• 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.

• Communications of Mathematical Education
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• v.34 no.4
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• pp.485-506
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• 2020

The purpose of this study is to analyze of the effect in Mathematics Teachers beliefs on their students beliefs by Latent Class Regression Model (LCRM). For this analysis, the study used the findings and surveys of Kang, Hong (2020) who developed a belief profile by analyzing the mathematical beliefs of 60 high school teachers and 1,850 second-year high school students learning from them through the Latent Class Analysis (LCA). As a result It was observed that 'Nature of Mathematics', 'Mathematic Teaching' and 'Mathematical Ability' of mathematics teachers beliefs influence the mathematical beliefs of students. The teacher's belief of 'Nature of Mathematics' statistically significant effects on students' beliefs in 'School Mathematics', 'Problem Solving', 'Mathematics Learning'. The teacher's belief of 'Teaching Mathematics', 'Mathematical Ability' statistically significant effects on students' beliefs in 'School Mathematics', 'Problem Solving', 'Self-Concept'. The results of this study can give a preview of the phenomenon in which teacher's mathematical beliefs are reproduced into student's mathematical beliefs. In addition, the results of observation of this study can be used to the contents that can achieve the purpose of reorientation for mathematics teachers.

• Communications of Mathematical Education
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• v.8
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• pp.189-207
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• 1999

본 연구의 목적은 초 ${\cdot}$ 중학생들의 수학적 신념을 알아보고, 그러한 신념을 형성하는 요인들을 수학 교실의 상호작용에서 찾아보는 것이었다. 이를 위해, 초등학교 5, 6학년과 중학교 1, 2, 3학년 학생들의 수학적 신념을 질문지로 조사하였으며 각급 학교의 수학 교실에서 벌어지는 교수-학습 과정을 비디오로 촬영하여 각 교실의 사회적 규범들을 비교 분석하였다. 그 결과로서, 학생들은 수학은 이미 만들어진 규칙과 용어들로 이루어졌고 그 규칙에 따라 주어진 문제를 풀어 답을 구하는 것이 수학적 활동이라고 인식하고 있었다. 한편, 이러한 신념은 각급 교실에 형성된 사회수학적 규범과 일치했으며, 특히 개념설명과 새로운 전략 및 오류에 대한 반응과 관련된 사회수학적 규범이 학생들의 수학적 활동을 제한함으로써 그들의 신념을 결정하고 있었다.

• Journal of the Korean School Mathematics Society
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• v.8 no.3
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• pp.343-356
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• 2005

The purpose of this study is to search whether mathematical beliefs have changed when new social norms are formed in math classroom through research using survey papers about mathematical beliefs and math class video photographing. In addition, it would search for social norms of mathematical classroom which affects to students' mathematical beliefs by analyzing culture of mathematical classroom. The result was that the class focusing only general social norms wasn't enough to change students' mathematical beliefs. And as we have examined sociomathematical norms of math classroom through analyzing culture of mathematics classroom, it has affected students' mathematical beliefs.

• School Mathematics
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• v.10 no.4
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• pp.649-669
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• 2008

The study focuses on what to consider and do for the improvement of math education of Korea by comparing two general high school students' and two specialized high school students' beliefs about mathematics and mathematics learning. The major topics compared in the beliefs are composed of perception of mathematics as a science, learning methods of mathematics. The results of the study show that two general high school students tend to set more low value on mathematics, especially in the value of implement, civilization, utility of mathematics than that of two specialized high school students.

• School Mathematics
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• v.18 no.3
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• pp.691-709
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• 2016

Understanding the belief of mathematics pre-service teachers is essential in conducting and designing the effective teacher education program. This study analyzed the mathematical belief of the elementary school pre-service teachers. The results of the study are as follows. First, persistence factor, which is the belief about solving mathematical problems, following teacher direction factor, which is the belief about mathematical studies, activity involvement factor, and interest factor, which is the belief about self-concept, showed much connection with other mathematical belief factors. Second, the stereotype factor, which is the belief about mathematics, are affecting the following teacher direction factor. The process factor, which is the belief about solving mathematical problems, are affecting the activity involvement factor. Third, as for the comparison of the mathematical beliefs according to grades, only the stereotype and usefulness factors, which are the beliefs about mathematics, and the benefit factor, which is the belief about self-concept, had statistically significant differences. Fourth, as for the comparison of the mathematical beliefs according to majors, all the mathematical beliefs except for the confidence factor and benefit factor, which is the belief about self-concept, had significant differences. Based on the results of this study, we need to establish the mathematical beliefs that the elementary school pre-service teachers should have, and prepare various measures such as education program for pre-service teachers and instruction-learning methods.

• Journal of Gifted/Talented Education
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• v.23 no.6
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• pp.947-963
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• 2013

This study investigated the difference of mathematical beliefs between common children and the gifted children, and then the effect of current mathematics gifted education on gifted children's mathematical belief. Gifted children from institution for gifted education and school based gifted classroom, and common children from regular classroom from S-city office of education in Gyenggi province were studied for this study. The results of this study was as follows. First, there was positive correlation between mathematics performance and mathematical belief. Second, common children and gifted children had significant difference in the degree of mathematical belief. And also, mathematically gifted students had much stronger and positive mathematical belief than common students before starting gifted education program. Third, there was no significant difference in common children and gifted children on the mathematical belief after they receive gifted education, but there were negative changes in gifted children from institution for gifted education on the mathematical belief after receiving gifted education.

• The Mathematical Education
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• v.59 no.4
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• pp.331-355
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• 2020

The purpose of this study is to systematically analyze the results of the existing research on mathematical beliefs, compare and synthesize the valuable results and to suggest implications for mathematical beliefs and research. As a result of checking the methodological quality of 59 articles in total using the MQA(Methodological Quality Assessment) checklist, most of them surveyed mathematical beliefs using questionnaires, and most of the studies were conducted on prospective teachers. As a result of systematic review, the conceptual characteristics of mathematical beliefs, object-specific characteristics, and the educational influence of mathematical beliefs were able to synthesize the meaning. Mathematical beliefs had important educational influences in the practice of teachers, students, and math classes. As the results of the study, we emphasize the importance of changing the beliefs of students and teachers in order to solve the problem of mathematical education, where students rely on private education rather than activity thinking, and teachers do not pay attention to students thinking. It has been shown that concrete support is needed for practicing participatory instruction focused on mathematical thinking.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.229-259
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• 2012

The purpose of the present study is to develop instrument of mathematical belief of middle school and high school students and to analysis results of test using the instrument. Based on the results of literature review, mathematical belief is the cumulative effects of self-assessment and self-concept in mathematical learning and achievement experience. Four sub-components of mathematical belief is identified belief of school mathematics, belief of mathematical problem solving, mathematical self-concept, belief of mathematical teaching and learning. The instrument was developed to investigate mathematical belief by reflecting Korean middle school and high school students' psychological characters. To develop the appropriate items for the mathematical belief, after reviewing literature thoroughly, first version of the instrument was developed and exploratory factor analysis and confirmatory factor analysis were conducted. Then, to reduce the effect of the gender difference and achievement level difference, Correlation Analysis and 1-way ANOVA was performed. Also, using multiple group confirmatory factor analysis, this instrument was investigated to see whether this can be used for both middle school and high school. The final items for middle school students is consisted 7 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 10 items of belief of mathematical teaching and learning. Instrument of mathematical belief for high school students is consisted 9 items of belief of school mathematics, 9 items of belief of mathematical problem solving, 11 items of mathematical self-concept, 11 items of belief of mathematical teaching and learning. This study examined the differences about mathematical belief's sub-factors shown by three groups of mathematics achievement level. Students of higher achievement level showed that the degree of most factors ware the highest excepting stereotype of belief of school mathematics. Also, Male students preferred more positive in mathematics belief than female students.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.377-411
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• 2021

This study aims to explore central and peripheral beliefs of mathematics teachers in the context of teaching and learning. For this purpose, this study analyzed teacher noticing of 8 mathematics teachers who are in-service in terms of mathematical beliefs using video-clips of math lessons. When the teachers in the video-clips seemed to have a teaching and learning problem, teachers who adopt noticing critized the classroom situation by reflecting his or her own mathematical beliefs and suggested alternatives. In addition, through noticing analysis, teachers' mathematical beliefs reflected in specific topics such as student participation in teaching and learning were compared to reveal their individual central and peripheral beliefs. Through these research results, this study proposed a model that extracts the central and peripheral beliefs of math teachers from the constraints of the teaching and learning context using noticing analysis. Additionally, it was possible to observe the teacher decision-making and expertise of mathematics teachers.