• Journal of Elementary Mathematics Education in Korea
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• v.18 no.2
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• pp.211-236
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• 2014

The purpose of this study is to investigate teacher's knowledge of concept of equality and derive implications about proper teaching methods. To solve these study problems, three elementary school teachers are chosen for this study, and a pencil-and paper tests for comprehension of the equality concept targeting 72 students for elementary school that the teachers are in charge of the students was carried out. Also, The semi-structured interview(using a questionnaire) was conducted for analyzing of the teachers' knowledge of the equality concept. The findings are as follows. First, during the lesson, the teachers' reading of equal sign has a decisive effect on the students' the way of reading. Second, teachers tend to interpret the concept of equality as a systematic analysis rather than a relational analysis, and use a equal sign focusing on meaning of 'same result'. So, Students also can't interpret the concept of equality as a relational analysis. Third, under the influence of teacher's feedback or reaction, making the mistake of the using equal sign of students reoccurred continually. Fourth, teachers misjudged some of examples of the nonstandard context equation for teaching elementary school students. Furthermore, during the lesson, they usually used a limited equality context. So, students can't have a chance to learn equality in a plenty of context. Thus, the knowledge of teachers and their lesson has decisive influence on the comprehension of students about the equality concept. So, Teacher has to focus on the meaning of the equality as a relational analysis and teach them in a plenty of context. With this, lots of study and in-service training are needed to enhance knowledge of teachers. And more of lesson programs and materials have to provided on the instruction manual for teaching the meaning of the equality.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• The Mathematical Education
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• v.51 no.2
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• pp.131-144
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• 2012

The purpose of this study is to investigate the change of mathematics pre-service teachers' teaching behaviors in microteaching. This study is organized along the following lines: 1) mathematics pre-service teachers conduct twice microteachings, 2) the microteaching recordings and lesson observation reports written by pre-service teachers are analyzed. Through reviewing the first microteaching, pre-service teacher have reviewed and found out improvements of their teaching. In the second microteaching, pre-service teachers' teaching behaviors have been positively and effectively changed with respect to teaching methods, proposal of learning objectives, prior knowledge usage, presenting lesson's content, concise descriptions, brief language usages, multimedia, and appropriate questions. However, they frequently used inappropriate expressions from their unconscious habits. Therefore, the educational institutions should provide opportunities involved in well-structured microteaching training program with pre-service teachers, which in turn, help pre-service teachers to have more positive teaching competence.

• 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.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.373-389
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• 2015

This study was to investigate the practice of the teachers who changed their teaching subject to Mathematics from other subjects. Teacher, A who had traditional belief and Teacher, B, non-traditional belief were chosen for the study through the questionnaire in Sep. 2014. The result indicated that Teacher, A in traditional belief showed teacher-centered teaching but Teacher, B in nontraditional belief showed inconsistent way of teaching in comparison to the original perspective. The later said she could not teach students as she wanted to teach because of the lack of knowledge of teaching as a math teacher. The difficulties Teacher, A encountered were: to handle too many works beyond teaching and to teach too many contents to cover without having enough time to prepare. Teacher, B didn't know how to teach students math in a constructivism way. They asked to offer them more in-service training program to develop their expertise for teaching mathematics.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.179-202
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• 2012

To implement effective technology-based education, we need knowledge for functional aspects of technology as well as design and procedural aspects of curriculums. Also, we need positive teaching efficacy. In this regard, we investigate the effects on teachers' TPACK and technology teaching efficacy on mathematics after make the teachers design and teach technology-based classes according to the ASSURE model which is suitable in designing technology-based educations. First, we let the teachers design and teach two unit hour classes. The first class had been done with the teachers learned functional aspects of technologybased educations, and the second one with them designed based on the steps in the ASSURE model. To analyze the effects of ASSURE model, we have performed a case-study for one teacher who had taken part in our college class. As a result, we conclude that the teacher's experiences in designing classes based on the ASSURE model help improve the teacher's TPACK and technology teaching efficacy on mathematics in a positive way.

• Communications of Mathematical Education
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• v.26 no.3
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• pp.301-316
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• 2012

Ball, Thames & Phelps(2008) introduced the idea of Mathematical Knowledge for Teaching(MKT) teacher. Specialized Content Knowledge(SCK) is one of six categories in MKT. SCK is a knowledge base, useful especially for math teachers to analyze errors, evaluate alternative ideas, give mathematical explanations and use mathematical representation. The purpose of this study is to analyze the elementary teacher's SCK. 29 six graders made word problems with respect to division fraction $9/10{\div}2/5$. These word problems were classified four sentence types based on Sinicrope, Mick & Kolb(2002) and then representative four sentence types were given to 10 teachers who have taught six graders. Data analysis was conducted through the teachers' evaluation of the answers(word problems) and revision of students' mathematical errors. This study showed how to know meanings of fraction division for effective teaching. Moreover, it suggested several implications to develop SCK for teaching and learning.

• Education of Primary School Mathematics
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• v.17 no.3
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• pp.189-203
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• 2014

The purpose of this study was to analyze the strengths and weaknesses resulting from a study of elementary mathematics lessons among in-service teachers and to discuss implications for the direction of improvement of the study on elementary mathematics lessons based on teacher learning community. The results of this study showed that the study on elementary mathematics lessons based on teacher learning community improved teacher knowledge related to teaching mathematics, enhanced teacher's accomplishment and self-esteem, made it possible for participant teachers to teach one another, created atmosphere in which teachers investigated instruction via sustainable and systematic lesson study. However, some limitations were noticed such as regulations by the social norms of the teacher learning community, the influence of an expert teacher, teachers' unprofessional decision making, and lack of systematic evaluation and reflection on lessons. Based on these results, this paper closes with critical implications to enhance teacher learning community.

• Journal of the Korean earth science society
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• v.34 no.5
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• pp.435-449
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• 2013

The purpose of this study was to investigate the difference of teachers' interaction with their students when teaching science in New York (NY) and in Korea. As part of the 2011 Korean International Teacher Fellows (KITF), supported by the Ministry of Education, Science and Technology (MEST) and the National Institute for International Education Development (NIIED), Korean science teachers observed, for six months, New York's science classes in terms of how teachers interact with their students and how students learn science during science instruction. The participants were 10 science teachers in five middle and high schools that taught Physics, Chemistry, Biology, Earth Science, and Environment Science in NY. The National Board for Professional Teaching Standards (NBPTS, 2003) and Instruction as Interaction (Cohen et al., 2003) were used as an instrument to identify each teacher's teaching and classroom interaction. Several characteristics of science classes in NY were revealed, which are different from Korean science classes. First, science teachers in NY dominantly put more focus on their subject of teaching during science interaction while, Korean science teachers not only teach science but also do counseling to students as a homeroom teacher. Second, science teachers in NY acknowledged the students' individuality and have positive experiences of professional development supported by their school and district more than Korean science teachers do. Third, science teachers in NY sometimes showed limited knowledge about the concepts of science and lack of collaboration with other science teachers. This characteristics may prevent the school from strengthening its subject program and keeping equity across the grade levels and courses.

• School Mathematics
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• v.15 no.2
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• pp.243-262
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• 2013

This study attempts to create an analytical framework of the transformation and transmission of knowledge by teachers to students. I focuses on the assertion that the cognitive thinking of a teacher is reflected in his use of mathematical language. Mathematical language is one of the critical elements of communicating mathematical knowledge to students. I examined the cognitive teaching style of different teachers as expressed in their use of mathematical language. An analytical framework of Mathematics Teaching styles was created integrating thinking factors of each visual and analytic style into 5 categories. After that, I regarding the teaching style of mathmatics teachers places its significance not on which teaching style is right or wrong but on identifying the strong and weak points of the teaching styles through actual analysis. With the help of this analytical framework, I conducted an analysis on the videotaped classes and found that the teachers were not biased to one side but in fact there were teachers who demonstrated visual, analytic or mixed teaching style. Therefore, I concludes that math teachers can analyze their teaching styles and improve them through the analytical framework provided in these findings.