• 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.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.125-141
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• 2005

For many years, the educational effects of instructional manipulatives in mathematics education have been investigated in classroom practice and educational research. This paper demonstrates how pattern block, a type of instructional manipulatives could be used and integrated in elementary mathematics areas in order to develop student's mathematical thinking Further, students' thinking process with pattern blocks is analysed to show their thinking process.

• Journal of the Korean School Mathematics Society
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• v.12 no.3
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• pp.247-265
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• 2009

In the 21C information-based society, there is an increasing demand for emphasizing communication in mathematics education. Therefore the purpose of this study was to research how properties of communication among small group members varied by mathematical problem types. 8 fourth-graders with different academic achievements in a classroom were divided into two heterogenous small groups, four children in each group, in order to carry out a descriptive and interpretive case study. 4 types of problems were developed in the concepts and the operations of fractions and decimals. Each group solved four types of problems five times, the process of which was recorded and copied by a camcorder for analysis, among with personal and group activity journals and the researcher's observations. The following results have been drawn from this study. First, students showed simple mathematical communication in conceptual or procedural problems which require the low level of cognitive demand. However, they made high participation in mathematical communication for atypical problems. Second, even participation by group members was found for all of types of problems. However, there was active communication in the form of error revision and complementation in atypical problems. Third, natural or receptive agreement types with the mathematical agreement process were mainly found for conceptual or procedural problems. But there were various types of agreement, including receptive, disputable, and refined agreement in atypical problems.

• Proceedings of the Korean Information Science Society Conference
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• 2011.06a
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• pp.233-236
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• 2011

일반적인 문서에 대한 정보 검색 연구는 활발히 진행되고 있으며, 일상 생활 속에서도 대중화되어 많이 사용되고 있다. 이에 따라 음성, 이미지 검색 등 특정 분야의 검색에 대한 연구도 활발히 진행되고 있지만, 수학식 검색에 대한 연구는 비교적으로 미비한 실정이다. 수학식 검색과 관련된 연구들은 대부분 MathML (Mathematical Markup Language), TeX 등으로 작성된 수학식을 대상으로 진행되었지만, 특정 언어나 별개의 수학 입력 툴들을 이용한 검색 방법은 일반 사용자들이 사용하기에는 쉽지 않다는 단점이 있다. 그래서, 본 논문에서는 일반 문서 검색과 마찬가지로, 수학식을 읽듯이 한글을 입력했을 때 색인어 추출 방법 및 검색 방법에 대해 제안한다. 실험을 위해서 수학 문제집에 나오는 1,432개의 수학식을 한글화 시켰고, 한글화된 결과에 대해 패턴 등을 추출하여 MRR (Mean Reciprocal Rank), $Rel_{EQ}$@N(Relevance evaluation at N)로 평가하였다. 100개의 한글 질의어에 대해 MRR@5로 계산된 수학식 검색 결과가 약 0.6 정도 되는 것을 확인할 수 있었고, 학습 데이터에 포함되지 않은 질의수학식 5개에 대해 $Rel_{EQ}$@5로 계산했을 때 평균 60% 의 정확률을 보였다.

• The Mathematical Education
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• v.62 no.2
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• pp.175-194
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• 2023

Despite the importance of pattern learning for elementary school students, few studies have investigated in detail the understanding of patterns of lower-grade students. This study aimed to analyze the understanding of patterns of second-grade elementary school students. Since the patterns in the second grade are taught through the unit called Finding Rules, students' understanding of patterns was compared and contrasted before and after they learned the unit. To this end, a written instrument to measure students' understanding of patterns was developed on the basis of previous studies on pattern learning for lower-grade students. A total of 189 students were analyzed. As a result of the study, the overall correct answer rates in the post-test were higher in most items than those in the pre-test, illustrating the positive effect of the specific unit. However, students found it difficult to find rules in which two components would change simultaneously either in geometric or numeric patterns, find patterns that would be similar in structure, represent geometric patterns into numeric patterns, find empty terms in increasing patterns, and reason the specific terms in patterns that can be differently interpreted. Based on these research results, this study sheds light on students' understanding of patterns and suggests implications to improve their understanding.

• 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.

• Communications of Mathematical Education
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• v.35 no.1
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• pp.1-14
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• 2021

Mathematics anxiety is a term for emotional and physical resistance to mathematics. Understanding students' mathematics anxiety is important not only in terms of improving mathematics academic achievement, but also in nurturing mathematics manpower necessary for the future society. In particular, mathematics anxiety is most likely to occur in elementary school, and it has a negative effect on subsequent learning. Therefore, it is important to understand the aspects of students' mathematics anxiety in elementary school. In this study, I presented the patterns of changes in students' mathematics anxiety over time and statistically verified them. As a result of a follow-up survey of 249 elementary school students' mathematics anxiety for 3 years from 4th to 6th grade, it was found that, rather than having a special pattern related to the formation of math anxiety, it may increase and decrease and vary depending on individual confirmed. Later, in this study, five patterns of Mathematics anxiety patterns were identified through statistical analysis. In addition, I confirmed that the students' interest about teachers' mathematics lessons was consistently influencing the change in mathematics anxiety. The results of this study will increase students' understanding of the formation of mathematics anxiety and can be used as basic data for the development of teaching and learning materials related to mathematics anxiety in the future and subsequent research.

• Education of Primary School Mathematics
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• v.1 no.2
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• pp.137-148
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• 1997

21세기를 눈앞에 두고 있는 오늘날의 사회에서는 변화에 적응할 수 있는 능력과 정보를 이해할 수 있는 능력이 더욱 필요하다. 따라서, 수학에서도 산술과 같은 기초적인 수학뿐 아니라 새로운 정보, 복잡한 정보를 이해하고 의사 소통하는 능력이 요구된다. 수학은 패턴의 과학이며 우리가 살고 있는 세상을 묘사하는 도구로서 자연 언어를 보충하는 의사소통의 한 형태이기도 하다. 그러므로 수학 수업에서는 기본 개념과 공식은 물론 의사소통 능력을 강조해야 한다(Mathematical Sciences Education Broad, 1990).(중략)

• School Mathematics
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• v.15 no.2
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• pp.459-479
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• 2013

The Purpose of this study was to explore the methods of generalization and errors pattern generated by mathematically gifted students and non-gifted students in elementary school. In this research, 6 problems corresponding to the x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns were given to 156 students. Conclusions obtained through this study are as follows. First, both group were the best in symbolically generalizing ax pattern, whereas the number of students who generalized $a^x$ pattern symbolically was the least. Second, mathematically gifted students in elementary school were able to algebraically generalize more than 79% of in x+a, ax, ax+c, $ax^2$, $ax^2+c$, $a^x$ patterns. However, non-gifted students succeeded in algebraically generalizing more than 79% only in x+a, ax patterns. Third, students in both groups failed in finding commonness in phased numbers, so they solved problems arithmetically depending on to what extent it was increased when they failed in reaching generalization of formula. Fourth, as for the type of error that students make mistake, technical error was the highest with 10.9% among mathematically gifted students in elementary school, also technical error was the highest as 17.1% among non-gifted students. Fifth, as for the frequency of error against the types of all patterns, mathematically gifted students in elementary school marked 17.3% and non-gifted students were 31.2%, which means that a majority of mathematically gifted students in elementary school are able to do symbolic generalization to a certain degree, but many non-gifted students did not comprehend questions on patterns and failed in symbolic generalization.

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.165-176
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• 2006

In this paper, we consider changes of algebra strands around the world. And we suggest needs of designing new computer environment where we make and manipulate geometric recursive patterns. For this purpose, we first consider relations among symbols, meanings and patterns. And we also consider Logo environment and characterize algebraic features. Then we introduce L-system which is considered as action letters and subgroup of turtle group. There are needs to be improved since there exists some ambiguity between sign and action. Based on needs of improving the previous L-system, we suggest new commands in JavaMAL microworld. So we design a microworld for recursive patterns and consider meanings of letters in new environments. Finally, we consider the method to integrate L-system and other existing microworlds, such as Logo and DGS. Specially, combining Logo and DGS, we consider the movement of such tiles and folding nets by L-system commands. And we discuss possible benefits in this environment.