• School Mathematics
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• v.9 no.2
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• pp.313-326
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• 2007

Recently in algebra curriculum, to recognizes and explains general nile expressing patterns is presented as the one alternative and is emphasized. In the seventh School Mathematic Curriculum regarding 'regularity and function' area, in elementary school curriculum, is guiding pattern activity of various form. But difficulty and problem of students are pointing in study for learning through pattern activity. In this article, emphasizes generalization process through research activity of pictorial/geometric pattern that is introduced much on elementary school mathematic curriculum and investigates various approach and strategy of student's thinking, state of symbolization in generalization process of pictorial/geometric pattern. And discusses generalization of pictorial/geometric pattern, difficulty of symbolization and suggested several proposals for research activity of pictorial/geometric pattern.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.113-116
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• 2006

본 논문은 소프트웨어 공정에 대하여 기호코팅을 이용한 유전자 알고리즘 기반 퍼지 다항식 뉴럴 네트워크 (Genetic Algorithms-based Fuzzy Polynomial Neural Networks ; gFPNN)의 모델을 제안한다. 유전자 알고리즘에는 이진코딩, 기호코팅, 실수코딩이 있다. 제안된 모델은 스트링의 길이에 따른 해밍절벽을 기호코딩으로 극복하였다. gFPNN에 전반부 멤버쉽 함수는 삼각형과 가우시안형의 멤버쉽 함수가 사용된다. 그리고 규칙의 후반부는 간략, 선형, 이차식 그리고 변형된 이차식 함수에 의해 설계된다. 실험적 예제를 통하여 제안된 모델의 성능이 근사화 능력과 일반화 능력이 우수함을 보인다.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.43-58
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• 2007

We review the eastern frog jump game and the western solitaire to apply the Baduk Pieces Game to mathematical education. This study introduce a didactical method of Baduk Pieces Game which is constructed with simplification, generalization, and extension. This didactical applications of the Baduk Pieces Game gives the students opportunities of patterns, generalization, and problem solving strategies.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.2091-2092
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• 2006

본 논문은 소프트웨어 공정에 대하여 유전자 알고리즘의 기호코딩을 이용한 정보입자 기반 퍼지 다항식 뉴럴 네트워크 (Information Granules based genetic Fuzzy Polynomial Neural Networks ;IG based gFPNN)의 모델 설계를 제안한다. 기존 퍼지 다항식 뉴럴네트워크의 구조 최적화를 위해 이진코딩을 사용하였다. 그러나 이진코딩에서 스트링의 길이가 길면 길수록 인접한 두 수 사이에 발생하는 급격한 비트 차이라는 해밍 절벽이 발생하였다. 이에 제안된 모델에서는 해밍절벽의 문제를 해결하기 위해 기호코딩을 사용하였다. 제안된 모델의 전반부 구조와 후반부 구조는 기존 모델에 구성을 그대로 사용한다. 실험적 예제를 통하여 제안된 모델의 근사화 능력과 일반화 능력이 우수함을 보인다.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.619-636
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• 2012

The main purpose of this study was to explore the process of generalization generated by mathematically gifted students. Specifically, this study probed how fourth, fifth, and sixth graders might generalize geometric patterns and represent such generalization. The subjects of this study were a total of 30 students from gifted classes of one elementary school in Korea. The results of this study showed that on the question of the launch stage, students used a lot of recursive strategies that built mainly on a few specific numbers in the given pattern in order to decide the number of successive differences. On the question of the towards a working generalization stage, however, upper graders tend to use a contextual strategy of looking for a pattern or making an equation based on the given information. The more difficult task, more students used recursive strategies or concrete strategies such as drawing or skip-counting. On the question of the towards an explicit generalization stage, students tended to describe patterns linguistically. However, upper graders used more frequently algebraic representations (symbols or formulas) than lower graders did. This tendency was consistent with regard to the question of the towards a justification stage. This result implies that mathematically gifted students use similar strategies in the process of generalizing a geometric pattern but upper graders prefer to use algebraic representations to demonstrate their thinking process more concisely. As this study examines the strategies students use to generalize a geometric pattern, it can provoke discussion on what kinds of prompts may be useful to promote a generalization ability of gifted students and what sorts of teaching strategies are possible to move from linguistic representations to algebraic representations.

• School Mathematics
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• v.13 no.4
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• pp.581-598
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• 2011

Given the growing agreement that algebra should be taught in the early stage of the curriculum, considerable studies have been conducted with regard to early algebra in the elementary school. However, there has been lack of research on how to organize mathematic lessons to develop of algebraic reasoning ability of the elementary school students. This research attempted to gain specific and practical information on effective algebraic teaching and learning in the elementary school. An exploratory qualitative case study was conducted to the fourth graders. This paper focused on the associative law of the multiplication. This paper showed what kinds of activities a teacher may organize following three steps: (a) focus on the properties of numbers and operations in specific situations, (b) discovery of the properties of numbers and operations with many examples, and (c) generalization of the properties of numbers and operations in arbitrary situations. Given the steps, this paper included an analysis on how the students developed their algebraic reasoning. This study provides implications on the important factors that lead to the development of algebraic reasoning ability for elementary students.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• Proceedings of the Botanical Society of Korea Conference
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• 1995.07a
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• pp.109-130
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• 1995

지난 반세기간에 우리나라에 채소 육종은 주요 채소의 주년공급을 가능하게 하였으며, 토지 생산성의 향상, 상품화율의 증대, 품질의 향상 등의 면에서도 괄목할 만한 성과를 거두었고 인공교잡은 물론이고 웅성불임성과 자가불화합성의 활용에 의한 1대잡종 품종의 일반화로 채소 산업의 발전에 크게 기여하였다. 앞으로는 기왕의 업적을 심화시키는 한편, 생산비를 절감하기 위한 생력화, 기계화 재배용 품종 및 내제초제성 품종의 개발 환경보호 및 식품안정성의 확보를 위한 내병층성 품종 개발, 수출시장과 다양화하는 국내의 시장기호에 대응하고 가공 식품의 표준화된 품질관리를 지원할 수 있도록 품질 면에서의 개량과 신작물 또는 신생태형 품종의 개발에도 더욱 노력이 필요하다. 이러한 육종목표를 달성하기 위한 유전자원의 확보는 더욱 어려워질 것이며 유전 양식이 복잡하고, 환경요인의 작용이 상대적으로 크기 때문에 전통적인 육종 방법만으로는 목표달성에 필요한 인적, 물적, 시간적 소요가 훨씬 증가될 전망이다. 유전변이의 창성 및 확대, 유용 대립인자의 도입, 동정 및 선발, 그리고 종자생산을 위한 자가 불화합성 및 웅성불임성과 개화·수정 관련 유전인자의 발현 조절에 분자유전학의 보완적 역할이 기대되며 이렇게 되면 전통육종과 분자유전학간의 잡종강세로 품종 개량의 효율은 크게 높아질 것이다.

• Journal of Intelligence and Information Systems
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• v.14 no.4
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• pp.1-18
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• 2008

By using previous similar case plans, the case-based planning (CBP) systems can generate efficiently plans for new problems. However, most existing CBP systems show limited functionalities for case retrieval and case generalization. Moreover, they do not allow their users to participate in the process of plan generation. To support efficient memory use and case retrieval, the proposed case-based planning system, JCBP, groups the set of cases sharing the same goal in each domain into individual case bases and maintains indexes to these individual case bases. The system applies the heuristic knowledge automatically extracted from the problem model to the case adaptation phase. It provides a sort of case generalization through goal regression. Also JCBP can operate in an interactive mode to support a mixed-initiative planning. Since it considers and utilizes user's preference and knowledge for solving the given planning problems, it can generate solution plans satisfying more user's needs and reduce the complexity of plan generation.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.4
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• pp.127-137
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• 1989

This paper describes hardware flow-chart and SDL-II, which are register-transfer level, to automate logic design. Hardware flow-chart specifies behavioral and structural charaterstics of generalized FSMs (Finite State Machine) usin the modified ASM (Algorithmic State Machnine) design techniques. SDL-II describes the hardware flow-chat which specifies the control and the data path of ASIC(Application Specific IC). Also many examples are enumerated to illustrate the features of hardware flow-chart and SDL-II.