지심리학 및 인지언어학 분야에서 시도한 어휘 표상, 특히 움직임과 관련된 동사의 인지도식에 관한 연구들을 비교해보고자 한다. 인간의 언어학적인 지식을 도식적으로 표상 하고자 하는 노력은 언어의 통사적인 외형에만 치중하는 연구에서는 언어의 의미구조를 파악하기 힘들다고 판단하고 의미적인 범주화를 중요시하게 되었다. 본 연구에서는 시각적 이미지 도식을 중점적으로 살펴보기로 한다. 이미지 도식은 공간적 위치 관계, 이동, 형상 등에 관한 지각과 결부되어 있다. 이미지로 나타낸 표상은 근본적으로 세상의 인식과 세상에 대한 행동방법을 사용하게 하는 유추적이고 은유적인 원칙에 기초하고 있다. 이러한 점에 있어서, 언술을 발화한 화자는 어느 정도 주관적인 행동의 능력과 그가 인식한 개념화에서부터 문자화시킨 표상을 구성한다. 인지 원칙에 입각한 의미 표상에 중점을 둔 도식으로는, Langacker, Lakoff, Talmy의 도식이 있다. 프랑스에서 톰 R. Thom과 같은 수학자들은 질적인 현상에 관심을 가져 형역학(morphodynamique)이론을 확립하였는데, 이 이론은 요즘의 인지 연구에 수학적 기초를 제공하였다. R. Thom, J. Petitot-Cocorda의 도식 및 구조 의미론의 창시자라고 불리는 B.Pottier의 도식이 여기에 속한다 J.-P. Descles가 제시한 인지연산문법(Grammaire Applicative et Cognitive)은 다른 인지문법과는 달리 정보 자동처리과정에서 사용할 수 있는 연산자와 피연산자의 관계에 기초한 수학적 연산작용을 발전시켰다. 동사의 의미는 의미-인지 도식으로 설명되는데, 이것은 서로 다른 연산자와 피연산자로 구성된 형식화된 표현이다. 인간의 인지 기능은 언어로 표현되며, 언어는 인간의 의사소통, 사고 행위 및 인지학습의 핵심적 기능을 담당한다. 인간의 언어정보처리 메카니즘은 매우 복잡한 과정이기 때문에 언어정보처리와 관련된 언어심리학, 인지언어학, 형식언어학, 신경해부학 및 인공지능학 등의 관련된 분야의 학제적 연구가 필요하다.

• Journal of Gifted/Talented Education
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• v.21 no.2
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• pp.269-286
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• 2011

The purpose of this thesis is to examine difficulties students face in the inquiry activities of quadratic surface throughout mathematically gifted students' analogical inference and the influence of Cabri 3D in students' inquiry activities. For this examination, students' inquiry activities were observed, data of inferring quadratic surface process was analyzed, and students were interviewed in the middle of and at the end of their activities. The result of this thesis is as following: First, students had difficulties to come up with quadratic surfaced graph in the inquiry activity of quadratic surface and express the standard type equation. Secondly, students had difficulties confirming the process of inferred quadratic surface. Especially, students struggled finding out the difference between the inferred quadratic surface and the existing quadratic surface and the cause of it. Thirdly, applying Cabri 3D helped students to think of quadratic surface graph, however, since it could not express the quadratic surface graph in a perfect form, it is hard to say that Cabri 3D is helpful in the process of confirming students' inferred quadratic surface.

• Journal of The Korean Association For Science Education
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• v.26 no.4
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• pp.546-558
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• 2006

The purpose of this study was to identify heuristically how abduction was used in a context of solving an earth-environmental problem. Thirty two groups of participants with different institutional backgrounds, i,e., inservice earth science teachers, preservice science teachers, and high school students, solved an open-ended earth-environmental problem and produced group texts in which their ways of solving the problem were written, The inferential processes in the texts were rearranged according to the syllogistic form of abduction and then analyzed iteratively so as to find thinking strategies used in the abductive reasoning. The result showed that abduction was employed in the process of solving the earth-environmental problem and that several thinking strategies were used for inferring rules from which abductive conclusions were drawn. The strategies found included data reconstruction, chained abduction, adapting novel information, model construction and manipulation, causal combination, elimination, case-based analogy, and existential strategy. It was suggested that abductive problems could be used to enhance students' thinking abilities and their understanding of the nature of earth science and earth-environmental problems.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.125-143
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• 2014

In this study, we analyzed a mathematical discussion in the Calculus II course of the Gifted Science Academy and individual interviews to determine the relationship between cognitive conflicts and commognitive conflicts. The mathematical discussion began with a question from a student who seemed to have a cognitive conflict about the osculating plane of a space curve. The results indicated that the commognitive conflicts were resolved by ritualizing and using the socially constructed knowledge, but cognitive conflicts were not resolved. Furthermore, we found that the cause of the cognitive conflict resulted from the student's imperfect analogical reasoning and the reflective discourse about it could be a learning opportunity for overcoming the conflict. These findings imply that cognitive conflicts can trigger the appearance of commognitive conflicts, but the elimination of commognitive conflicts does not imply that cognitive conflicts are resolved.

• Journal of The Korean Association For Science Education
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• v.28 no.6
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• pp.565-578
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• 2008

The purpose of this study is to search for the factors that influence students' understanding of the nature of science through the experience of the cognitive processes of authentic open inquiries. The freshmen of a science high school practiced authentic open inquiries reflecting epistemological characteristics of authentic science. The case study was conducted with four focus students who were successful or unsuccessful at learning the nature of science during the authentic open inquiry activity. Questions that the focus students asked during the inquiries as well as students' answers to pre- and post-VNOS (C type) were analysed, and then elaborated in the semi-structured interview. The findings suggest that open inquiry activities provide the inquiry contexts that help science high school students to understand the nature of science, and that the characteristics of students' cognition influence the understanding of the nature of science. For instance, designing experiments with their own research questions had an influence on the students' understanding about the scientific methods and the diversity of research types, and drawing conclusions from their own data made students experience scientific reasoning. In addition, the experience of collecting anomalous data helped students to understand the role of inferences in generating scientific knowledge and the creative nature of scientific knowledge. In this inquiry context, the reflective thinking that came from proactive discussion among students, made students think about the validity of the designing experiments and interpreting data, and helped them to understand the uncertain nature of reasoning and the diverse nature of scientific methods. Moreover, divergent thinking linked to analogical thinking helped students to understand the creative nature of science.

• Journal of Korean Society of Transportation
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• v.18 no.4
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• pp.107-115
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• 2000

We suggest a method which solves the planar, two vehicle collision reconstruction problem. The method based on the Principle of impulse and momentum determines the pre-impact velocity components from Post-impact velocity components, vehicle Physical data and collision geometry. A novel feature is that although the impact coefficients such as the restitution coefficient and the impulse ratio are unknown, the method can estimate automatically the coefficients and calculate the pre-impact velocity components. This reverse calculation is important for vehicle accident reconstruction, since the pre-impact velocities are unknown and Post-impact Phase is the starting Point in a usual collision analysis. However. an inverse solution is not always Possible with the analytical rigid-body impact model. Mathematically, one does not exist under the common velocity condition. On the other hand, our method has a capability of reverse calculation under the condition if the absorbed energy during the collision process can be estimated using the crush profile. To validate the developed collision reconstruction a1gorithm, we use car-to-car collision test results. The analysis and experimental results agree well in the impact coefficients and the Pre-impact velocity components.

• Journal of The Korean Association For Science Education
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• v.27 no.9
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• pp.930-943
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• 2007

The purpose of this study was to investigate if students may actually experience scientific reasoning based on an epistemology of authentic science during authentic open inquiry. The samples were 86 10th graders in a science-high school in Seoul. The experimental group practiced authentic open inquiry and the control group practiced traditional school science inquiry in five weeks. Then, the questions students asked while performing inquiry tasks were analyzed. The frequency of the questions asked by students was almost same between two groups, however, the types of questions were different. The frequency of thinking questions in experimental group was higher than the control, and the difference was statistically significant (P<.01). Particularly, the frequency of expansive thinking questions and anomaly detection questions was much higher in experimental than the control group. Judging from the result, with the students from the experimental group asking questions reflecting on the epistemology of authentic science such as scientific methods, anomalous data, and uncertainty about reasoning, students may understand authentic science features during the activities of open authentic inquiry. The result from comparing questions according to the inquiry subject showed that more openness caused the higher frequency of anomaly detection questions and strategy questions, but that inductive thinking questions and analogical thinking questions were connected to inquiry subject rather than the openness of the inquiry.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.247-282
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• 2011

In the elementary school mathematics textbooks of the 7th national curriculum, just simple construction education is provided by having students draw a circle and triangle with compasses and drawing vertical and parallel lines with a set square. The purpose of this study was to examine the mathematical thinking of sixth-grade elementary school students in the construction process in a bid to give some suggestions on elementary construction guidance. As a result of teaching the sixth graders in gifted and nongifted classes about the equal division of line segments and evaluating their mathematical thinking, the following conclusion was reached, and there are some suggestions about that education: First, the sixth graders in the gifted classes were excellent enough to do mathematical thinking such as analogical thinking, deductive thinking, developmental thinking, generalizing thinking and symbolizing thinking when they learned to divide line segments equally and were given proper advice from their teacher. Second, the students who solved the problems without any advice or hint from the teacher didn't necessarily do lots of mathematical thinking. Third, tough construction such as the equal division of line segments was elusive for the students in the nongifted class, but it's possible for them to learn how to draw a perpendicular at midpoint, quadrangle or rhombus and extend a line by using compasses, which are more enriched construction that what's required by the current curriculum. Fourth, the students in the gifted and nongifted classes schematized the problems and symbolized the components and problem-solving process of the problems when they received process of the proble. Since they the urally got to use signs to explain their construction process, construction education could provide a good opportunity for sixth-grade students to make use of signs.

• Journal of Korean Elementary Science Education
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• v.41 no.2
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• pp.338-355
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• 2022

This study explored the effects of pre-service elementary teachers' inquiries into science class dilemmas. By closely examining the characteristics of the pre-service teachers' inquiry processes and changes in their educational decisions, the effectiveness of using dilemmas as part of teacher education was determined. Twenty fourth-year university pre-service teachers participated and conducted inquiries into science class dilemmas over seven weeks. Based on pre- and post-questionnaires, KWHL tables, inquiry reports, discussions, and group class presentations, the major factors that influence the pre-service teacher's decision-making changes were extracted. The pre-service teachers found the science inquiry process meaningful when exploring the science topics covered in the dilemmas, and claimed that elementary school students would be able to engage in meaningful science explorations if they learned science through inquiry. Furthermore, the pre-service teachers explored the thinking processes and background knowledge of the students in different ways. Documents such as teacher's guides and the curriculum were examined and the students' thought processes were identified through interviews with the teachers and students, which were found to reflect their educational decision-making. Moreover, it was recognized by the pre-service teachers that depending on the situation, alternative teaching methods were possible. The focus on the unstructured dilemma problems provided the pre-service teachers with problem-solving situations that triggered scientific inquiry and exploration of student thinking and revealed the complexity of science teaching and learning. Based on these results, the teacher education implications for using dilemma cases are discussed.