• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.769-789
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• 2016

Pattern activities are useful to develop functional thinking of young students, but there has been lack of research on how to teach patterns. This study explored teaching methods of geometric patterns for developing functional thinking of elementary school students, and then analyzed the lessons in which such methods were implemented. For this, three classrooms of fourth grades in elementary schools were selected and three teachers taught geometric patterns on the basis of the same lesson plan. The lessons emphasized noticing the commonality of a given pattern, expanding the noti ce for the commonality, and representing the commonality. The results of this study showed that experience of analyzing the structure of a geometric pattern had a significant impact on how the fourth graders reasoned about the generalized rules of the given pattern and represented them in various methods. This paper closes with several implications to teach geometric patterns in a way to foster functional thinking.

• Education of Primary School Mathematics
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• v.1 no.1
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• pp.3-22
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• 1997

본 연구는 첫째로는 수학교육에서 패턴이 강조되는 이론적 근거를 찾고자 역사적 맥락에서 수학의 성격변화를 탐색하였다. 수학의 성격 변화를 통하여 수학은 수의 탐구, 기하의 탐구, 운동ㆍ변화ㆍ공간의 탐구, 수학 연구의 도구에 대한 탐구로 그 영역을 점차 확대하여 왔으며, '수학은 패턴의 과학이다'라는 정의는 수학이 폭넓어짐에 따라 수학이 무엇인가에 대한 수학의 본성에 접근하는 논의라고 할 수 있다. 이러한 수학에 대한 새로운 관점은 수학교육의 새로운 방향 모색에 시사하는 바를 살펴보고, 특히 수학교실의 변화에 따른 패턴의 강조를 살펴보았다. 둘째로는 수학적 패턴을 밝힘과 동시에 수학 교육에서 수학적 패턴 분석의 틀을 마련하고자 수학적 패턴의 유형화를 시도하였다. 패턴의 속성에 따른 유형화와 패턴의 생성 방식에 따른 유형화를 통하여 수학적 패턴의 유형을 마련하였다. 초등학교 수학에서 다루어지는 패턴은 어떠한 것인가를 현행 4학년 수학교과서 및 익힘책에 제한하여 유형화한 틀로서 조사 분석하였다. 셋째로는 수학적 패턴에 관한 지도 방안의 모색으로서, 지도의 기본 방향을 설정하고 수학적 패턴에 관한 교수 전략을 마련하였다. 교수전략은 크게 패턴에서의 규칙 찾기, 패턴을 변형ㆍ확장하기, 자신의 새로운 패턴 만들기, 패턴을 수학적으로 설명하기로 나누고, 각각에 3-4개의 세부 전략과 세부 전략에 따른 예를 제시하였다.

• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.497-504
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• 2004

• Education of Primary School Mathematics
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• v.26 no.1
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• pp.45-63
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• 2023

The activity of finding rules is useful for enhancing the algebraic thinking of elementary school students. This study analyzed the pattern activities of a finding rules unit in 10 different government-authorized mathematics curricular materials for fourth graders aligned to the 2015 revised national mathematics curriculum. The analytic elements included three main activities: (a) activities of analyzing the structure of patterns, (b) activities of finding a specific term by finding a rule, and (c) activities of representing the rule. The three activities were mainly presented regarding growing numeric patterns, growing geometric patterns, and computational patterns. The activities of analyzing the structure of patterns were presented when dealing mainly with growing geometric patterns and focused on finding the number of models constituting the pattern. The activities of finding a specific term by finding a rule were evenly presented across the three patterns and the specific term tended to be close to the terms presented in the given task. The activities of representing the rule usually encouraged students to talk about or write down the rule using their own words. Based on the results of these analyses, this study provides specific implications on how to develop subsequent mathematics curricular materials regarding pattern activities to enhance elementary school students' algebraic thinking.

• Spatial Information Research
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• v.6 no.1
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• pp.11-23
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• 1998

Map generalization functions to visualize the spatial data or to change their scale by changing the level of details of data. Until recently, the studies on map generalization have concentrated more on line features than on point features. However, point features are one of the essential components of digital maps and cannnot be ignored because of the great amount of information they carry. This study, therefore, aimed to find out a detailed procedure of point features' generalization. Particularly, this work chose the distribution pattern of point features as the most important factor in the point generalization in investigating the geometric characteristics of source data. First, it attempted to find out the characteristics of distribution pattern of point features through quadrat analysis with Grieg-Smith method and nearest-neighbour analysis. It then generalized point features through the generalization threshold which did not alter the characteristics of distribution pattern and the removal of redudant point feautres. Therefore, the generalization procedure of point features provided by this work maintained the geometric characteristics as much as possible.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.1
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• pp.65-80
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• 2010

The aims of our study are to investigate the nature of mathematical reasoning and the teaching of mathematical reasoning in school mathematics. We analysed the process of shaping deduction in ancient Greek based on Netz's study, and discussed on the comparison between his study and Freudenthal's local organization. The result of our analysis shows that mathematical reasoning in elementary school has to be based on children's natural language and their intuitions, and then the mathematical necessity has to be formed. And we discussed on the sequences and implications of teaching of the sum of interior angles of polygon composed the discovery by induction, justification by intuition and logical reasoning, and generalization toward polygons.

• 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.

• School Mathematics
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• v.19 no.1
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• pp.117-135
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• 2017

Even though patterns and correspondence serve a fundamental basis of function for elementary students, there has been lack of research in this field. This study explored prior studies to extract the key instructional elements on how to teach patterns and correspondence. This study then analyzed the unit of 'patterns and correspondence' in the mathematics textbooks in terms of four key instructional elements (i.e., relation to real-life contexts, diversity of pattern tasks, exploration for a correspondence relationship, and teaching variables). The results of this study showed that topics dealing with patterns and correspondence were represented with relation to real-life contexts but diversity of pattern tasks and exploration for a correspondence relationship were needed to be further considered in the textbooks. Another noticeable result was that teaching variables was not explicitly addressed in the textbooks. Based on these results, this study provides textbook writers with implications on what to further consider in dealing with patterns and correspondence.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.697-715
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• 2023

The purpose of this study is to investigate the overall understanding of patterns by second- and third-grade elementary school students. For this purpose, 12 classes per grade were selected from 10 schools, and a 46-item test was administered to 216 second graders and 223 third graders. The results of the study showed that in most cases, there was no statistically significant difference in the understanding of patterns between second- and third-graders. The exception occurred regarding the 10 items of identifying the structure of a pattern: Second-graders did better than third-graders regarding 8 items, whereas vice versa regarding 2 items. The items that both second- and third-graders struggled with included finding multiple components of a given pattern, comparing the structures between patterns, and guessing a particular term in an open pattern. Based on these findings, this paper discusses second- and third-graders' understanding of patterns and suggestions for further instruction.