• School Mathematics
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• v.16 no.1
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• pp.111-133
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• 2014

This study aims to explore mathematical belief system and core belief factors to be found. The mathematical belief system becomes an auto regulation device for students' using mathematical knowledge in mathematical situations and provides them with the context to perceive and understand mathematics. They have individual mathematical beliefs for each of mathematics subject, mathematical problem solving, mathematical teaching and learning and self-concept, and these beliefs of students construct mathematical belief system according to mutual relationships among the mathematical beliefs. Using correlation analysis and multiple regression, mathematical belief system was structuralized and core belief factors were found. Mathematical belief system is structuralized and, as a result the core belief factors that are psychological centrality of high school students' mathematical belief system are found to be persistence, challenge, confidence and enjoyment. These core belief factors are formed on the basis of personal experiences and they are personal primitive beliefs that cannot be changed with ease and cannot be shared with other people but they are related with many other beliefs influencing them.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.433-452
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• 2009

This study investigated the teaching strategies of two exemplary American teachers regarding word problems and their impact on students' ability to both understanding and solving word problems. The teachers commonly explained the background details of the background of the word problems. The explanation motivated the students' mathematical problem solving, helped students understand the word problems clearly, and helped students use various solving strategies. Emphasizing communication, the teachers also provided comfortable atmosphere for students to discuss mathematical ideas with another. The teachers' continuous questions became the energy for students to plan various problem solving strategies and reflect the solutions. Also, this research suggested a complementary model for Polya's problem solving strategies.

• Journal of Educational Research in Mathematics
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• v.15 no.2
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• pp.107-130
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• 2005

The aims of this study are to identify Dewey's theory on mathematics education and to clarify its influence on the modern theories of mathematics education. For this purpose, we have examined Dewey's theory of knowledge named as pragmatism or instrumentalism, and studied the Dewey's theory of education in which he maintained education is the reconstruction of experiences. And then, we have examined Dewey's theory on mathematics education, such as theory of mathematics, purpose of mathematics education, contents of mathematics education, and methods of mathematics education respectively. After that, we have analyzed how his theory on mathematics education is connected with the diverse theories of modern mathematics education, such as Piaget's operational constructivism, Freudenthal's theory of realistic mathematics education, Polya's theory on mathematical problem-solving, and social constructivism. Through this study, we might say that Dewey's theory on mathematics education is a prototype of modern theories of mathematics education and a comprehensive paradigm which is very suggestive to the phenomena of mathematics education.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.3
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• pp.689-696
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• 2015

In this study, a learning system based on smart learning is proposed so that students with learning disabilities can learn the effective use of meta-cognitive to solve problems arising during the learning process. The features of the proposed system are as follow. First, it is possible to achieve students' individualized learning by use of smart devices and smart education system. Second, it is possible to provide the constant repetition learning for students. Third, students can improve their achievement using the proposed app. The proposed smart education system using meta-cognition was applied to some learning disabilities students. The following results were obtained. First, the disabled students could have an interest in learning math and improve confidence. Second, the student's mathematical problem-solving skills have improved. Third, students' individualized and self-directed learning was achieved.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.323-340
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• 2021

The purpose of this case study is to explore the similarities revealed in the process of solving and generalizing word problems related to systems of linear equations in two variables according to covariational reasoning. As a result, student S, who reasoned with coordination of value level, had a static image of the quantities given in the situation. student D, who reasoned with smooth continuous covariation level, had a dynamic image of the quantities in the problem situation and constructed an invariant relationship between the quantities. The results of this study suggest that the activity that constructs the relationship between the quantities in solving word problems helps to strengthen the mathematical problem solving ability, and that teaching methods should be prepared to strengthen students' covariational reasoning in algebra learning.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.519-536
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• 2018

This study is intended to develop a numeracy program for late-adult learners. For this study, firstly, characteristics of numeracy were analyzed and based on those characteristics, numeracy learning contents for late-adult learners were selected. Also, teaching and learning materials were developed by linking the mathematics contents selected to experience-based real lives of late-adult learners. When this numeracy program was applied to late-adult learners, it was observed that there was a change in the affective domain like interest at the early stage of learning and that as learning continued, mathematical elaboration occurred by way of mathematical formalization. In conclusion, this study has significance by re-defining arithmetic for late-adults from a perspective of numeracy, based on experience of late-adults, and making a contribution to mathematical elaboration of late-adult learners so non-formal problem-solving processes of lat-adult learners can be justified as elaborate mathematical problem-solving.

• The Mathematical Education
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• v.58 no.3
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• pp.443-458
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• 2019

Mathematical modeling has been a crucial topic in mathematics education as students' problem solving competency are regarded as a core skill for future society. Despite of the importance of mathematical modeling in school mathematics, there have been very limited studies relating pre-service teachers' knowledge and perceptions on mathematical modeling. In this vein, this study aimed to investigate pe-service mathematics teachers' perceptions on mathematical model, mathematical modeling and educational use of mathematical modeling, and their relationships. The current study utilized a survey consisted of 18 items. The responses of 210 pre-service mathematics teachers to the survey items were quantitatively analyzed using descriptive statistics, analysis of variance, exploratory and confirmatory factor analysis, the structural equation model, and multi group analysis. The results of analysis of variance revealed that pre-service teachers in difference groups (majors, grades, and experiences with mathematical modeling) showed statistically significant differences in mean values. Moreover, according to the results from the structural equation modeling analysis, pre-service mathematics teachers' perceptions on mathematical model and modeling affected their perceptions on educational use of mathematical modeling. In addition, depending on their pre-experiences with mathematical modeling, pre-service teachers represented a different relationship between perceptions on mathematical modeling and educational use of mathematical modeling. Implications for future studies and mathematics classrooms were discussed.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.85-110
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• 2005

The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.

• Journal of the Korean School Mathematics Society
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• v.6 no.1
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• pp.65-85
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• 2003

The purpose of this research is to increase mathematical problem solving abilities VIa STAD evaluation after completing classes. to which ST AD group study is applied, and promoting the learning accomplishments of students by developing gradual self-leading learning materials about the research project on ' How to use an hour math class efficiently\ulcorner ' For this purpose, the items below were studied. Firstly, gradual self-leading learning materials were developed and applied which were composed of textbook abstracts, basic problems, developing problems and intensive problems rather than existing textbooks. Secondly, the ST AD group study model was selected and applied which invokes competitions among small groups of which learning goals were clear. individual responsibility was important. and successive opportunities were equal. The evaluation using STAD at each end of a chapter was announced instantly using the EXCEL scoring system. Though the results of experimental classes were limited in their size. experimental time, and class selection, there were meaningful changes in the aspect of being able to heighten the accomplishment desire of students by inducing voluntary competitions among small groups without any student omitted. As the result of applying this research to my class, the ST AD group study using gradual self-leading learning materials invoked the interests of students and increased learning accomplishments via increasing problem solving abilities in mathematics. The ST AD group study was easy to use by beginning teachers, and its process was simple. It increased interactions among students and learning motives because its compensation system was open to all students. Among various studying methods for small groups. STAD group study is expected to be widely used for mathematics classes.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.1
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• pp.105-129
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• 2016

The elements of mathematical processes include mathematical reasoning, mathematical problem-solving, and mathematical communications. Proportion reasoning is a kind of mathematical reasoning which is closely related to the ratio and percent concepts. Proportion reasoning is the essence of primary mathematics, and a basic mathematical concept required for the following more-complicated concepts. Therefore, the study aims to analyze the proportion reasoning ability of sixth graders of primary school who have already learned the ratio and percent concepts. To allow teachers to quickly recognize and help students who have difficulty solving a proportion reasoning problem, this study analyzed the characteristics and patterns of proportion reasoning of sixth graders of primary school. The purpose of this study is to provide implications for learning and teaching of future proportion reasoning of higher levels. In order to solve these study tasks, proportion reasoning problems were developed, and a total of 22 sixth graders of primary school were asked to solve these questions for a total of twice, once before and after they learned the ratio and percent concepts included in the 2009 revised mathematical curricula. Students' strategies and levels of proportional reasoning were analyzed by setting up the four different sections and classifying and analyzing the patterns of correct and wrong answers to the questions of each section. The results are followings; First, the 6th graders of primary school were able to utilize various proportion reasoning strategies depending on the conditions and patterns of mathematical assignments given to them. Second, most of the sixth graders of primary school remained at three levels of multiplicative reasoning. The most frequently adopted strategies by these sixth graders were the fraction strategy, the between-comparison strategy, and the within-comparison strategy. Third, the sixth graders of primary school often showed difficulty doing relative comparison. Fourth, the sixth graders of primary school placed the greatest concentration on the numbers given in the mathematical questions.