• Communications of Mathematical Education
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• v.23 no.2
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• pp.399-428
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• 2009

2007 Renewed Korea Elementary Mathematics Curriculum introduce algebra 6th grade. According to many studies about introducing algebra, it is desirable to teach 6th graders algebra through generalization of patterns. In this study, 6th graders' understanding processes and difficulties in pattern generalization were analyzed and possiblities of introducing algebra to 6th graders through pattern generalization were examined.

• 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.

• School Mathematics
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• v.14 no.3
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• pp.357-375
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• 2012

This research intends to examine how 6th graders (age 12) generalize various increasing patterns. In this research, 6 problems corresponding to the ax, x+a, ax+c, ax2, and ax2+c patterns were given to 290 students. Students' generalization methods were analysed by the generalization level suggested by Radford(2006), such as arithmetic and algebraic (factual, contextual, and symbolic) generalization. As the results of the study, we identified that students revealed the most high performance in the ax pattern in the aspect of the algebraic generalization, and lower performance in the ax2, x+a, ax+c, ax2+c in order. Also we identified that students' generalization methods differed in the same increasing patterns. This imply that we need to provide students with the pattern generalization activities in various contexts.

• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.232-233
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• 1998

이 논문에서는 시간지원 데이터베이스를 대상으로 하여 시간 간격과 시간 위상을 지닌 데이터에서의 정보를 탐사한다. 그리고 시간지원 데이터베이스에서의 시간 정보 유형을 제시하고 이에 따라 탐사되는 패턴의 유형을 분류한다. 또한 시간에 대한 계층적 구조인 시간 계층을 도입하고 이를 이용하여 각 항목의 유효시간 정보를 일반화시킨다. 시간 계층에 의한 유효시간의 일반화에 있어서 발생하는 시간 정보 유형의 변화와 패턴 유형의 변화를 살펴본다. 그리고 시간 간격 변화에 따른 패턴 정보의 발견을 예를 들어 기술한다. 이 논문에서는 시간 계층을 이용하여 시간 간격을 변화시킬 경우 발견되는 새로운 유형의 패턴 지식을 탐사하고 이를 제시한다.

• School Mathematics
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• v.5 no.3
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• pp.343-360
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• 2003

In this paper, we deal with the teaching of algebra based on patterns and generalization. The past algebra curriculum starts with letters(variables), algebraic expressions, and equations, but these formal approaching method has many difficulties in the school algebra. Therefore we insist the new algebraic approaches should be needed. In order to develop these instructions, we firstly investigate the relationship of patterns and algebra, the relationship of generalization and algebra, the steps of generalization from patterns and levels of difficulties. Next we look into the algebra instructions based arithmetic patterns, visual patterns and functional situations. We expect that these approaches help students learn algebra when they begin school algebra.

• Proceedings of the Korea Information Processing Society Conference
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• 2006.11a
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• pp.405-408
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• 2006

사용자들의 특성에 맞게 개인화되고 세분화된 위치 기반 서비스를 제공하기 위해서는 방대한 이동객체의 위치 이력 데이터로부터 유용한 패턴을 추출하기 위한 시간 패턴 탐사가 필요하다. 기존의 시간 패턴 탐사 기법들은 이동 객체의 시간에 따른 공간 속성들의 변화를 충분히 고려하지 못하거나, 시공간 속성을 동시에 고려한 패턴 탐사는 가능하나 제약을 가진 공간 정보를 포함하는 패턴 탐사 문제에는 적용하기 어렵다. 따라서 이동 객체의 위치 이력 데이터들에 대한 시공간적 속성들을 동시에 고려하여 다양한 이동 패턴들 중 공간 제약을 만족하는 패턴들을 추출하기 위한 새로운 이동 패턴 탐사 기법이 요구된다. 이러한 패턴 탐사 기법의 개발을 위해서는 상세 수준의 위치 이력 데이터들을 공간 영역 정보 형태로 변환하는 위치 일반화 접근법이 필요하다. 이에 본 논문에서는 객체의 위치값과 공간 영역간의 위상 관계를 고려하여 이동 객체의 위치 속성에 대한 공간영역으로의 일반화 방법을 제안한다. 이동 객체의 상세 수준의 위치 정보에서는 의미있는 패턴을 찾기가 어렵기 때문에 데이터 전처리 과정을 통해 일반화된 데이터 집합을 형성함으로써 효율적인 이동 객체의 시간 패턴 마이닝을 유도할 수 있다.

• 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.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2002.06a
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• pp.81-82
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• 2002

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.205-225
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• 2014

This study analyzed how two sixth graders recognized, generalized, and represented functional relationships in exploring geometric growing patterns. The results showed that at first the students had a tendency to solve the given problem using the picture in it, but later attempted to generalize the functional relationships in exploring subsequent items. The students also represented the patterns with their own methods, which in turn had an impact on the process of generalizing and applying the patterns to a related context. Given these results, this paper includes issues and implications on how to foster functional thinking ability at the elementary school.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.2
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• pp.95-102
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• 2004

In this paper, Experience Sensitive Cumulative Neural Network (ESCNN) is introduced, which can cumulate the same or similar experiences. As the same or similar training patterns are cumulated in the network, the system recognizes more important information in the training patterns. The functions of forgetting less important information and attending more important information resided in the training patterns are surveyed and implemented by simulations. The system behaves well under the noisy circumstances due to its forgetting and/or attending properties, even in 50 percents noisy environments. This paper also describes the creation of the generalized patterns for the input training patterns.