수학 과제 분석을 통한 예비 초등 교사의 전문성 신장

방정숙 ( Jeong Suk Pang ) 한국수학교육학회 2007 수학교육 Vol.46 No.4

내용 : 측정 영역의 핵심 교수·학습 요소에 의한 좋은 수학 수업 분석

방정숙 ( Jeong Suk Pang ),김정원 ( Jeong Won Kim ),김혜정 ( Hye Jeong Kim ) 한국수학교육학회 2012 初等 數學敎育 Vol.15 No.2

Considerable efforts have been attempted to identify what makes high-quality mathematics instruction, including diversity and variability across different educational systems and cultural contexts. As the instructional elements related to effective mathematics teaching can be commonly applied to different content domains, they may be efficient in selecting such teaching. However, such elements may not reflect on the specific but essential features of each domain. This paper compared and contrasted two sets of measurement teaching practices, which were recognized as good instruction, in terms of how the key elements of measurement domain were implemented. As such this paper is expected to accumulate significant knowledge about elements of effective mathematics instruction that are specialized in a particular content domain of measurement. This paper suggests that domain-specific approach be considered in studying good mathematics teaching.

시리즈 A : 학생중심 초등수학 교실문화의 구현과 난제

방정숙 ( Jeong Suk Pang ) 한국수학교육학회 2006 수학교육 Vol.45 No.4

범자연수와 연산에 관한 수학 교과서 분석 -일반화된 산술로서의 대수 관점을 중심으로-

방정숙 ( Jeong Suk Pang ),최지영 ( Ji Young Choi ) 한국수학교육학회 2011 수학교육 Vol.50 No.1

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students` algebraic thinking in the elementary grades.

예비 초등 교사들의 분수 나눗셈에 대한 지식 분석

방정숙 ( Jeong Suk Pang ),Ye Ping Li 한국수학교육학회 2008 수학교육 Vol.47 No.3

한국 학생들의 수학과 수학 학습에 대한 가치 인식: 초등학교 6학년과 중학교 3학년을 중심으로

방정숙 ( Pang Jeongsuk ),조수윤 ( Cho Sooyun ),( Seah Wee Tiong ) 한국수학교육학회 2016 수학교육 Vol.55 No.4

What an individual values and regards as important has a significant impact on his or her learning. Classroom instruction would be even more effective if what the teacher regards as important in his or her pedagogical practice are aligned with what students regard as important too. Given this background, this study sought to find out what Korean students valued about mathematics and mathematics learning using a questionnaire developed by Seah (2005). The participants were 409 students from Grade 6 and 407 students from Grade 9 in Korea. The results of this study showed that students put the biggest emphasis on ideological aspects of mathematics, specifically rationalism, among mathematical values. The students also valued product, computation, process, exposition, and recalling among values related to the learning of mathematics. A comparative analysis between the two groups of students showed that sixth graders tended to think more positively with regards to each value than ninth graders. On the basis of these results, this paper raises some issues about students` values in mathematics learning. It also suggests that teachers need to consider what students value and regard as important in their mathematics learning to bring about even more effective instruction.

초등학교 교사들의 수학교육 목적 인식 실태 조사

방정숙 ( Jeong Suk Pang ),정유경 ( Yoo Kyung Jung ),김상화 ( Sang Hwa Kim ) 한국수학교육학회 2011 初等 數學敎育 Vol.14 No.3

수학수업을 통해서 학생들에게 기대되는 학습 목표를 제대로 구현하기 위해서는 무엇보다 수학을 왜 가르치고 배워야 하는지에 대한 교사의 올바른 인식이 필수적이다. 이에 본 연구에서는 초등학교 교사들이 수학교육의 목적을 어떻게 인식하고 있는지 설문 조사를 실시하였다. 연구 결과 교사들은 합리적·논리적 사고 발달, 실용성, 도구 교과로서 수학을 인식하는 비중이 높은 반면에 세계에 대한 이해, 심미성, 의사소통 및 사회성 발달로서의 수학을 인식하는 비중은 상대적으로 낮았다. 한편 학문적 가치와 관련해서는 교사가 직접 서술한 수학학습의 이유에는 별반 나타나지 않은 반면에 리커트 척도에 의한 응답에서는 높게 나타나는 특징이 있었다. 교사의 인식은 성별에 따라서 통계적으로 유의미한 차이는 없었으나 5년 미만의 교육경력을 가진 교사가 그렇지 않은 교사집단에 비해 대체적으로 수학교육 목적을 긍정하는 비율이 낮았다. 이와 같은 연구 결과를 토대로 본 논문에서는 교사의 수학교육 목적 인식에 따른 시사점을 살펴보았다. It is necessary for the teacher to understand why teach mathematics in order to implement the visions and expectations of the national mathematics curriculum in her actual classroom. This study conducted a survey of examining how elementary school teachers might understand the purpose of teaching mathematics. The results of this study showed that teachers` conceptions of the purpose of teaching mathematics were related mainly to the development of Logical thinking, practical use of mathematics in everyday Life, and a tool for studying other subjects or disciplines. However, teachers did not perceive much other purposes of mathematics education such as understanding the world, appreciating aesthetic value of mathematics, and developing communicative ability as well as sociality. Whereas teachers did not think of the significance of mathematics as an intellectual field when asked to write down how they would explain students why they had to Learn mathematics, they tended to strongly agree it in the Likert-scale responses. Teachers` conceptions were not different according to their gender but teachers with Less than five years` teaching experience were relatively negative than others with more experience. Given these results, this study provided issues and implications of teachers` conceptions of the purpose of teaching mathematics.

초등학교 수학 교과서 및 익힘책에 제시된 변수 개념에 관한 분석

방정숙 ( Jeongsuk Pang ),조선미 ( Sunmi Cho ),김정원 ( Jeongwon Kim ) 한국수학교육학회 2017 수학교육 Vol.56 No.1

The concept of variable is a big idea to develop algebraic thinking. Variable has multiple meanings such as the unknown, a tool for generalization, and the relationship between varying quantities. In this study we analyzed in what ways the meanings of variable were presented in the current elementary mathematics textbooks and workbooks. The results showed that the most frequent meaning of variable was `the unknown`, `a tool for generalization`, and `the relationship between varying quantities` in order. A close look at the results revealed that the same symbol was often used in representing different values of variable as the unknown. In taking variable as a tool for generalization, questions to provoke generalization were sometimes included not in the textbooks but in the teachers` manuals. The main focus in dealing with variable as the relationship between varying quantities was on finding out the dependent values compared to the independent ones. Building on these results, this study is expected to suggest implications for how to deal with variable concept in elementary mathematics instructional materials.

초등학교 3학년 학생들의 대수적 사고에 대한 실태 분석

방정숙 ( Pang Jeongsuk ),최인영 ( Choi Inyoung ) 한국수학교육학회 2016 初等 數學敎育 Vol.19 No.3

<div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div><div style="display:none">fiogf49gjkf0d</div> Given the importance of developing algebraic thinking from early grades, this study investigated an overall performance and main characteristics of algebraic thinking from a total of 197 third grade students. The national elementary mathematics curriculum in Korea does not emphasize directly essential elements of algebraic thinking but indicates indirectly some of them. This study compared our students` performance related to algebraic thinking with results of Blanton et al. (2015) which reported considerable progress of algebraic thinking by emphasizing it through a regular curriculum. The results of this study showed that Korean students solved many items correctly as compatible to Blanton et al. (2015). However, our students tended to use ‘computational` strategies rather than ‘structural` ones in the process of solving items related to equation. When it comes to making algebraic expressions, they tended to assign a particular value to the unknown quantity followed by the equal sign. This paper is expected to explore the algebraic thinking by elementary school students and to provide implications of how to promote students` algebraic thinking.

초등학교 수학 교과서에 제시된 패턴 지도방안에 대한 분석

방정숙 ( Jeong Suk Pang ),선우진 ( Woojin Sun ) 한국수학교육학회 2016 初等 數學敎育 Vol.19 No.1

패턴을 다루는 여러 가지 활동은 초등학생들의 대수적사고를 신장하는데 매우 효과적이다. 이에 본 연구는 초기대수(early algebra)적 관점에서 패턴을 지도하는 세 가지주요 활동인 패턴의 구조를 분석하는 활동, 패턴에서 두변수 사이의 관계를 탐색하는 활동, 패턴의 일반화된 규칙을 추론하고 표현하는 활동을 중심으로 현행 초등학교 수학 교과서에 제시된 패턴 지도방안을 분석하였다. 분석결과 패턴의 구조를 분석하는 활동은 교과서 상에서 명시적으로 고려되지 않았다. 반면 패턴에서 두 변수 사이의 관계를 탐색하는 활동은 주로 대응표를 활용하여 전 학년에서 다루어졌고, 패턴의 일반화된 규칙을 추론하고 표현하는 활동은 저학년에서는 패턴의 규칙을 비형식적으로 표현하는 활동을 통하여, 고학년에서는 패턴의 규칙을 수식이나 기호를 사용하여 형식적으로 표현하는 활동을 통하여 다루어졌다. 한편 다른 수학 내용과의 연계성 측면에서 패턴의 지도방안을 분석한 결과, 현행 초등학교 수학 교과서에서는 패턴 활동이 규칙성 영역에 해당하는 일부 단원에서만 한정적으로 다루어지고 있었다. 이와 같은 연구결과를 토대로 본 연구는 초등학생들의 대수적 사고를 신장하기 위한 패턴 지도방안과 관련하여 구체적인 시사점을 제공하고자 한다. Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.