• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.865-884
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• 2010

The purpose of this research was to analyze the characteristics of teachers' questionings in the geometry field and suggest the characteristics of teacher questioning to enhance students' mathematical creativity. Teacher questioning plays a role to students' mathematical achievements, mathematical thinking, and their attitudes toward mathematics. However, there has been little research on the roles of teacher questioning on students' mathematical creativity. In this research, researchers analyzed teachers' questions concerning the concepts of triangles in the geometric areas of 4th grade Korean revised 2007 mathematics textbooks. We also analyzed teachers' questionings in the three lessons provided by the Jeju Educational Internet Broadcasting System. We classified and analyzed teachers' questionings by the sub-factors of creativity. The results showed that the teachers did not use the questionings that appropriately enhances students' mathematical creativity. We suggested that teachers need to be prepared to ask questions such as stimulating students' various mathematical thinking, encouraging many possible responses, and not responding with yes/no. Instead, teachers need to encourage students to explain the reasons of their responses and to take part in learning activities with interest.

• School Mathematics
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• v.10 no.3
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• pp.423-441
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• 2008

The purpose of this study was to examine the Pedagogical Content Knowledge(PCK) of teachers and their educational practice in the category of plane figure, to make a comparative analysis of their PCK and educational practice, and to discuss the relationship between their PCK and the characteristics of their instruction. Instruction of four selected elementary school teachers was analyzed to find out their educational practice. In conclusion, the characteristics of the PCK and actual instruction of the teachers could be listed as below: First, as a result of comparing their PCK and educational practice on plane figure by applying selected analysis criteria, there was a close correlation between their PCK and actual instruction. Second, the teachers had various levels of PCK on different areas. Especially, there was a large disparity in mathematical content knowledge and knowledge of teaching methods. Third, the teachers who had plenty of PCK were more excellent in textbook reconstructing, and those who fell behind in terms of PCK were more reliant on textbooks as if the textbooks had been the Bible.

• Communications of Mathematical Education
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• v.32 no.1
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• pp.97-111
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• 2018

This study is to establish the domains and the standards of instructional evaluation on the teacher knowledge dealing with the knowledge of 'teaching and learning methods and assessment'. Especially, in this study, the instruction assessment standards are developed focused on the six types of mathematics competencies such as problem solving, communication, reasoning, creativity and collaboration, information and handling, attitude and practice which were emphasized in the mathematical curriculum revised in 2015. By the result, seventh evaluation domains such as an instruction involving problem-solving activity, an instruction involving reasoning activity, instruction involving communication activity, instruction on information and handling activity, instruction involving learners' achievement level and attitude, instruction involving the development of assessment method and tool, instruction applying on assessment result were new established. According to those domains, the 19 instructional evaluation standards were developed totally. This study is limited to consider the domain of 'teaching and learning methods and assessment' among the domains of teacher knowledge, while dealing with the elements of mathematics competencies in the standards. However, instructional evaluation standards reflecting these competencies should be developed in the other diverse domains of teacher knowledge.

• 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.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.159-177
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• 2020

Education researchers have been continuously interested in the teacher's ability to design lessons and conducted various studies in order to improve the teacher's professionalism in determining the quality of school instruction. So, this study explored the change of instructional design through the lesson reflection of pre-service mathematics teachers who participated in practicum settings. As a result, in the lesson plan prepared by pre-service mathematics teachers, the motivation to induce learning in the introduction stage, to present the learning contents in the development stage, and to reconstruct the formative evaluation of the closing stage was the highest rate. And the categories of the reconstructed contents appeared intensively in terms of curriculum contents and teaching and learning methods. This result can be attributed to the lack of experience in designing and performing lessons by pre-service mathematics teachers, so it suggests that the opportunity to design and conduct classes that take into account the practical aspects of education should be provided in the preparation process for pre-service mathematics teachers.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.109-135
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• 2012

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out the following research such as : 1) development of the standards on teaching evaluation between 2004 and 2006, and 2) investigation on the elements of Teacher Knowledge. The purposes of development of evaluation standards for mathematics teaching through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those studies focused on the knowledge of subject matter knowledge, knowledge of learners' understanding, teaching and learning methods and assessments, and teaching contexts. For this purpose, the part of subject matter knowledge was consisted of four evaluation domains such as the knowledge of curriculum reconstruction, knowledge of mathematical contents, methodological knowledge, mathematical value. The part of Learners' unders tanding included the evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies. The part of teaching methods and evaluation was consisted of seventh evaluation domains such as instruction involving instructional goal and content, instruction involving problem-solving activity, instruction involving learners' achievement level and attitude, instruction on communication skills, planning of assessment method and procedure, development on assessment tool, application on assessment result in class were new established. Also, the part of teaching context was consisted of four evaluation domains such as application of instructional tools and materials, commercial manipulatives, environment of classroom including distribution and control of class group, atmosphere of classroom, management of teaching contexts including management of student. According to those evaluation domains of each teacher knowledge, elements on teaching evaluation focused on the teacher's knowledge were established using the instructional evaluation framework, which is developed in this study, including the four areas of obtaining, planning, acting, and reflecting.

• Journal of the Korean School Mathematics Society
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• v.13 no.4
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• pp.569-594
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• 2010

On the standards or elements of teaching evaluation, the Korea Institute of Curriculum and Evaluation(KICE) has carried out several research as follows : 1) establishment of observation elements for selecting examples of good mathematics instruction between 2001 and 2002, 2) development of the standards on teaching evaluation between 2004 and 2006, and 3) investigation on the elements of Pedagogical Content Knowledge including understanding of learners between 2007 and 2008. The purposes of development of mathematics teaching evaluation standards through those studies were to improve not only mathematics teachers' professionalism but also their own teaching methods or strategies. In this study, the standards were revised and modified by analyzing the results of those three studies (namely, evaluation standards) focused on the teacher knowledge of learners' understanding. For this purpose, the meaning of learners' understanding was also investigated in-depth. Finally, the concrete elements on teaching evaluation focused on the teacher knowledge of learners' understanding in math class were new developed, based on the literature reviews on learners' understanding. Then, those evaluation elements were developed according to the five domains of learners' understanding such as evaluation domains such as students' intellectual and achievement level, students' misconception in math, students' motivation on learning, students' attitude on mathematics learning, and students' learning strategies.

• Education of Primary School Mathematics
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• v.23 no.4
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• pp.191-206
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• 2020

The purpose of this study was to find an implication for a direction to improve professional development in mathematics by exploring elementary school teachers' perception of the need for professional development in mathematics. To this end, 4 elementary school teachers were organized into one focus group, and group discussion materials were collected and analyzed based on cases of mathematics professional development needs. As a result of the study, the elementary school teachers' perception that the need for professional development in mathematics is both unnecessary and necessary. The perception of unnecessary was influenced by the easy level of elementary school mathematics content and the ease of teaching. Also, the perception of necessary factors were considering various aspects of mathematics teaching, changing the accumulation of failures in mathematics classes, maintaining authority of students, demand for class improvement due to social change, the impact of school work, the influence of the community of professional development and peers in school, and efforts to grow as teachers. Based on these results, the author discussed ways to promote teachers' participation in mathematics professional development by considering elementary school teachers' perceptions of the need of mathematics professional development.

• School Mathematics
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• v.7 no.4
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• pp.445-467
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• 2005

The purpose of this study was to investigate mathematics teaching of an elementary school teacher and to understand the meaning of it. This study was a qualitative case study using by analyzing metaphors. The notion of metaphors was newly set up. Traditionally, it had been regarded as a mere tool for better understanding, but it was recognized as the primary source of all of our concept(Sfard, 1998). The subject of this case study was a researcher 'I' and also an elementary school teacher. The three selves named Mee1, Mee2, Mee3, respectively. Mee1 was the 'I' who developed the 4th graders' activities on mathematical patterns in 1996 and wrote mathematics textbook for the 4th graders in 1998-1999. Mee2 was the 'I' who taught mathematical patterns to her students in 2002. Mee3 was the 'I' who criticized the teaching of Mee2 in 2005. [ADVENTURE], [HIDE-AND-SEEK], and [FIREWORKS DISPLAY] were deter-mined to be key metaphors of mathematics teaching. [ADVENTURE] of Mee] was focused on profound understanding of mathematics, [HIDE-AND-SEEK] of Mee2 on construction of mathematics, and [FIRE-WORKS DISPLAY] of Mee3 on making meaning and participating in communities. Studies of metaphors give us the power of understanding mathematics teaching and also generate it. And viewing mathematics teaching via metaphors makes teaching studies open to new ways.

• School Mathematics
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• v.12 no.4
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• pp.507-530
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• 2010

The purpose of this study was to help teachers for their teaching practice by analyzing the excellent lesson videos. To analyze the lesson videos between teacher and students, the researchers classified excellent lesson classes into four types as 'Discourse type', 'Representation type', 'Operation type' and 'Complex type' by mathematical communication pattern and kept close watch each lesson videos. Mathematical communication of the best discourse type classroom was analyzed in terms of questioning, explaining, and the sources of mathematical ideas. As a result, the number of Discourse type classes was 6. Operation type classes were 16 owing to characteristic of elementary class. Representation type class was 1 and Complex type class was 1. The Classes excluding Operation type was more planned by teachers. Teachers need to know about mathematical communication accurately because they designed just 5 lesson plan considering mathematical communication of students and only one of the lessons has the intellectual purpose of communication. Furthermore teachers should reflect questioning for student-to-student in their lesson plan.