• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.463-483
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• 2003

In the learning of mathematics, students experience the semiotic activities of representing and interpreting mathematical signs. We called these activities as the representing and interpreting of mathematical signs. On the foundation of Peirce's three elements of the sign, we analysed that students constructed the representamen to interpret the concept of correlation as for the object, "as one is taller, one's size of foot is larger" 4 middle school students who participated the gifted center in Seoul, arranged the statistical data, constructed their own representamen, and then learned the conventional signs as a result of the whole class discussion. In the process, students performed the detailed representing and interpreting of signs, depended on the templates of the known signs, and interpreted the process voluntarily. As the semiotic activities were taken place in this way, it was needed that mathematics teacher guided the representing and interpreting of mathematical signs so that the representation and the meaning of the sign were constructed each other, and that students endeavored to get the negotiation of the interpretants and the representamens, and to reach the conventional representing.

• Communications of Mathematical Education
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• v.16
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• pp.123-137
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• 2003

본 논문의 목적은 삼각함수의 학습에 테크놀로지가 기여할 수 있는 방법적인 측면과 인지적인 효과를 명시하는 것이다. 테크놀로지가 삼각함수의 학습에 기여할 수 있는 네 가지 방법론적인 면을 '수학과 학생들의 실제 경험의 연결', '수학적 대상과 수학적 관계의 구체화', '수학의 다양한 표현 체계의 연결', '사고력 중심의 수학교육 추구'의 관점에서 논한다. 이 네 가지 방법론적인 측면 중 '수학적 대상과 수학적관계의 구체화'와 '수학의 다양한 표현 체계의 연결'을 중심으로 삼각함수의 학습법을 예시하면서 이 두 가지 방법이 어떻게 인지적으로 기여하는지를 보여준다.

• School Mathematics
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• v.9 no.4
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• pp.467-486
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• 2007

In mathematical modeling activity modeling process is usually an iterative process. When model can not be solved, the model needs to be simplified by treating some variables as constants, or by ignoring some variables. On the other hand, when the results from the model are not precise enough, the model needs to be refined by considering additional conditions. In this study we investigate the role of spreadsheet model in model refinement and modeling process. In detail, we observed that by using spreadsheet model students can solve model which can not be solved in paper-pencil environment. And so they need not go back to model simplification process but continue model refinement. By transforming mathematical model to spreadsheet model, the students can predict or explain the real word situations directly without passing the mathematical conclusions step in modeling process.

• Education of Primary School Mathematics
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• v.25 no.4
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• pp.395-410
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• 2022

Nominalization is one of the grammatical metaphors, and it is the representation of verbal meaning through noun equivalent phrases. In mathematical word problems, texts using nominalization have both the advantage of clarifying the object to be noted in the mathematization stage, and the disadvantage of complicating sentence structure, making it difficult to understand the sentences and hindering the experience of the full steps in mathematical modelling. The purpose of this study is to analyze word problems in the textbooks from the perspective of nominalization, a linguistic element, and to derive implications in relation to students' difficulties during solving the word problems. To this end, the types of nominalization of 341 word problems from the content domain of 'Numbers and Operations' of elementary math textbooks according to the 2015 revised national curriculum were analyzed in four aspects: grade-band group, main class and unit assessment, specialized class, and mathematical expression required word problems. Based on the analysis results, didactical implications related to the linguistic expression of the mathematical word problems were derived.

• School Mathematics
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• v.14 no.1
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• pp.1-28
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• 2012

The purpose of the study are to identify factors of mathematical visualization through the thirty students of highschool 2nd year and to investigate how each visualization factor is used in mathematics problem solving process. Specially, this study performed the qualitative case study in terms of the five of thirty students to obtain the high grade in visuality assessment. As a result of the analysis, visualization factors were categorized into mental images, external representation, transformation or operation of images, and spacial visualization abilities. Also, external representation, transformation or operation of images, and spacial visualization abilities were subdivided more specifically.

• The Mathematical Education
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• v.45 no.3 s.114
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• pp.345-365
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• 2006

This study, to effectively teach the concepts, principles and problem solving ability of the 2nd graders' learning of numbers and operations, offers realistic problem situation and focuses on the learning based on 'mathematization', one of the most important principles of RME (Realistic Mathematics Education) which is the mathematics education trend of Netherlands influenced by Freudenthal's theory. The instruction is applied to forty-one students of the 2nd grader for six weeks in twelve series in an elementary school, located in Seoul. To investigate the effects of the mathematising experience instruction for improving mathematical abilities, the group takes tests before and after the instruction. Also the qualitative analysis on the students' mathematising aspects through students' output at the instruction process is taken into account to evaluate the instruction's effects. The result shows that the mathematising experience instruction for improving mathematical abilities is proved to improve students' understanding of mathematical concepts and principles and their problem solving ability in learning numbers and operations after carrying out this instruction. Also the result indicates that students' mathematising aspects are mostly horizontal and vertical mathematization.

• Education of Primary School Mathematics
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• v.26 no.2
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• pp.83-97
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• 2023

Nominalization is one of the grammatical metaphors that makes it easier to mathematize the target that needs to be converted into a formula, but it has the disadvantage of making problem understanding difficult due to complex and compressed sentence structures. To investigate how this nominalization affects students' problem-solving processes, an analysis was conducted on 233 third-grade elementary school students' problem solving of eight arithmetic word problems with or without nominalization. The analysis showed that the presence or absence of nominalization did not have a significant impact on their problem understanding and their ability to convert sentences to formulas. Although the students did not have any prior experience in nominalization, they restructured the sentences by using nominalization or agnation in the problem understanding stage. When the types of nominalization change, the rate of setting the formula correctly appeared high. Through this, the use of nominalization can be a pedagogical strategy for solving word problems and can be expected to help facilitate deeper understanding.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.233-255
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• 2021

The purpose of this study is to develop math anxiety scale for middle school students for planning and implementing math anxiety treatment programs. In this study, we describe the process of developing and validating math anxiety scale for middle school students and detailing exploratory factor analysis and confirmatory factor analysis to verify construct validity. As a result of the study, we developed the Math Anxiety Scale for Middle School Students (MASS-M) of 30 items with four factors: mathematical curriculum content, mathematical attitude, mathematical test, and environment. As a math anxiety factor for middle school students, MASS-M was developed, which includes mathematical anxiety factors such as mathematical test factor and environmental factor, especially mathematical curriculum content factor describing mathematical treatment, and mathematical attitude factor describing psychological treatment. MASS-M, derived from this study, is a standardized scale for measuring math anxiety in middle school students and is expected to serve as the basis for maintaining consistency in research on math anxiety in middle school students and developing programs to treat math anxiety in middle school students.

• Communications of Mathematical Education
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• v.11
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• pp.437-450
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• 2001

본고는 ICME-9에서 발표되었던 Alan Bishop과 B. D‘Ambrosio의 논문을 중심으로 미래의 수학교육방향을 고찰해보고자 시도되었다. 민주화는 교육의 한 측면으로 항상 제시되어왔음에도 불구하고 수학 교육에서는 명확하게 제시되어진 일이 거의 없다. 우리 모두가 여전히 수학은 일부 공부 잘하고 머리 좋은 사람들만이 잘 할 수 있는 과목이라고 생각하여왔고 그러한 생각은 학교 졸업 후 사회에 나가서도 특권의식으로 발전한다. 그러나 수학이 메마르고 특권주의적 과목이 아닌 보편적이고 민주적인 과목 즉, “모두를 위한 수학교육”이 되어야 함을 자세히 살펴보았다.

• School Mathematics
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• v.15 no.4
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• pp.785-799
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• 2013

The researchers developed the teaching-learning materials for 9th grade mathematically gifted students in terms of the hypothesis that the students would have opportunity for problem solving and develop various mathematical thinking through the mathematical modeling lessons. The researchers analyzed what mathematical thinking abilities were shown on each stage of modeling process through the application of the materials. Organization of information ability appears in the real-world exploratory stage. Intuition insight ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the pre-mathematical model development stage. Mathematical abstraction ability, spatialization/visualization ability, mathematical reasoning ability and reflective thinking ability appears in the mathematical model development stage. Generalization and application ability and reflective thinking ability appears in the model application stage. The developed modeling assignments have provided the opportunities for mathematically-gifted students' mathematical thinking ability to develop and expand.