• The Mathematical Education
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• v.59 no.1
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• pp.63-80
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• 2020

This study analyzed 3,114 articles published in KCI journals and 1,636 articles published in SSCI journals from 2000 to 2019 in order to compare domestic and international research trends of mathematics education using a topic modeling method. Results indicated that there were 16 similar research topics in domestic and international mathematics education journals: algebra/algebraic thinking, fraction, function/representation, statistics, geometry, problem-solving, model/modeling, proof, achievement effect/difference, affective factor, preservice teacher, teaching practice, textbook/curriculum, task analysis, assessment, and theory. Also, there were 7 distinct research topics in domestic and international mathematics education journals. Topics such as affective/cognitive domain and research trends, mathematics concept, class activity, number/operation, creativity/STEAM, proportional reasoning, and college/technology were identified from the domestic journals, whereas discourse/interaction, professional development, identity/equity, child thinking, semiotics/embodied cognition, intervention effect, and design/technology were the topics identified from the international journals. The topic related to preservice teacher was the most frequently addressed topic in both domestic and international research. The topic related to in-service teachers' professional development was the second most popular topic in international research, whereas it was not identified in domestic research. Domestic research in mathematics education tended to pay attention to the topics concerned with the mathematical competency, but it focused more on problem-solving and creativity/STEAM than other mathematical competencies. Rather, international research highlighted the topic related to equity and social justice.

• Education of Primary School Mathematics
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• v.23 no.1
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• pp.45-61
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• 2020

The concept of equality is given as a way of reading the equal sign without dealing it explicitly in elementary school mathematics. The meaning of the equal sign can be largely categorized as operational and relational views. However, most elementary school students understand the equal sign as an operational symbol for just writing the required answers. It is essential for them to understand a relational concept of the equal sign because algebraic thinking in middle school mathematics is based on students' understanding of a relational view of the equal sign. Recently, the relational meaning of the equal sign is emphasized in arithmetic. Hence it is necessary for elementary school students to have some activities so that they experience a relational meaning of the equal sign. In this study, we investigate the meaning of the equal sign and contexts of the equal sign in elementary school mathematics to discuss explicit ways to emphasize the concept of equality and relational views of the equal sign.

• The Mathematical Education
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• v.59 no.3
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• pp.217-235
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• 2020

This study examined Korean fourth-grade students' performance by gender on the Trends in International Mathematics and Science Study(TIMSS) 2011 and 2015 mathematics assessment. We first identified items which had significantly higher mean scores by gender to decide which gender did better on a certain domain(domain-level analysis). Then, we examined the content of items(item-level analysis) to understand which items lead to gender differences in mathematics achievement. Our findings showed that about 80% of the items on both assessments did not show statistically significant differences between males and females. However, there were meaningful gender differences in the other 20% items. On both assessments, females had more items with significantly higher mean scores than males on the Shapes domain, and males had more those items on the Numbers and Measurement domains and all cognitive domains(Knowing, Applying, and Reasoning). In particular, females outperformed males on items related to identifying two- and three-dimensional shapes and drawing lines and angles and identifying them. Conversely, males had higher performance than females on items related to the pre-algebraic thinking, fractions and decimals, estimation of number differences, unit of length, and measuring time, height, and volume. The effect sizes for each item ranged from .12 to .33 and the mean effect size of all items across both assessments was .20, which indicated significant gender differences but small.

• Journal of Educational Research in Mathematics
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• v.27 no.1
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• pp.51-67
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• 2017

Analogical reasoning is a mathematically useful way of thinking. By analogy reasoning, students can improve problem solving, inductive reasoning, heuristic methods and creativity. The purpose of this study is to analyze the analogical reasoning of preservice mathematics teachers while constructing quadratic curves defined by eccentricity. To do this, we produced tasks and 28 preservice mathematics teachers solved. The result findings are as follows. First, students could not solve a target problem because of the absence of the mathematical knowledge of the base problem. Second, although student could solve a base problem, students could not solve a target problem because of the absence of the mathematical knowledge of the target problem which corresponded the mathematical knowledge of the base problem. Third, the various solutions of the base problem helped the students solve the target problem. Fourth, students used an algebraic method to construct a quadratic curve. Fifth, the analysis method and potential similarity helped the students solve the target problem.

• School Mathematics
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• v.5 no.4
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• pp.477-506
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• 2003

In this paper, we analyze nine-grade students' conceptions of parameters, their relation to unknowns and variables and the process of understanding of letters in problem solving of equations and functions. The roles of letters become different according to the letters-used contexts and the meaning of letters Is changed in the process of being used. But, students do not understand the meaning of letters correctly, especially that of parameter. As a result, students operate letters in algebraic expressions according to the syntax without understanding the distinction between the roles. Therefore, the parameter of learning should focus on the dynamic change of roles and the flexible thinking of using letters. We develop a self-regulation model based on the monitoring working question in teaching-learning situations. We expect that this model helps students understand concepts of letters that enable to construct meaning in a concrete context.

• Education of Primary School Mathematics
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• v.20 no.3
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• pp.205-224
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• 2017

A model method has been known as the main characteristic of Singaporean elementary mathematics textbooks. However, little research has been conducted on how the model method is employed in the textbooks. In this study, we extracted contents related to the model method in the Singaporean elementary mathematics curriculum and then analyzed the characteristics of the model method applied to the textbooks. Specifically, this study investigated the units and lessons where the model method was employed, and explored how it was addressed for what purpose according to the numbers and operations. The results of this study showed that the model method was applied to the units and lessons related to operations and word problems, starting from whole numbers through fractions to decimals. The model method was systematically applied to addition, subtraction, multiplication, and division tailored by the grade levels. It was also explicitly applied to all stages of the problem solving process. Based on these results, this study described the implications of using a main model in the textbooks to demonstrate the structure of the given problem consistently and systematically.

• School Mathematics
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• v.13 no.1
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• pp.65-88
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• 2011

Epistemological development process of the Fundamental Theorem of Calculus is considered in a history of mathematical notions and the genetic process of the Fundamental Theorem is arranged by the order of geometric, algebraic and formalization steps. Based on this, we studied students' episte- mological obstacles and error and analyzed the content of textbooks related the Fundamental Theorem of Calculus. Then, We developed the "Folding Back Model" of the fundamental theorem of calculus for students to lead meaningful faithfully. The Folding Back Model consists of "the Framework of thou- ght"(figure V-1) and "the Model of genetic understanding of concept"(figure V-2). The framework of thought in the Folding Back Model is included steps of pedagogical intervention which is used "the Monitoring working questions"(table V-3) by the mathematics teacher. The Folding Back Model is applied the Pirie-Kieren Theory(1991), history of mathematical notions and students' epistemological obstacles to practical use of instructional design. The Folding Back Model will contribute the professional development of mathematics teachers and improvement of thinking skills of students when they learn the Fundamental Theorem of Calculus.