• 대한수학교육학회지:수학교육학연구
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• 제12권4호
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• pp.473-491
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• 2002

This article analyzes mathematics education from dialectical materialism acknowledging the objectivity of knowledge. The thesis that knowledge is objective advances to the recognition that knowledge will be internalized, and an idea of zone of proximal development(ZPD) is established as a practice program of internalization. The lower side of ZPD, i.e. the early stage of internalization takes imitation in a large portion. And in the process of internalization the mediational means play an important role. Hereupon the role of mathematics teacher, the object of imitation, stands out significantly. In this article, treating the contents of study as follows, I make manifest that teaching and learning in mathematics classroom are united dialectically: I hope to findout the method of teaching-learning to mathematical knowledge from the point of view that mathematical knowledge is objective; I look into how analysis into units, as the analytical method of Vygotsky, has been developed from the side of mathematical teaching-learning; I discuss the significance of mediational means to play a key role in attaining the internalization in connection with ZPD and re-illuminate imitation. Based on them, I propose how the role of mathematics teachers, and the principle of organization to mathematics textbook should be.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권2호
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• pp.217-230
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• 2006

The purpose of this study is to inquire the building process of Pedagogical Content Knowledge of prospective mathematics teachers about the function concepts. For this purpose, We performed the following steps; First, we performed the survey relaying to the prospective mathematics teachers' teaching experiences, capabilities of their error evaluation of the students, and viewpoints about the function concepts. Second, we performed the survey on the subject-matter knowledge about the function concepts and the key items of designing teaching plans about the function concepts. And then, we interviewed the participants to check the results of the surveys and to supplement the necessary contents. The collected data was relatively correlative and analyzed in the process. As a result, we found the followings; First, subject-matter knowledge of prospective mathematics teachers about the function concepts is different depending on the grades. Second, prospective mathematics teachers are building more extended function concepts through the major subjects. Third, the major subjects are important to build the Pedagogical Content Knowledge of function concepts. Fourth, teaching experience plays an important role in transforming subject-matter knowledge of function concepts to Pedagogical Content Knowledge of it. Fifth, building the Pedagogical Content Knowledge means transferring the teacher's viewpoint from himself/herself to the learner.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제6권1호
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• pp.1-28
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• 2002

This study explored teachers (n = 219) from northern, central, southern and eastern Taiwan concerning their views about children's learning difficulties, mathematical instruction and school mathematics curricular. Results showed that teachers' mathematics knowledge or their instruction methods had no significant influence on their views of children's learning difficulties. Even though teachers indicated that understanding of abstract mathematical concepts was the most prominent difficulty for children, they tended to employ direct instruction rather than constructive and cooperative problem solving in their teaching. However, teachers' views of children's learning difficulties did influence their instructional practice. Results from in-dept interviews revealed that there were some obstacles that prevented teachers from putting constructiveism perspectives of instruction into teaching practice. Further investigation is needed to develop a better understanding of epistemology and teaming psychology as well as to help teachers create constructive learning situations.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제6권1호
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• pp.39-51
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• 2002

This study described an elementary teacher's practical knowledge of selecting and using mathematical tasks for promoting students' understanding and discourse. The informant of this ethnographic inquiry was a third grade teacher and has 10 years of teaching experience. According to the analysis of multiple data sources, this study showed that based on his beliefs about the development of understanding of mathematics and discourse, he continually employed two different types of tasks: open-ended tasks and tasks from students' mistakes and comments during discourse. Teachers' practical knowledge of teaching mathematics and the classroom norms for students' understanding and discourse are suggested to be given attention for further research on this area.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권3호
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• pp.171-185
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• 2014

Mathematically deductive reasoning skill is one of the major learning objectives stated in senior secondary curriculum (CDC & HKEAA, 2007, page 15). Ironically, student performance during routine assessments on geometric reasoning, such as proving geometric propositions and justifying geometric properties, is far below teacher expectations. One might argue that this is caused by teachers' lack of relevant subject content knowledge. However, recent research findings have revealed that teachers' knowledge of teaching (e.g., Ball et al., 2009) and their deductive reasoning skills also play a crucial role in student learning. Prior to a comprehensive investigation on teacher competency, we use a case study to investigate teachers' knowledge competency on how to teach their students to mathematically argue that, for example, two triangles are congruent. Deductive reasoning skill is essential to geometry. The initial findings indicate that both subject and pedagogical content knowledge are essential for effectively teaching this challenging topic. We conclude our study by suggesting a method that teachers can use to further improve their teaching effectiveness.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제8권2호
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• pp.97-113
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• 2004

The purpose of this study is to develop instructional methods for the formalized algorithm through informal knowledge in teaching division of fractions. The following results have been drawn from this study: First, before students learn formal knowledge about division of fractions, they knowledge or strategies to solve problems such as direct modeling strategies, languages to reason mathematically, and using operational expressions. Second, students could solve problems using informal knowledge which is based on partitioning. But they could not solve problems as the numbers involved in problems became complex. In the beginning, they could not reinvent invert-and-multiply rule only by concrete models. However, with the researcher's guidance, they can understand the meaning of a reciprocal number by using concrete models. Moreover, they had an ability to apply the pattern of solving problems when dividend is 1 into division problems of fractions when dividend is fraction. Third, instructional activities were developed by using the results of the teaching experiment performed in the second research step. They consist of student's worksheets and teachers' guides. In conclusion, formalizing students' informal knowledge can make students understand formal knowledge meaningfully and it has a potential that promote mathematical thinking. The teaching-learning activities developed in this study can be an example to help teachers formalize students' informal knowledge.

• 대한수학교육학회지:수학교육학연구
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• 제16권3호
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• pp.251-272
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• 2006

이 연구는 수학 수업개선에 초점을 맞춘 관행공동체의 형성과 참여를 통해서 교사들의 변화를 탐색하는데 그 목적이 있다. 수업개선 관행공동체를 통해서 교사들은 수학 수업에 관한 다양한 담론과 지식을 공유하게 되고 결과적으로 수학 수업전문성 신장을 위한 다양한 기회를 갖게 되었다. 이 연구에서는 교사들의 변화를 신념과 수업관행의 측면에서 접근하였다. 그 결과 아동들의 수학 학습방법에 대한 교사들의 신념 측면에서 지속가능한 수학 수업개선의 가능성을 보여 주었다. 또한, 수업관행의 변화 측면에서 교사들의 수학 수업이 학습자 중심 경향으로 변화하고 있는 것으로 드러났다. 이러한 변화는 설문분석에서뿐만 아니라 실제 수업분석 결과에서도 그대로 드러나고 있다. 결국 성공적이고 지속가능한 수학 수업의 변화를 위해서는 수업의 변화에 대한 가치 및 수학 교과와 관련된 전문적인 지식을 공유할 수 있는 환경이 조성되어야 함을 본 연구는 시사한다.

• 대한수학교육학회지:수학교육학연구
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• 제25권4호
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• pp.675-690
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• 2015

본 연구는 초등 예비교사에게 필요한 수학지식을 가르치는 효과적인 수단으로서 수학적 과제의 특징을 논의하고 그에 맞게 과제를 설계하고 교사교육에 실행한 사례를 제시하였다. 그 결과 예비교사들은 '격자점 정삼각형 만들기' 라는 수학적 과제를 해결하면서, 주어진 상황을 수학적 문제로 변환하고 기존 지식과의 연결을 통해 문제를 변형하고 해결하며, 기존의 수학적 개념을 새로운 관점에서 보는 경험을 할 수 있었다. 이러한 경험이 예비교사의 교육에 대한 관점의 변화와 어떻게 연결되는지 그리고 교사교육에 적합한 수학적 과제 설계를 위한 조건에 대해 논의하였다.

• 대한수학교육학회지:학교수학
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• 제17권2호
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• pp.179-202
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• 2015

본 연구는 교사교육에 수학사를 교육적으로 적용하는 방안을 살펴보고, 조선산학 프로그램을 설계 진행하여 예비교사들의 교수를 위한 수학지식 증진 프로그램으로서 조선 산학의 활용가능성을 탐색하였다. 조선산학 프로그램은 사회 문화적 측면과 인지적 측면의 목적에 초점을 맞추어 조선산학 발달의 사회 문화적 배경을 비롯하여 조선산학의 수학적 내용과 학교수학 교육과정과의 연계성을 학습할 수 있도록 구성하였다. 예비 초등교사 89명을 대상으로 프로그램을 진행한 결과, 조선산학의 익숙하지 않은 맥락이 수학적 사고를 자극하는 역할을 함으로써 교사들의 교과내용지식을 보다 풍부하게 할 수 있으며, 특정 수학 주제를 가르치기 위하여 필요한 교사지식을 보완하기 위한 소재로 조선산학이 활용가능하다는 것을 확인하였다. 또한 조선산학과 학교수학의 연계가능성을 생각해보게 하고 연계 내용의 교수방안에 대한 아이디어를 제시하게 함으로써 교사들의 내용교수지식 증진에 기여할 수 있으며, 수학의 사회 문화적 관점을 형성하는 기회로 활용할 수 있다고 보았다.

• 한국수학교육학회지시리즈A:수학교육
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• 제45권1호
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• pp.75-96
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• 2006

The purpose of this study was to analyze how elementary pre-service teachers learned the pedagogical content knowledge of mathematics and to understand the challenges and difficulties that they experienced in the course of student teaching. A qualitative case study provided an in-depth description of the whole three weeks of student teaching process. Four pre-service teachers and two mentor teachers participated in this study. Multiple data collection techniques were used; classroom observations, in-depth interviews, document analysis, and researcher's field notes. The results of this study showed how pre-service teachers learn PCK of mathematics in designing mathematics lessons, understanding mathematics learners and delivering mathematics lessons and what are the difficulties and challenges they experienced. Finally this study discussed about some suggestions to pre-service program and future research.