• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.469-489
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• 2017

Teachers are the primary agent of didactic transposition. In the process of transposing mathematical knowledge presented in mathematics curriculum and textbooks to mathematical knowledge for teaching in a classroom, teachers are significantly influenced by not only teachers' personal factors but also circumstances and constraints existing inside and outside of classrooms. Therefore, to understand teachers' didactic transposition, we need to analyze influence of institutional and socio-cultural factors on teachers' didactic transposition process. Identifying factors and constraints influencing teachers' didactic transposition provides important opportunities to have a deeper understanding of teachers' didactic transposition and develop their classroom practices. This study analyzed secondary mathematics teachers' perspectives on didactic transposition by exploring factors influencing their didactic transposition process using their reflective journal about their classroom practices. As a result, we identified the five factors influencing participating teachers' didactic transposition. We also found that different teachers had different extent of influence of five factors on their didactic transposition. Based on the results, we discussed ways to help mathematics teachers' didactic transposition.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.377-394
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• 2019

The purpose of this study is to scrutinize the characteristics of a teacher's discursive competence on the basis of mathematical competencies. For this purpose, we observed all semester-long classes of a middle school teacher, who changed her own teaching methods for the last 20 years, collected video clips on them, and analyzed classroom discourse. Data analysis shows that in problem solving competency, she helped students focus on mathematically important components for problem understanding, and in reasoning competency, there was a discursive competence which articulated thinking processes for understanding the needs of mathematical justification. And in creativity and confluence competency, there was a discursive competence which developed class discussions by sharing peers' problem solving methods and encouraging students to apply alternative problem solving methods, whereas in communication competency, there was a discursive competency which explored mathematical relationships through the need for multiple mathematical representations and discussions about their differences. These results can provide concrete directions to developing curricula for future teacher education by suggesting ideas about how to combine practices with PCK needed for mathematics teaching.

• The Mathematical Education
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• v.44 no.4 s.111
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• pp.477-496
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• 2005

This study looked into the procedures of and the status on the implementation of the new 7th national curriculum at the secondary school level. It examined the processes taken by the local boards of education in due course of facilitating the schools with the new curriculum implementation. More specifically the study examined, 1) the degree to which the particular innovation(i.e., student-centered, flexible and autonomous school-based curriculum, etc.) is being implemented as planned; and 2) how it is being implemented. It conducted a situation-oriented analysis in cooperation with three local boards of education. Classroom observations, teacher interviews, questionnaires for teachers and supervisors were utilized and the three major criteria of interpreting the result were the three core concepts of the 7th national curriculum, that is, the degree of '(1)reorganization, (2)student-centeredness and (3)diversification/ specialization' of the curriculum. Detailed documentation on the processes of the local bureaus of education and on the classroom practices are made in order to provide schools and policy makers with relevant and practical suggestions for further improvement of curriculum implementation. Ultimately, The greater the awareness of the intention of the new curriculum on the part of both the staff at the local school boards and teachers, the greater the degree of implementation. And the higher the quality of planning to meet problems, the greater the degree of implementation. Continuous efforts are needed to involve teachers in the process of curriculum implementation. The greater the active support of the teachers, the greater the degree of implementation.

• The Mathematical Education
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• v.43 no.4
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• pp.321-335
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• 2004

This study looked into the procedures of and the status on the implementation of the new 7th national curriculum at the elementary school level. It examined the processes taken by the local boards of education in due course of facilitating the schools with the new curriculum implementation. More specifically the study examined, 1) the degree to which the particular innovation(i.e., student-centered, flexible and autonomous school-based curriculum, etc.) is being implemented as planned; and 2) how it is being implemented. It conducted a situation-oriented analysis in cooperation with three local boards of education. Classroom observations, teacher interviews, questionnaires for teachers and supervisors were utilized and the three major criteria of interpreting the result were the three core concepts of the 7th national curriculum, that is, the degree of '(1) reorganization, (2)student-centeredness and (3)diversification/ specialization' of the curriculum. Detailed documentation on the processes of the local bureaus of education and on the classroom practices are made in order to provide schools and policy makers with relevant and practical suggestions for further improvement of curriculum implementation. Ultimately, The greater the awareness of the intention of the new curriculum on the part of both the staff at the local school boards and teachers, the greater the degree of implementation. And the higher the quality of planning to meet problems, the greater the degree of implementation. Continuous efforts are needed to involve teachers in the process of curriculum implementation. The greater the active support of the teachers, the greater the degree of implementation.

• Education of Primary School Mathematics
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• v.3 no.2
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• pp.89-101
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• 1999

The reform movements of current mathematics education have based on several major ideas, in order to provide a new vision of the teaching and loaming of mathematics. Of the ideas, the motto of communication of mathematics appears to be a significant factor to change teaching practices in mathematics classroom. Through Vygotsky's sociocultural theory, the psychological background is presented for both supporting the motto and extracting important suggestions of the reform of mathematics education. The development of higher mental functions is explained by internalization, semiotic mediation, and the zone of proximal development. Above all, emphasis is put on the concepts of scaffolding and inter subjectivity related to the zone of proximal development. Seven implications are proposed by Vygotsky's sociocultural theory for the new forms of the teaching and learning of mathematics.

• School Mathematics
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• v.17 no.4
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• pp.593-611
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• 2015

Under the assumptions that teachers' beliefs toward mathematics education play a role of a filter between teachers' knowledge and teaching practices, this study surveyed and analyzed elementary teachers' beliefs toward mathematics education: helping students to understand mathematics concepts, addressing students' mathematical misconceptions, engaging students in mathematics classroom, and improving students' mathematical thinking. From the analysis of survey results of the study, I found that there were dominant components in elementary teachers' beliefs system regarding teaching mathematics. In addition, there are some constructs affected by teachers' characteristics such as gender and educational backgrounds. In this study, I presented a representative model of elementary teachers' beliefs system toward mathematics education.

• School Mathematics
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• v.11 no.2
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• pp.207-225
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• 2009

Well posed problems for mathematically gifted students provide an effective method to design 'problem solving-centered' classroom activities. In this study, we analyze mathematical problems posed by teachers in distance learning as a part of an advanced training which is an enrichment in-service program for gifted education. The patterns of the teacher-posed problems are classified into three types such as 'familiar,' 'unfamiliar,' and 'fallacious' problems. Based on the analysis on the teacher-posed problems, we then suggest a practical plan for teachers' problem posing practices in distance learning.

• Education of Primary School Mathematics
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• v.13 no.1
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• pp.13-24
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• 2010

Mathematics educators oriented to reform-based curricular have asserted that mathematics teachers should lead instructions where all students in their classrooms are able to participated. In this paper, some practices for them to implement it are discussed. Before explaining them, some discussions are made about students ability to construct knowledge. One of them is that teachers should know different learners construct different understandings because of their differences of prior knowledge and reasoning ability. Also, it was discussed that teachers consider classroom environments, assigning children's sitting and tasks in the light of learning. The reason to state them is that perspectives of them should be changed. Finally, "Teacher's careful listening to learners' responses", "Why do think in that way?, How do you know?, What is it meant?", "accepting ideas from all learners", "no supporting a particular idea", "utilizing waiting time", and "teacher's responses to learner's errors and mistakes" are discussed as practices for letting all learners be participated in the mathematics instruction.

• Journal of Elementary Mathematics Education in Korea
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• v.11 no.1
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• pp.23-42
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• 2007

Learners who have taken learner-centered instruction is expected to construct conceptually mathematical knowledge which is. If so, they can have some ability to solve problems they are confronted with in the first time. To know this, First graders who have been in learner-centered instruction during 1 school year was given 7+52+186 which usually appears in the national curriculum for 3rd grade. According to the results, most of them have constructed the logic necessary to solve the given problem to them, and actually solve it. From this, it can be concluded that first, even though learners are 1st graders they can construct mathematical knowledge abstractly, second, they can apply it to the new problem, and third consequently they can got a good score in a achievement test.

• The Mathematical Education
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• v.62 no.3
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• pp.341-362
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• 2023

This study analyzed student noticing in a lesson that emphasized relational understanding of equal signs for first graders from four aspects: centers of focus, focusing interactions, mathematical tasks, and nature of the mathematical activity. Specifically, the instructional factors that emphasize the relational understanding of equal signs derived from previous research were applied to a first-grade addition and subtraction unit, and then lessons emphasizing the relational understanding of equal signs were conducted. Students' noticing in this lesson was comprehensively analyzed using the focusing framework proposed in the previous study. The results showed that in real classroom contexts centers of focus is affected by the structure of the equation and the form of the task, teacher-student interactions, and normed practices. In particular, we found specific teacher-student interactions, such as emphasizing the meaning of the equals sign or using examples, that helped students recognize the equals sign relationally. We also found that students' noticing of the equation affects reasoning about equation, such as being able to reason about the equation relationally if they focuse on two quantities of the same size or the relationship between both sides. These findings have implications for teaching methods of equal sign.