• Journal of Elementary Mathematics Education in Korea
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• v.15 no.3
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• pp.533-557
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• 2011

The purpose of this study was to understand PCK to improve professionalism of teachers and derive implications about proper teachings methods. For achieving these research purposes, different PCK and teaching methods in class of three teachers(A, B, C) were compared and analyzed targeting division of decimals for 6th grade. For this study, criteria of PCK analysis of teachers was set, PCK questionnaires were produced and distributed, teachers had interviews, PCK of teachers were analyzed, division of decimals class for 6th grade was observed and analyzed, and PCK of teachers and their classes were compared. The implications deriving from comparative analyzing PCK and classes are as follows. First of all, there was a close relation between PCK and classes, leading to a need for efforts of increasing PCK of teachers in every field in order to realize effective classes. Secondly, self study and in-service training are needed to enhance PCK of teachers. Thirdly, more of expertises and materials have to be provided on the instruction manual for teachers.

• Journal of The Korean Association of Information Education
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• v.5 no.2
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• pp.268-278
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• 2001

This study is design and implementation of diagnosis module using item response theory to assess level of student's knowledge in web-based instruction systems. Item response theory uses responses to items on a test or survey questionnaire to simultaneously locate both the items on the latent trait defined by the set of items while simultaneously scaling each item on the very same dimension. Existing method of measurement in web-based instruction system provided dichromatic learning after to be assess just with the total scores of exam. This measurement has an error that do not consider the level of student's knowledge. Moreover, this method can't perform an exact diagnosis of student knowledge and make student modeling to construct intelligent tutoring system. In this study, we present that design and implement a diagnosis module using item response theory to assess level of student's knowledge in web-based instruction systems

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.411-430
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• 2017

This study examined the understanding of 24 pre-service teachers about the three contexts for constructing the exponential graphs. The three contexts consisted of the infinite points context (2009 revision curriculum textbook method), the infinite straight lines context (French textbook method), and the continuous compounding context (2015 revision curriculum textbook method). As the result of the examination, most of the pre-service teachers selected the infinite points context as easier context for introducing the exponential graph. They noted that it was the appropriate method because they thought their students would easily understand, but they showed the most errors in the graph presentation of this method. These errors are interpreted as a lack of content knowledge. In addition, a number of pre-service teachers noted that the infinite straight lines context and continuous compounding context were not appropriate because these contexts can aggravate students' difficulty in understanding. What they pointed out was interpreted in terms of knowledge of content and students, but at the same time those things revealed a lack of content knowledge for understanding the continuous compounding context. In fact, considering the curriculum they have experienced, they were not familiar with this context, continuous compounding. These results suggest that pre-service teacher education should be improved. Finally, some of the pre-service teachers mentioned that using technology can help the students' difficulties because they considered the design of visual model.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.63-77
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• 2016

SENKs (Students who Emigrated from North Korea to South Korea) are exposed to the general problem of Su-Po-Ja(mathematics give-uppers) as well as their own difficulty in learning mathematics. In this study, we conducted the FGI (focus group interview) in order to examine the recognition on mathematics teaching and learning in South Korea with 6 SENKs and 3 teachers who teach the SENKs. As a result, it was found that SENKs' had difficulties in understanding math because of the differences in math terminology used in South and that in North Korea, the unfamiliar problem situation used in math lesson, and the shortage of time for solving math problem. And the teachers reported that they had difficulties in teaching great deal of basic math, SENKs' weak will to learn math, and SENKs' lack of understanding about problem situation because of the inexperience about culture and society in South Korea.

• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.203-222
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• 2020

Because the role of the teacher is important for the education to actualize the goals of the curriculum, the interest about the teacher's knowledges has been addressed as an important research topic. Among them, the pedagogical content knowledge is the knowledge that can emphasize the professionalism of the teacher. In this study, I analyzed the elementary pre-service teachers' the problem solving strategies that they imagined the methods that elementary school students can think about fraction division. Pre-service teachers who participated in this study were completed all of the mathematics education courses in the pre-service teachers' education courses. The research was conducted using the four type-problems of fraction division. The results showed that elementary pre-service teachers responded in the order of equal sharing problem-measurement division-partitive division-context of determination of a unit rate problem. They presented significant responses not only with typical algorithms but also with pictures or expressions. On the basis of this research, we have to take an interest in the necessity of sharing and recognizing various methods of fraction division in pre-service teachers education.

• School Mathematics
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• v.13 no.4
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• pp.675-696
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• 2011

This study was designed to understand PCK to improve professionalism of teachers and derive implications about proper teachings methods. For achieving these research purposes, different PCK and teaching methods in class of three teachers were compared and analyzed targeting arithmetic operation unit of fraction. For this study, criteria of PCK analysis of teachers was set, PCK questionnaires were produced and distributed, teachers had interviews, PCK of teachers were analyzed, two times fraction class was observed and analyzed, and PCK of teachers and their classes were compared. Followings are results to analyze PCK of teachers about fraction. In relation to PCK of three teachers, first of all, A teacher accurately understood concepts of fraction and learners' errors that may occur when they study fraction. Also, he(she) proposed concrete teaching strategies for fraction based on manipulated materials. B teacher also understood concepts of fraction and learners' errors accurately too. On the other hand, C teacher laid stress on knowledge to stress principles and taught that they are bases for every class. These results mean that self-training and inservice- training should be efficiently upgraded to improve PCK of teachers.

• Communications of Mathematical Education
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• v.19 no.1 s.21
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• pp.15-24
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• 2005

오늘날 제 7차 교육과정은 학습자의 사고과정과 능력을 다양한 평가방식으로 실시하도록 권유하고 있다. 이러한 목적을 구현하기 위하여 수학과 평가는 교수-학습에 유용한 평가, 과정 중심의 평가, 다양한 방법을 활용하는 평가가 되어야 할 것이다. 이는 학습자로 하여금 스스로 학습하도록 가정하는 인식론적 변화에 바탕을 둔 최근의 평가 동향과 맥을 같이 하고 있다. 평가에서 학생의 수학활동 역시 특히 인지적 영역의 다양성을 지닌 개인에 의하여 이루어지기 때문에 수학 평가는 단편적인 정형화된 지식이 아닌 문제 해결의 전략이나 발견술과 같은 요소에서 강조되고 있는 비정형의 문제들을 통한 메타인지적인 발달과정을 고려해야 한다. 본 연구에서는 학생이 준개방형 평가문제를 해결하는 과정을 통해 자신이 얼마나 알고 있는가를 인식하며 자신의 문제 해결 전략을 점검하고 평가하는 인지적 능력에서 일어나는 변화를 알아보는 데 그 목적이 있다. 지금 현재 연구가 진행 중이며 본 연구의 결과는 다음 논문집에 발표할 예정이다.

• 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.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.163-180
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• 2019

This study introduces a development of calculus contents which makes to understand the main concepts of calculus in a short period of time and to enhance problem solving and computational thinking for complex problems encountered in the real world for college freshmen with diverse backgrounds. As a concrete measure, we developed 'Teaching and Learning' contents and Python-based code for Calculus I and II which was used in actual classroom. In other words, the entire process of teaching and learning, action plan, and evaluation method for calculus class with Python based coding are reported and shared. In anytime and anywhere, our students were able to freely practice and effectively exercise calculus problems. By using the given code, students could gain meaningful understanding of calculus contents and were able to expand their computational thinking skills. In addition, we share a way that it motivated student activities, and evaluated students fairly based on data which they generated, but still instructor's work load is less than before. Therefore, it can be a teaching and learning model for college mathematics which shows a possibility to cover calculus concepts and computational thinking at once in a innovative way for the 21st century.

• School Mathematics
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• v.15 no.4
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• pp.921-940
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• 2013

This study is to analyze mathematically gifted middle school students' characteristics of mathematical thinking and the teacher's role in teaching and learning about the central projection and perspective drawing. And it will help to develop teaching and learning materials for the mathematically gifted. The result of this study is as followings : mathematically gifted middle school students show the various characteristics of mathematical thinking like as intuitive insight, generalization, logical thinking & mathematical abstraction and so on, and the teacher plays roles as instructional designer, facilitator, technical assistant and counselor.