• Education of Primary School Mathematics
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• v.17 no.3
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• pp.173-188
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• 2014

The aim of the case study presented in this paper was to explore mathematics curriculum knowledge of a South Korean elementary teacher. An in-depth case study is applied to examine mathematics curriculum knowledge that influences teachers' instructional process including analysis of diverse artifacts such as lesson plan, observation and interviews. Findings of this study suggest that mathematics curriculum knowledge has direct relevance to teaching a lesson, designing a lesson and assessing students' work. In addition, this study identified that mathematics curriculum knowledge may be divided into two sub-categories: vertical mathematics curriculum knowledge and horizontal mathematics curriculum knowledge. The results of this case study help our understanding of South Korean elementary teachers' mathematics curriculum knowledge, which has a deep impact on their teaching practice. Moreover, this cross-national research offers implications for researchers, policymakers, and teachers in U.S. as well as those in South Korea.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.295-308
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• 2007

The purpose of this paper was to investigate the pedagogical content knowledge of a middle school mathematics teacher manifested in his mathematics instruction by identifying the components of the pedagogical content knowledge of the teacher. For the purpose of the study, I conducted an interpretive case study by collecting qualitative data. The results showed that the pedagogical content knowledge of the teacher was characterized by: (a) knowledge of mathematics including connection among topics and various ways of solving problems; (b) knowledge of students' understanding involving students' misconceptions, common errors, difficulties, and confusions; and (c) knowledge of pedagogy consisting of his efforts to motivate his students by providing realistic applications of mathematical topics and his use of materials.

• Communications of Mathematical Education
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• v.18 no.1 s.18
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• pp.297-308
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• 2004

본 연구에서는 먼저, 수학교사에게 필요한 지식으로 교과, 학생, 교수학적 내용 지식이 필요함을 문헌을 통해 정리하였다. 교사의 지식과 수업 실제에 관한 세 편의 논문을 분석한 결과 교사의 수학에 대한 충분한 이해가 학생의 학습과 효과적인 교수에 절대적인 영향을 미친다고 주장할 수 없음을 알 수 있었다. 그러나 수학에 대한 바른 이해는 학생의 질문에 적절한 반응을 할 수 있도록 하며, 수업을 계획하고 교실에서 이루어지는 담화를 수학적으로 원활하게 조절할 수 있도록 도움을 줄 수도 있었다. 따라서 수학을 잘 아는 것이 효과적인 교수·학습을 보장하지는 못하지만, 교사가 잘 알지 못하는 것을 가르칠 수는 없다는 결론을 얻었다.

• School Mathematics
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• v.5 no.3
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• pp.297-314
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• 2003

Mathematics students must appropriate their mathematical knowledge which has the definition and theorem of mathematics, algorithm, reasonable thought, heuristic, and mathematics language, and so on. That is, students should construct, use, and apply their own knowledge during learning. Appropriation of mathematical knowledge is practicable when mathematics language is in charge of many functions that Vygotsky cited. To reach the potential development level with mathematics language, students need the zones that they interact themselves and peers, as well as teacher. On that ground, this study presented the interactional zones of IZPD, ZPP, and ZAD, and modeled mathematics learning. By the case of 2 students, we found that ZPP and ZAD were necessary and important.

• Journal of Educational Research in Mathematics
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• v.18 no.1
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• pp.1-24
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• 2008

The purpose of this study is to uncover weaknesses in the constructivism in mathematics education and to search for ways to complement these deficiencies. We contemplate the relationship between the capability of construction and the performance of it, with the view of the 'Twofold-Structure of Mind.' From this, it is claimed that the construction of mathematical knowledge should be to experience and reveal the upper layer of Mind, the Reality. Based on the examination on the conflict and relation between the structuralism and the constructivism, with reference to the 'theory of principle' and the 'theory of material force' in Neo-Confucianist theory, it is asserted that the construction of mathematical knowledge must be the construction of the structure of mathematical knowledge. To comprehend the processes involved in the construction of the structure of mathematical knowledge, the epistemology of Michael Polanyi is studied. And also, the theory of mathematization, the historico-genetic principle, and the theory on the levels of mathematical thinking are reinterpreted. Finally, on the basis of the theory of twofold-structure, the roles and attitudes of teachers and students are discussed.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.617-630
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• 2015

A perspective of the nature of teacher knowledge has a significant impact on why and how we study teacher knowledge. The purpose of this study was to explore the mathematics knowledge in teaching (MKiT) in terms of meanings, characteristics, and analytic methods. MKiT regards teacher knowledge as practical knowledge that has meanings only when it is employed in teaching mathematics. Various components of teacher knowledge interact one another in teaching mathematics. Given this, teacher knowledge is regarded as an organism specific to teaching contexts and it needs to be analyzed by observing lessons or a teacher's actions related directly to the lessons. This paper is expected to induce research on teacher knowledge from the MKiT perspective and urge researchers to have a profound understanding of the nature and analytic methods of teacher knowledge. Some implications of future research are included.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.39-52
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• 2012

Research in teachers' knowledge for teaching mathematics (KTM) has been gradually growing for the past several years. With various conceptualizations about what teachers need to teach mathematics, there have been studies to find out the relationship between teachers' KTM and their students' achievement. In this paper, I reviewed various conceptualizations of teacher's mathematical knowledge for teaching, and existing qualitative and quantitative studies about this relationship. Based on the review, I identified the challenges to studying this relationship mainly focusing on the existence of a phase-teaching practice-between teachers' KTM and students' learning. Considering the challenges that have been identified in the literature review, I proposed topics for future studies that would contribute to our understanding how the teachers' KTMare related to their students' achievement, and investigate further about whether and how teacher-student interaction in classroom is related to changes in teachers' KTM.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.349-368
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• 2023

The purpose of this study is to explore ways for students to connect conceptual and procedural knowledge in mathematical modeling lessons. Accordingly, we selected the greatest common divisor among the learning contents in which elementary school students have difficulties connecting conceptual and procedural knowledge. A mathematical modeling lesson was designed and implemented to solve problems related to the greatest common divisor while connecting conceptual and procedural knowledge. As a result of the analysis, it was found that the mathematical modeling lesson had positive effects on students solving problems by connecting conceptual and procedural knowledge. In addition, through actual class application, a teaching and learning plan was derived to meaningfully connect conceptual and procedural knowledge in mathematical modeling lessons.

• School Mathematics
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• v.14 no.2
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• pp.233-253
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• 2012

The purpose of the study investigate mathematics content knowledge(MCK) of prospective teachers in differential area. 70 prospective teachers were asked to perform six questions based on Cho's MCK (2010, 2011). The results show that depending on whether they experience any teacher education program, the level of prospective teachers' mathematics content knowledge may vary. In particular, prospective teachers struggled with an unfamiliar problem situations. We also found that prospective mathematics teachers have some difficulty in solving problem about the use of mean value theorem and derivative.

• School Mathematics
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• v.11 no.3
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• pp.369-387
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• 2009

Recently there has been a high request for support for teachers' professional development and quality control to meet the demand of educational policy to introduce teacher evaluation, master teacher status, incentives for teacher competency, etc. It has been suggested that reeducation and support for professional development would be more effective to beginning teachers with a high developmental potential than to experienced teachers with routinized instruction. Since 2005, KICE-TLC has conducted research on the development of teacher supporting programs such as teaching consultation and pedagogical content knowledge(PCK) in school subjects. In line with the current education policy and previous research by KICE, this research has been conducted to meet the need for novice teacher induction by developing consulting program focused on PCK. The goal of this research was to (1) explore the in-depth meaning of PCK in light of teaching consultation, (2) conduct a preliminary study on how to develop teaching consulting programs for secondary beginning teachers, (3) develop teaching consulting programs focused on pedagogical content knowledge (PCK), and (4) suggest implications for educational policy regarding pre-service and in-service teachers' continuing professional development and support.