• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.39-65
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• 2013

This study intended to draw some suggests for the development of mathematics teachers' expertise through the comparison research of pre-service and in-service teachers' PCK about questioning in elementary mathematics class. For this purpose, questionnaire survey was conducted to some pre-service and in-service teachers about the PCK concerning the way how questioning during mathematics class. This survey revealed the following implications. First, from the perspective of mathematics classroom, it is still more important the practical knowledge about how to teach which is evolutionally developed passing through the experience and currier of teaching than theoretical knowledge itself. Comparing the teachers' PCK about the two related knowledge types of mathematics contents, in case of procedural knowledge related PCK it was more asked of teachers' expertise than the case of conceptual knowledge related PCK. Thirdly, in case of learners' incorrect answer, for the desirable teaching it should be a questioning focused on whether there being or not the systematic among the learners' incorrect answer, and in case of appreciating the learners' understanding about the presently taught contents the questioning should be constructed considering the relevant contents early learned.

• 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.

• The Mathematical Education
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• v.52 no.4
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• pp.567-586
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• 2013

The purpose of this study was to introduce the Knowledge Quartet (KQ) framework by which we can analyze teacher knowledge revealed in teaching mathematics. Specifically, this paper addressed how the KQ framework has been developed and employed in the context of research on teacher knowledge. In order to make the framework accessible, this paper analyzed an elementary school teacher's knowledge in teaching her fifth grade students how to figure out the area of a trapezoid using the four dimensions of the KQ (i.e., foundation, transformation, connection, and contingency). This paper is expected to provide mathematics educators with a basis of understanding the nature of teacher knowledge in teaching mathematics and to induce further detailed analyses of teacher knowledge using some dimensions of the KQ framework.

• School Mathematics
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• v.4 no.4
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• pp.555-563
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• 2002

The purpose of this paper is to try formulating a working definition of connection of informal and formal mathematical knowledge. Many researchers have suggested that informal mathematical knowledge should be connected with school mathematics in the process of learning and teaching it. It is because informal mathematical knowledge might play a important role as a cognitive anchor for understanding school mathematics. To implement the connection of them we need to know what the connection means. In this paper, the connection between informal and formal mathematical knowledge refers to the making of relationship between common attributions involved with the two knowledge. To make it clear, it is discussed that informal knowledge consists of two properties of procedures and conceptions as well as formal mathematical knowledge does. Then, it is possible to make a connection of them. Now it is time to make contribution of our efforts to develop appropriate models to connect informal and formal mathematical knowledge.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.265-287
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• 2013

The purpose of this study was to analyze the trends of domestic research on teacher knowledge in mathematics in terms of its conceptualizations of teacher knowledge, topics, methods, subjects, and content domains. For this purpose, the papers published in 9 professional journals during the recent 14 years (1999-2012) were analyzed by 5 criteria. The results of this study showed that the concept of PCK was the most frequent, whereas its subcategories appeared in different forms. The most frequent research topic was survey of teacher knowledge. The qualitative research methodology was more frequently used than the quantitative methodology, whereas mixed one was hardly used. The subjects for research included a little more elementary school teachers than secondary counterparts, but did similarly both pre-service and in-service teachers. Whereas both the research on number and operations in elementary mathematics education and the research on function in secondary were active, the rest of content domains were not. On the basis of these results, this paper provides several implications for future research direction in teacher knowledge in mathematics.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.691-715
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• 2015

This study explored preservice secondary mathematics teachers' mathematical knowledge for teaching [MKT]. In order to measure preservice teachers' MKT, we developed items according to Ball, Thames & Phelps (2008)'s domains and conducted to 53 preservice teachers. Also, we interviewed 1 preservice teacher with the items and a set of interview questions. The findings from the data analysis suggested as follows: a) overall, the preservice teachers scored average 30.2 out of 100; b) the preservice teachers appeared to be unable to explain students' difficulties in learning a specific mathematical idea and how they would respond to and resolve such difficulties.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.1
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• pp.19-38
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• 2005

There are differences in manner to be shown according to a basic point of view about knowledge in division which is traditional algorithm. The 1st and 2nd stage show didactic transpositions less systemic. The 3rd stage, which were influenced by the new math, uses logical mechanism. The 4th stage shows conceptual knowledge of the division independently. The 5th and 6th stage use concrete models which shows a course. The 7th stage constitutes contents systematically and shows many chances which focus on the formation of knowledge. The suggestions derived from such transition should be considered in the practice class and an elementary mathematics textbooks for meaningful learning.

• The Mathematical Education
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• v.30 no.3
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• pp.71-89
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• 1991

• Journal of the Korean School Mathematics Society
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• v.8 no.1
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• pp.1-17
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• 2005

The purpose of this paper was to investigate the mathematical knowledge and perspective of elementary school teachers in the development and evaluation of students' mathematical tests, analyse test questions, and suggest several principles for the several issues of making and evaluating test-questions. The researcher surveyed 268 elementary school teachers who attended a teachers training program at the A university during January, 2005. The data were analysed by the patterns. The patterns were ambiguity or uncorrectly-described test questionnaires, wrong interpretation of students' responses by the teachers, teacher's deficiency of student' levels and perspectives of mathematics, problematic questionnaires against test-making method, and so forth. Teachers are encourages to cross check to avoid the above problems, to have a strong mathematical knowledge, and to see students' mathematical answers in a flexible manners.

• Journal of Educational Research in Mathematics
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• v.26 no.2
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• pp.269-285
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• 2016

PCK(pedagogical content knowledge) has been frequently discussed in the field of subject matter education as well as education in general. Considering the fact that PCK characterizes teacher professionalism, and the distinction of mathematics education from neighboring disciplines, PCK is one of the core concepts in the discourse of mathematics education. This study focused on KCS(knowledge of content and students) among the areas of PCK. The purpose of this study to investigate the KCS of pre-service teachers attending a private university located in Seoul. An in-depth interview with 30 pre-service teachers was conducted in a semi-structured manner, using four questions dealing with common student errors, students' understanding of content, and student developmental sequences. The pre-service teachers gave mathematical answers while in others they gave priority to pedagogical considerations. The implication drawn from the interview data is that the teacher training program should fully reflect the complexity of mathematical concepts which appeared in school mathematics over several grade levels and content areas.