• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.429-451
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• 2012

This paper examined eight novice elementary teachers' knowledge in terms of the types and sources of students' errors and teaching strategies on plane figures through a questionnaire and teachers' discussion. The teachers tended to predict students' diverse error types, but they attributed the sources of such errors mainly to their characteristics. The analysis of teachers' responses of teaching strategies revealed that they recognized the importance of the teacher's clear explanation and students' own problem-solving, while they were somewhat negative in presenting diverse examples and classifying, drawing, or constructing figures. Building on these results, this paper provides the implications for novice teachers' professional development programs.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.71-84
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• 2012

The purpose of this study is to analyze some Korean elementary pre-service teachers' Mathematical Knowledge for Teaching(MKT) and compare the results with those obtained by Kwon, Nam, & Kim(2009), so that we can provide some suggestions to improve education of elementary mathematics subject at Korean teachers colleges. For this purpose, we selected the MKT items on number and operations which were adapted for Korean in-service teachers by Kwon et al. The survey consisting of those items was administered to 88 Korean elementary pre-service teachers at teachers college, J University. The results are the following: First, the respondents, elementary pre-service teachers, showed that they already had a sufficient amount of Content Knowledge(CK) on number and operations, but that their level of Knowledge of Content and Students(KCS) was insufficient. This means we need to strengthen our students' KCS in education of elementary mathematics subject at our teachers colleges. Second, there was a strong correlation, in both CK and KCS, of item difficulty felt by the respondents with that by the Kwon et al's in-service teachers. Third, although the respondents valued the MKT items more than the above-mentioned elementary in-service teachers, about 70% of them said the items were never learned at their college. Furthermore, they had different opinions on some of the items from their counterparts'. The suggestions we get here are we need to first consider the results in improving education of elementary mathematics subject at our teachers colleges and second develop MKT items suitable for the situation of Korean schools and curriculums in order to obtain exact estimations of Korean elementary pre-service teachers' MKT.

• The Mathematical Education
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• v.63 no.2
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• pp.295-318
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• 2024

This narrative review explores the transformative potential of immersive virtual reality (IVR) in enhancing high school students' mathematics competence, viewed through the lens of the technological, pedagogical, and content knowledge (TPACK) framework. This review comprehensively illustrates how IVR technologies have not only fostered a deeper understanding and engagement with mathematical concepts but have also enhanced the practical application of these skills. Through the careful examination of seminal papers, this study carefully explores the integration of IVR in high school mathematics education. It highlights significant contributions of IVR in improving students' computational proficiency, problem-solving skills, and spatial visualization abilities. These enhancements are crucial for developing a robust mathematical understanding and aptitude, positioning students for success in an increasingly technology-driven educational landscape. This review emphasizes the pivotal role of teachers in facilitating IVR-based learning experiences. It points to the necessity for comprehensive teacher training and professional development to fully harness the educational potential of IVR technologies. Equipping educators with the right tools and knowledge is essential for maximizing the effectiveness of this innovative teaching approach. The findings also indicate that while IVR holds promising prospects for enriching mathematics education, more research is needed to elaborate on instructional integration approaches that effectively overcome existing barriers. This includes technological limitations, access issues, and the need for curriculum adjustments to accommodate new teaching methods. In conclusion, this review calls for continued exploration into the effective use of IVR in educational settings, aiming to inform future practices and contribute to the evolving landscape of educational technology. The potential of IVR to transform educational experiences offers a compelling avenue for research and application in the field of mathematics education.

• Journal of the Korean School Mathematics Society
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• v.12 no.1
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• pp.1-25
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• 2009

The purpose of this research is the investigation of mathematics pre service teachers' disposition. Their disposition will be used for preposition of preservice Leacher program for making pre service teachers' participate any program willingly and extend their thinking. For this research, the researcher collected various data from investigation-presentation, report for practice and beauty of mathematics, micro teaching, and peer-evaluation. Preservice teachers had positive attitude for mathematics. They described their feeling, thinking and reflection about various methods of instruction and prefer to have micro teaching. They described that the investigation-presentation was needed to change some. From the results, the teacher preparation program is needed to integrate theory and practice to make preservice teachers gain profound knowledge on pedagogical content knowledge by making them high their interest and sensitivity on mathematics.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.343-376
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• 2018

The purpose of this study is to compare and analyze the perceptions of TPACK for mathematics teachers who practice the technology-using lessons. In addition, by looking at the part where the perception is expressed in the actual class and the part where the difference of recognition can be revealed, it is possible to provide the direction to teachers who want to practice the technology-using lessons in the future. To do this, two mathematics teachers were selected using purposeful sampling. And we conducted research study and interview in order to analyze the characteristics of the teacher's general background and TPACK recognition, and we analyzed the video, the class materials, and the interview contents for teaching practices from the perspective of TPACK. As a result, the two mathematics teachers practicing the technology-using lessons were connected with the actual class situation focusing on the sub-knowledges of TPACK recognizes as having a lot of them. In addition, technology-based lessons were able to confirm that the functional capabilities of technology alone were not sufficient conditions to lead effective instruction. Finally, teaching method using technology has been confirmed that experience-based field practice can be more important than simply knowing mathematics content, technology, teaching method. Based on the results of this study, it is possible not only to provide methodological guidance to teachers who practice the technology-based instruction, but also to suggest the direction of TPACK research or the development of teacher training program in the future.

• Journal of Educational Research in Mathematics
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• v.22 no.4
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• pp.495-515
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• 2012

This study is to diversely analyze teachers' Pedagogical Content Knowledge (PCK) regarding to the area of plane figures and discuss the consideration for the materialization of the effective class in learning the area of plane figures by identifying the improvements based on problems indicated in PCK. The subjects of inquiry are what the problems with teachers' PCK regarding to the area of plane figures are and how they can be improved. In which is the first domain of PCK, teachers need to fully understand the concept of the area and the properties and classification of the area and length, recognized the sequence structure as a subject of guidance and improve the direction which naturally connects the flow of measurement by using random units in guidance of the area. In which is the second domain of PCK, teachers need to establish understanding of the concept for the area and understanding of a formula as a subject matter object and improve the activity, discovery and research oriented class for students as a guidance method by escaping from teacher oriented expository class and calculation oriented repetitive learning. They also need to avoid the biased evaluation of using a formula and evenly evaluate whether students understand the concept of the area as a performance evaluation method. In which is the third domain of PCK, teachers need to fully understand the concept of the area rather than explanation oriented correction and fundamentally teach students about errors by suggesting the activity to explore the properties of the area and length. They also need to plan a method to reflect student's affective aspects besides a compliment and encouragement and apply this method to the class. In which is the fourth domain of PCK, teachers need to increase the use of random units by having an independent consciousness about textbooks and supplementing the activity of textbooks and restructure textbooks by suggesting problematic situations in a real life and teaching the sequence structure. Also, class groups will need to be divided into an entire group, individual group, partner group and normal group.

• The Mathematical Education
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• v.62 no.1
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• pp.57-78
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• 2023

Students' engagement in lessons not only determines the direction and result of the lessons, but also affects academic achievement and continuity of follow-up learning. In order to provide implications related to teaching strategies for encouraging students' engagement in elementary mathematics lessons, this study implemented lessons for middle-low achieving fifth graders using open-ended tasks and analyzed characteristics of students' engagement in the light of the framework descripors developed based on previous research. As a result of the analysis, the students showed behavioral engagement in voluntarily answering teacher's questions or enduring difficulties and performing tasks until the end, emotional engagement in actively expressing their pleasure by clapping, standing up and the feelings with regard to the topics of lessons and the tasks, cognitive engagement in using real-life examples or their prior knowledge to solve the tasks, and social engagement in helping friends, telling their ideas to others and asking for friends' opinions to create collaborative ideas. This result suggested that lessons using open-ended tasks could encourage elementary students' engagement. In addition, this research presented the potential significance of teacher's support and positive feedback to students' responses, teaching methods of group activities and discussions, strategies of presenting tasks such as the board game while implementing the lessons using open-ended tasks.

• The Mathematical Education
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• v.61 no.1
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• pp.157-178
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• 2022

Mathematics teachers' content knowledge is an important asset for effective teaching. To enhance this asset, teacher's knowledge is required to be diagnosed and developed. In this study, we employed problem-posing and problem-solving tasks to diagnose preservice teachers' understanding of fraction multiplication. We recruited 41 elementary preservice teachers who were taking elementary mathematics methods courses in Korea and the United States and gave the tasks in their final exam. The collected data was analyzed in terms of interpreting, understanding, model, and representing of fraction multiplication. The results of the study show that preservice teachers tended to interpret (fraction)×(fraction) more correctly than (whole number)×(fraction). Especially, all US preservice teachers reversed the meanings of the fraction multiplier as well as the whole number multiplicand. In addition, preservice teachers frequently used 'part of part' for posing problems and solving posed problems for (fraction)×(fraction) problems. While preservice teachers preferred to a area model to solve (fraction)×(fraction) problems, many Korean preservice teachers selected a length model for (whole number)×(fraction). Lastly, preservice teachers showed their ability to make a conceptual connection between their models and the process of fraction multiplication. This study provided specific implications for preservice teacher education in relation to the meaning of fraction multiplication, visual representations, and the purposes of using representations.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.511-536
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• 2017

The present study aims to investigate ways in which pre-service secondary mathematics teachers anticipate 1) students' responses to specific mathematical tasks which are chosen or devised by the participating pre-service teachers as requiring students' higher cognitive demand and, 2) their roles as math teachers to scaffold students' mathematical thinking. To achieve the goal, we had our pre-service teachers to engage in an adapted version of Spangler & Hallman-Thrasher(2014)'s Task Dialogue writing activity whose focus was to develop pre-service elementary teachers' ability to orchestrate mathematical discussion. 14 pre-service teachers who were junior at the time enrolled in the Mathematics Teaching Method Course were subjects of the current study. In-depth analysis of both Task Dialogues which pre-service secondary mathematics teachers wrote and audiotapes of the group discussions while they wrote the dialogues suggests the following results: First, the pre-service secondary teachers anticipated how students would approach a task based on their own teaching experiences. Second, they were challenged not only to anticipate more than one correct students' responses but to generate questions for the predicted correct-responses to bring forth students' divergent thinking. Finally, although they were aware that students' knowledge should be the crucial element guiding their decision-making process in teaching, they tended to lower the cognitive demands of tasks by providing students with too much guidance which brought forth the use of procedural knowledge. The study contributes to the field as it provides insights as to what to attend in designing teacher education course whose goal is to provide a foundation for developing pre-service teachers' ability to effectively orchestrate mathematical discussion.

• Journal of The Korean Association For Science Education
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• v.27 no.4
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• pp.346-353
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• 2007

In order to be efficient in teaching, a teacher should understand the current learner's level through diagnostic evaluation. This study has examined the major issues arising from the noble diagnostic assessment tool based on the theory of knowledge space. The knowledge state analysis method is actualizing the theory of knowledge space for practical use. The knowledge state analysis method is very advantageous when a certain group or individual student's knowledge structure is analyzed especially for strong hierarchical subjects such as mathematics, physics, chemistry, etc. Students' knowledge state helps design an efficient teaching plan by referring their hierarchical knowledge structure. The knowledge state analysis method can be enhanced by computer due to fast data processing. In addition, each student's knowledge can be improved effectively through individualistic feedback depending on individualized knowledge structure. In this study, we have developed a diagnostic assessment test for measuring student's learning outcome which is unattainable from the conventional examination. The diagnostic assessment test was administered to middle school students and analyzed by the knowledge state analysis method. The analyzed results show that students' knowledge structure after learning found to be more structured and well-defined than the knowledge structure before the learning.