• 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.11 no.3
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• pp.335-349
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• 2009

The purpose of this study is to explore how a mathematics teacher's beliefs about mathematics and teaching and learning and mathematics and how such beliefs are related to her knowledge manifested in her mathematics instruction. The study illustrates images of teaching practice of an American mathematics teacher in middle grades mathematics classrooms. Results suggest that the teacher seems consistent in teaching in terms of her beliefs about mathematics and learning and teaching mathematics in some degrees. In particular, the teacher's beliefs affected the ways in which mathematics teacher organized and structured her lessons.

• 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.

• 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.

• The Mathematical Education
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• v.60 no.3
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• pp.281-295
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• 2021

This study examines the breadth and depth of knowledge of the teacher employment test for secondary mathematics. For the breadth of knowledge, we attempted to figure out the range of knowledge in terms of the content areas using the standards from the Korea Society Educational Studies in Mathematics[KSESM](2008). For the depth of knowledge, we chose Anderson & Krathwohl(2001) framework to analyze levels of each item in the test. The results from the analysis of 180 items in the teacher employment test between 2014 and 2021 show that while items in mathematics education have considerable variation in terms of range and levels of knowledge, those in some subjects of mathematics can be found only certain level of knowledge. i.e., merely certain topics or levels of knowledge have been heavily evaluated. Thus, considering the breadth and depth of knowledge teachers should have, the current exam needs to be improved in terms of teacher knowledge. It does not mean that every topic and every level of knowledge should be evaluated. However, it is a meaningful opportunity to think about what kinds of knowledge teachers should have in relation to K-12 mathematics curriculum and how we can evaluate the knowledge. More collaborative effort is inevitable for the improvement of teacher knowledge and teacher employment test.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.357-371
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• 2010

This study aimed to investigate how two eighth-grade mathematics teachers' pedagogical content knowledge is manifested in their classroom instruction. A case study was conducted for the study. The results revealed similarities and differences in the teachers' knowledge manifested in their mathematics classrooms and that the two teachers had slightly different structures of pedagogical content knowledge. One teacher is more dependent on his knowledge of mathematics and knowledge of students' understanding and the other teacher on her knowledge of instructional process and, to a lesser extent, knowledge of mathematics.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.123-142
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• 2011

Recently, a number of researches acknowledge the importance of 'reflection' and 'reflective teacher education,' and they highlight the implication of 'reflection' on the teacher's profession or the teacher education. The reflective thought is interpreted as a subject that should be taught or a sort of strategy that a teacher should learn, while the aspect is excluded that reflection is the interaction between the innate knowledge and the practice. As a result, the reflective teacher education programs that increase the level of reflection are developed and practiced, and the reflection is accepted as a tool for increasing teacher professionalism. Reflective teaching is en essential and basic element for the development of teacher knowledge. In particular, such teacher knowledge might be being gradually expanded by a teacher's self-assessment on reflection on his own instruction. For this reason, this study develops an assessment framework on instruction which is comprized of teacher knowledge and instructional process. To accomplish this, in this study, teacher knowledge is considered as a whole practice knowledge combined by subject matter knowledge, understanding of learners, teaching and learning methods and assessment, and instructional environment. Also, success on instruction in mathematics class might depend on the acquisition of teacher knowledge, instructional planning, instructional execution, and furthermore reflection on instruction. Especially, this study emphasizes that 'reflection on instruction', the most important step of instruction be reflected and examined by the teacher himself.

• Research in Mathematical Education
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• v.14 no.4
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• pp.323-332
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• 2010

It is the development of a mathematics teachers' teaching knowledge that manifests a mathematics teacher's professional knowledge growth. It is becoming a direct and effective approach of conversion of mathematical knowledge into the knowledge of mathematics teaching. Through the investigation, the study revealed that the knowledge conversion process of mathematics teachers in middle school is restricted by three aspects including eight factors. From this point, the authors have structured the path and model on influencing factors of middle school Mathematics Teaching Knowledge Conversion (MPCK), and discuss the mechanism of the transformation process.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.695-717
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• 2013

Teacher knowledge needed for teaching is bound to be revealed in teaching the subject matter in relation to the given instructional context. Given this, recent studies on mathematics teacher knowledge tend to analyze actual Mathematical Knowledge in Teaching [MKiT]. This study focused on the dimension of transformation and its related codes in Knowledge Quartet, which has been recognized as a MKiT framework, and analyzed a Korean teacher's transformation knowledge revealed in her elementary mathematics teaching. The analysis showed that the codes related to the dimension of transformation were useful in analyzing teacher knowledge in the Korean context. However, a few codes need to be revised or added for more suitability. On the basis of these results, this paper closes with implications for analyzing teacher knowledge in mathematics teaching.

• 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.