• Journal of Science Education
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• v.32 no.1
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• pp.1-18
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• 2008

We investigated 8th grade science textbooks and their instructor's manuals treating the ideal condition for isochronism of a simple pendulum. The isochronism, i.e. the period is independent of amplitude, is satisfied only if the amplitude is very small. This is so called "ideal condition" for isochronism of a simple pendulum. Most textbooks and instructor's manuals are found not to state this ideal condition properly, which often leads to the deviation between experimental data and theoretical calculation. This difference between theoretical and experimental results makes students to create a sense of alienation from the real world and eventually keeps them away from physics. We thus study the cycloidal pendulum as an alternative method to test the isochronism regardless of amplitude and discuss the practical utility of it in class.

• Education of Primary School Mathematics
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• v.14 no.2
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• pp.117-134
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• 2011

The purpose of this research was to analyze mathematical task types to enhance creativity. Creativity is increasingly important in every field of disciplines and industries. To be excel in the 21st century, students need to have habits to think creatively in mathematics learning. The method of the research was to collect the previous research and papers concerning creativity and mathematics. To search the materials, the researcher used the search engines such as the GIL and the KISTI. The mathematical task types to enhance creativity were categorized 16 different types according to their forms and characteristics. The types of tasks include (1) requiring various strategies, (2) requiring preferences on strategies, (3) making word problems, (4) making parallel problems, (5) requiring transforming problems, (6) finding patterns and making generalization, (7) using open-ended problems, (8) asking intuition for final answers, (9) asking patterns and generalization (10) requiring role plays, (11) using literature, (12) using mathematical puzzles and games, (13) using various materials, (14) breaking patterned thinking, (15) integrating among disciplines, and (16) encouraging to change our lives. To enhance students' creativity in mathematics teaching and learning, the researcher recommended the followings: reshaping perspectives toward teaching and learning, developing and providing creativity-rich tasks, applying every day life, using open-ended tasks, using various types of tasks, having assessment ability, changing assessment system, and showing and doing creative thinking and behaviors of teachers and parents.

• Journal of Educational Research in Mathematics
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• v.24 no.1
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• pp.67-82
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• 2014

The term "objectification" has various definitions or perspectives. Nevertheless, it's pursued commonly by groups from various perspectives who emphasize the activities of becoming aware of a process as a totality, realizing that transformations can act on that totality, that is, turning processes into object. The purpose of this study is to identify how students objectify the concept of repetition regarding permutation and combination and find difficulties of objectification focusing on teacher's and students' discourse from common emphasis on previous researches associated with objectification. Students objectified the concept of repetition by replacing talk about processes with talk about objects regarding repetition and using discursive forms that presented phenomena in an impersonal way. The difficulties of objectification were derived from close linkage between the way of using keywords regarding repetition and everyday language.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.125-143
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• 2014

In this study, we analyzed a mathematical discussion in the Calculus II course of the Gifted Science Academy and individual interviews to determine the relationship between cognitive conflicts and commognitive conflicts. The mathematical discussion began with a question from a student who seemed to have a cognitive conflict about the osculating plane of a space curve. The results indicated that the commognitive conflicts were resolved by ritualizing and using the socially constructed knowledge, but cognitive conflicts were not resolved. Furthermore, we found that the cause of the cognitive conflict resulted from the student's imperfect analogical reasoning and the reflective discourse about it could be a learning opportunity for overcoming the conflict. These findings imply that cognitive conflicts can trigger the appearance of commognitive conflicts, but the elimination of commognitive conflicts does not imply that cognitive conflicts are resolved.

• Journal of Elementary Mathematics Education in Korea
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• v.23 no.3
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• pp.305-321
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• 2019

Rapid demographic changes such as international marriages and immigration have led to the transition of Korea to a multicultural society, thereby causing the need for education for multicultural students. In particular, there is a growing need to support Korean Language Learners (KLLs) who learn in Korean in their classrooms and whose native language is a foreign language. This study aims to adapt some teaching strategies of the SIOP model developed in the U.S. for English Language Learners(ELLs) to fit classroom situations in Korea and apply them to the Korean language learners to analyze the features of mathematical communication and to examine the possibility of a change in mathematical errors. Specifically, three KLLs in 5th grade participated in seven geometry lessons adapting some characteristics of SIOP model and then, their mathematical communication and mathematical errors were analyzed. The results of this study are expected to provide didactical implications for identifying characteristics of KLLs and for setting direction for teaching them mathematics.

• School Mathematics
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• v.18 no.1
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• pp.127-141
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• 2016

This study analyzes modes related to use of graph representation that appears to solve high school students quadratic function problem based on the graph using modes of Chauvat. It was examined the extent of understanding of the quadratic function of students through the flexibility of the representation of the Bannister (2014) from the analysis. As a result, the graph representation mode in which a high school students are mainly used is a nomographic specific mode, when using operational mode, it was found to be an error. The flexibility of Bannister(2014) that were classified to the use of representation from the point of view of the object and the process in the understanding of the function was constrained operation does not occur between the two representations in understanding the function in the process of perspective. Based on these results, the teaching on use graph representation for the students in classroom is required and the study of teaching and learning methods can understand the function from various perspectives is needed.

• School Mathematics
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• v.18 no.1
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• pp.105-126
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• 2016

Math classes has been regarded as an independent area of a teacher and his/her students of a particular class. In Recent discussions about the professional development of teachers, for the improvement of practices, the point of view of that the community of teachers must work together is spreading. What are the considerations in organization and operation of learning communities for professional development of teachers? In this study, we analyzed the case of the learning community of math teachers in a Science Academy for the purpose of improving math classes to promote the participation of learners. Research results show that teachers share the principles and goals of mathematics teaching through the learning community. Also, through participation in learning communities, the members were practicing the lessons improved by reflection on the lessons of his/her and their colleagues. These results provide implication that it is important to provide opportunities for objectifying his/her classes through the learning community for a substantial improvement in math classes.

• School Mathematics
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• v.18 no.1
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• pp.193-214
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• 2016

Teachers' questioning plays an important role in mathematics teaching and learning by asking students to react or to participate in mathematical discourse. Previous studies on teachers' questioning have not focused on how to questioning to formulate an effective mathematical discourse which is contributed by students because studies mostly analyzed and categorized teachers' questions according to cognitive levels of questions without consideration of context. Therefore, this study explored characteristics of teachers' questioning to formulate an effective characteristics of teachers' questioning to formulate an effective mathematical discourse in mathematics classrooms. By reviewing and analyzing mathematics discourse and studies on teachers' questioning theoretically, we presented openness, sharedness, and productivity as characteristics of teachers' questioning. Through a middle school mathematics teacher's case, we examined three characteristics were necessary to formulate an effective mathematical discourse. Based on results from theoretical analysis and case analysis, we discussed that openness, sharedness, and productivity would be useful as a framework to analyze teachers' questioning.

• School Mathematics
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• v.11 no.4
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• pp.625-642
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• 2009

This paper presents an overview of theories about ethnomathematics to seek for implications for multicultural mathematics education. Initiated by anthropological inquiries into mathematics outside of Europe, research of ethnomathematics has revealed the facets of mathematics as a historicocultural construct of a community. Specifically, it has been shown that mathematics is culturally relative knowledge system situated within a certain communal epistemological norms. This implies that indigenous mathematics, which had traditionally been regarded as primitive and marginal knowledge, is a historicocultural construct whose legitimacy is conferred by the system of the communal epistemological norms. The recognition of the cultural facets in mathematics has faciliated the reconsideration of what is legitimate mathematics. what is mathematical competence, and what teaching and learning mathematics is an about. This paper inquires multicultral discourses of mathematics education that research of ethnomathematics provides and identifies its implications concerning multicultural mathematics education.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.407-422
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• 2013

The purposes of this study are to investigate the change in the teacher efficacy beliefs of elementary pre-service teachers in mathematics during the student teaching, and to suggest the direction of the student teaching program for improving the pre-service teachers' efficacy beliefs in mathematics. For this, 93 elementary pre-service teachers participated. After the 4 weeks of practice, any changes in their teacher efficacy beliefs in mathematics were analyzed and the positive and negative causes of the differences were discussed. Consequently, their teacher efficacy beliefs in mathematics meaningfully decreased. The analysis of the cause of the decrease indicated that the teacher efficacy beliefs in teaching mathematics, rather than in the management of their mathematics class, meaningfully decreased. The meetings with the subjects also revealed that they had more negative experience with class teaching and were not able to gain much positive experience with it after all.