• School Mathematics
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• v.13 no.4
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• pp.615-632
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• 2011

The purpose of the study was to investigate the mathematical knowledge for teaching (MKT) of pre-service and in-service mathematics teachers on the concept of vector. 80 pre-service and 124 in-service mathematics teachers were asked to perform three questions based on MKT's subdomain. The results show that pre-service teachers have stronger common content knowledge(CCK). On the other hand, in-service teachers have stronger specialized content knowledge(SCK), knowledge of content and teaching(KCT) compared to those of pre-service teachers. The paper proposes CCK, SCK and KCT about the concept of vector and discusses the relationships between subdomains of MKT.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.447-462
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• 2003

The purpose of this study was to Investigate the preservice elementary teachers' pedagogical content knowledge of addition and subtraction. The subjects for data collection were 29 preservice elementary teachers and data were collected through open ended problems. The findings imply that the preservice elementary teachers show low level of understanding of addition and subtraction such as the word problem posing and the contexts of part-part-whole and compare. The research results indicate that the preservice elementary teachers possess primarily a procedural knowledge of pedagogical content knowledge and don't understand relationship with real-world situation. This study provide the information available on developing program for preservice elementary teachers.

• Research in Mathematical Education
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• v.18 no.3
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• pp.171-185
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• 2014

Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers' lack of relevant subject content knowledge. However, recent research findings have revealed that teachers' knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers' knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive reasoning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.547-565
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• 2010

The study aims to compare between two lectures of elementary mathematics education in United States and Korea based on the Ball et al.'s classification of mathematical knowledge for teaching. The lecturers are a professor of University in United States and me. In both lectures, subjects and contents of lectures are much similar but there are many different things. And the differences are mainly due to the area of pedagogical content knowledge, especially either knowledge of content and students or knowledge of content and teaching. Also the different courses of both universities are one of important causes of the differences. The study will be able to contribute to the studies on the improvement of our course, elementary mathematics education.

• School Mathematics
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• v.17 no.4
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• pp.613-632
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• 2015

In this study, we hope to reveal teacher knowledge necessary to address student errors and difficulties about ratio and rate. The instruments and interview were administered to 3 in-service primary teachers with various education background and teaching experiments. The results of this study are as follows. Specialized content knowledge(SCK) consists of profound knowledge about ratio and rate beyond multiplicative comparison of two quantities and professional knowledge about the definitions of textbook. Knowledge of content and students(KCS) is the ability to recognize students' understanding the concept and the representation about ratio and rate. Knowledge of content and teaching(KCT) is made up of knowledge about various context and visual models for understanding ratio and rate.

• The Mathematical Education
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• v.48 no.4
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• pp.399-417
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• 2009

The purpose of this study was to explore the adaptability of U.S. multiple-choice items to measure Mathematical Knowledge for Teaching (MKT) in Korea. For this purpose, the authors selected the number and operations form B which was developed by Learning Mathematics for Teaching (LMT) project at the University of Michigan and then adapted items in terms of general cultural context, school cultural context, mathematical substances, and language in Korea. The survey was administrated to 77 Korean in-service teachers who had more than three years of teaching experiences. Based on the survey, the authors compared the data to that of U.S. teachers who had participated California's Mathematics Professional Development Institute. As a result, the survey measures less knowledge Korean teachers than more knowledgable Korean teachers and there are strong correlations of relative item difficulties between Korean teachers and U.S. teachers for both Content Knowledge (CK) items and Knowledge of Content and Students (KCS) items. This study implies the future direction for developing items to measure teacher knowledge as well as designing effective teacher education programs.

• Research in Mathematical Education
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• v.25 no.2
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• pp.135-158
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• 2022

This study aimed to building models to understand the relationships between reasoning resources and content knowledge. We applied Support Vector Machine and linear models to the data including fifth graders' scores in the Cornel Critical Thinking Test and the Iowa Assessments, demographic information, and learning science approach (a student-centered approach to learning called the Science Writing Heuristic [SWH] or traditional). The SWH model showing the relationships between critical thinking domains and academic achievement at grade 5 was developed, and its validity was tested across different learning environments. We also evaluated the stability of the model by applying the SWH models to the data of the grade levels. The findings can help mathematics educators understand how critical thinking and achievement relate to each other. Furthermore, the findings suggested that reasoning in mathematics classrooms can promote performance on standardized tests.

• School Mathematics
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• v.15 no.2
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• pp.443-457
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• 2013

This study investigated the perceptions of beginning teachers about teacher knowledge. Reflections and improvement of their class knowledge have been perceived as the most important factors by beginning teachers. In terms of utilization of actual classes, teacher knowledge, mathematical concepts and correlations such as connection linked to class contents and hierarchy have been used the most. Among the needed teachers knowledge, knowledge of student understanding and mathematics content knowledge was the most essential knowledge that could be mainly formed through classroom experience and teacher training program. On the other hand, knowledge about technology and assessment was not necessary or useful factor for beginning teachers. To facilitate formation of beginning teachers' knowledge, teacher introductory program, mentoring program, interactive relationship with teacher education institutes, curriculum improvement for teacher education institute and the development and dissemination of various teachers training program would be required.

• The Mathematical Education
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• v.56 no.4
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• pp.407-434
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• 2017

The purpose of this study is to develop and verify the TPACK measurement tool for middle and high school mathematics teachers in the Korean context. Also, by clarifying the relationship between subordinate factors of Mathematics teachers' TPACK, an attempt was made to provide suggestions on the designs and directions for the in-service and pre-service teacher education and the programs for improving mathematics teachers' TPACK in the future. In order to achieve this goal, TPACK factors of mathematics teachers were extracted by reviewing literature on PCK, MKT, and TPACK. Then, content validity, basic statistical survey, reliability verification, exploratory factor analysis, confirmatory factor analysis, and structural equation model verification were conducted sequentially. At first, preliminary analysis was carried out on 79 mathematics teachers, and 76 items excluding the items with extreme value and reliability were included in the basic statistical analysis. And secondly, an exploratory factor analysis was conducted on 376 mathematics teachers, and this instrument consisted of 7 subordinate factors(CK, PK, TK, PCK, TCK, TPK, TPACK) and 61 items. Also by conducting confirmatory factor analysis and structural equation model test with 254 mathematics teachers, the measurement tool was confirmed the validity and reliability through statistically significant analysis. Then, the importance of integrated knowledge was confirmed by looking at the relationship between the TPACK factors of in-service mathematics teachers. The integrated knowledge(PCK, TCK, TPK) has played a crucial role in the formation of TPACK rather than the knowledge of CK, PK, and TK alone. Finally, the validity of TCK was confirmed through the structural equation modeling of TPACK. TCK not only directly affected TPACK, but also indirectly through TPK. According to these affirmative results, this measurement tool is claimed to be suitable for measuring the factors of Mathematics teachers' TPACK, and also the structural equation model can be regarded as a suitable model for analyzing the structural relationship of mathematics teachers' TPACK.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.87-98
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• 1997

A practice is classified into the practice as a content and the practice as a method. The former means that the practical nature of mathematical knowledge itself should be a content of mathematics and the latter means that one should teach the mathematical knowledge in such a way as the practical nature is not damaged. The practical nature of mathematics means mathematician's activity as it is actually done. Activities of the mathematician are not only discovering strict proofs or building axiomatic system but informal thinking activities such as generalization, analogy, abstraction, induction etc. In this study, it is found that the most instructive ones for the future users of mathematics are such practice as content. For the practice as a method, students might learn, by becoming apprentice mathematicians, to do what master mathematicians do in their everyday practice. Classrooms are cultural milieux and microsoms of mathematical culture in which there are sets of beliefs and values that are perpetuated by the day-to-day practices and rituals of the cultures. Therefore, the students' sense of ‘what mathematics is really about’ is shaped by the culture of school mathematics. In turn, the sense of what mathematics is really all about determines how the students use the mathematics they have learned. In this sense, the practice on which classroom instruction might be modelled is that of mathematicians at work. To learn mathematics is to enter into an ongoing conversation conducted between practitioners who share common language. So students should experience mathematics in a way similar to the way mathematicians live it. It implies a view of mathematics classrooms as a places in which classroom activity is directed not simply toward the acquisition of the content of mathematics in the form of concepts and procedures but rather toward the individual and collaborative practice of mathematical thinking.