초등학교 3∼4학년군 수학 교과서에 의도된 교과 역량 분석

방정숙 ( Pang Jeongsuk ),황지남 ( Hwang Jinam ) 한국수학교육학회 2021 初等 數學敎育 Vol.24 No.1

Despite the necessity and significance of mathematical competencies in the 2015 revised mathematics curriculum, there has been lack of studies analyzing textbooks in which such competencies are intended in detail through various tasks. Given this background, this paper analyzed how mathematical competencies and their sub-elements have been represented in the mathematics textbooks for third and fourth grade. The findings of this study showed that ‘communication’ was the most prevalent mathematical competence, followed by ‘reasoning’, ‘creativity and integration’, ‘information processing’, ‘attitude and practice’, and ‘problem solving’ in order. This study also explored the characteristics of mathematical competencies in the textbooks by analyzing which sub-elements per competence were popular. With illustrative examples, this paper is expected to provide for textbook developers with implications on how to represent mathematical competencies throughout the textbooks.

초등학교 1학년 학생들의 수학 익힘 문항에 대한 오답 분석

방정숙(Pang, JeongSuk),이유진(Lee, YuJin) 학습자중심교과교육학회 2019 학습자중심교과교육연구 Vol.19 No.3

본 연구의 목적은 학생들의 수학 익힘 문항에 대한 응답을 분석하여 문항 이해 부족으로 인한 오답률이 높은 문항들의 특성을 도출하는 것이다. 이를 위해 2018년 3월부터 7월 말까지 초등학교 1학년 1학기 수학 익힘 180문항에 대한 88명의 학생 응 답을 수집하였으며, 오답을 무응답, 수학 개념 오류, 문항 이해 부족으로 나누어 분석하였다. 그 결과 1학년 학생들은 문항 해결에 필요한 정보가 부족하거나, 비슷한 활동임에도 수학 교과서와 문항 제시 방식이 다른 경우 문항을 이해하기 어려워했 다. 이 외에도 주어진 자료가 부적절하거나 명확하지 않은 경우, 추가 조건이나 지시어가 많은 경우에도 문항을 제대로 파악하지 못했다. 연구 결과를 토대로, 수학 익힘의 개발 및 수정 방안에 대한 시사점을 논의하였으며, 수학 익힘을 효과적으로 활용 할 수 있는 방안에 대한 기초 자료로서 활용할 수 있을 것이라 기대된다. The purpose of this study is to explore the characteristics of problems with which students solve incorrectly. For this, 88 first-grade students in an elementary school solved all the problems of the workbook for the first semester while they were learning mathematics. Students incorrect answers were classified by non-response, errors in mathematical concepts, and the lack of understanding of problems. The results of this study showed that the first-year students had a difficulty in understanding the problems if there was lack of information to solve the problems or a difference between the mathematics textbook and the workbook despite the similarities in problems. In addition, the students made errors when the problems were unclear to them or when the problems had additional conditions or directives. Based on the results of the study, this paper suggests implications on how to develop and revise the workbook, and to use it in a classroom.

수학적 추론 중심의 스마트 수업 모형 적용

방정숙(Pang, JeongSuk),여승현(Yeo, SheungHyun) 학습자중심교과교육학회 2013 학습자중심교과교육연구 Vol.13 No.6

최근 스마트교육에 대한 관심이 부각되었으나 수학교육에서 이를 어떻게 활용해야하는지에 대한 연구는 많이 이루어지지 않고 있다. 이에 본 연구는 스마트시범 학교의 6학년을 대상으로 수학적 추론 중심의 스마트 수업 모형을 적용하여 실제 수업에서의 여러 가지 양상을 스마트 교육 요소와 수학적 추론 요소를 중심으로 분석하였다. 분석 결과 스마트 교육 요소와 관련하여 핵심역량 중 특히 협력이 효율적으로 이루어졌고, 다양한 상호작용 중 학생과 학생 간의 상호작용이 의미 있게 드러났으며, 활용도구 측면에서는 스마트기기와 특화 어플리케이션이 각 학습 주제에 부응되는 방향으로 효율적으로 활용됨을 알 수 있었다. 또한, 수학적 추론 요소와 관련하여 여러 가지 요소들이 수업 전반에 걸쳐 비교적 잘 드러났는데, 특히 구체적 사례로부터 공통 요소를 확인하는 과정과 추론을 확장하여 일반화하는 과정이 부각되었다. 이와 같은 연구 결과를 토대로 본 논문은 스마트 수업 모형을 초등 수학교육에 적용 할 때의 시사점을 제공하였다. Despite the recent emphasis on the SMART learning little research has been conducted as for what a teacher needs to do in teaching mathematics. This paper applied a mathematical reasoning-centered SMART instructional model to sixth graders in a designated SMART pilot school and then analyzed common aspects of 8 instructions in terms of SMART education elements and mathematical reasoning elements. An analysis of SMART education elements showed that cooperation among core competencies was employed effectively and that interactions between students appeared meaningfully. Smart devices and specialized applications were efficiently used according to each content. Various elements related to mathematical reasoning appeared throughout the lessons. Specifically it was noticeable for students to find out the common rule among multiple cases and to generalize their conjecture. On the basis of these results this paper suggested several implications of applying smart instructional models to elementary mathematics education.

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 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.

수학 수업을 위한 초등 교사의 지도안 작성 실태 조사

방정숙(Pang, JeongSuk),조수윤(Cho, Sooyun) 학습자중심교과교육학회 2014 학습자중심교과교육연구 Vol.14 No.4

Despite the significance of lesson plan as a foundation of implementing effective instruction, there have been lack of studies in this area. Given that a teacher is the planner of her instruction, it is necessary to explore in what ways a teacher constructs and employs her lesson plan. This study conducted a survey of lesson plan for elementary mathematics instruction with regard to teachers conception of purpose, content, method, frequency, use, and alternative of their lesson plans. The results of this study showed that many teachers focused on the achievement of lesson objectives and the maintenance of a planned lesson flow, considering more what they should do than what students need to do. Teachers also tended to construct a lesson plan mainly when they were expected to do on the basis of teachers manuals or their colleagues plans. They used their lesson plans mainly for the given lesson. On the basis of these results, this paper raised issues and suggested implications of constructing a lesson plan. 좋은 수업 구현을 위한 기초로써 수업 계획이 중요하지만, 이에 대한 연구는 상대적으로 부족하다. 수업의 설계자가 교사임을 감안하면, 실제 교사가 어떻게 지도안을 작성하고 활용하는지에 대한 연구의 필요성이 부각된다. 이에 본 연구에서는 초 등학교 교사를 대상으로 수학 수업을 위한 지도안의 필요성 및 목적, 내용, 작성 방법, 작성 빈도 및 시간, 활용, 대안적 지도안의 방향에 대해 설문 조사를 실시하고 그 결과를 분석하였다. 연구 결과, 많은 교사들이 주로 학습 목표 도달 및 수업 흐름 을 유지하기 위한 목적 아래, 학생들의 활동보다는 교사 활동에 초점을 두고, 교사용 지도서나 다른 교사의 지도안을 참고하여 필요한 경우에만 지도안을 작성하고 대개 해당 수업만을 위해 지도안을 활용하는 것으로 드러났다. 이와 같은 결과를 토대로 본 논문은 지도안 작성과 관련된 제반 쟁점들을 논의하고 수업 설계와 관련된 시사점을 제공하였다.

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.

한국, 일본, 홍콩, 핀란드, 싱가포르 초등 수학 교과서의 합동과 대칭에 대한 비교·분석

방정숙,김유경,Pang, JeongSuk,Kim, YuKyung 한국수학교육학회 2017 수학교육 Vol.56 No.3

This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach. Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures. This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.

싱가포르의 초등학교 수학 교과서 분석: 모델 메소드(model method)를 중심으로

방정숙,김은경,Pang, JeongSuk,Kim, EunKyung 한국수학교육학회 2017 初等 數學敎育 Vol.20 No.3

싱가포르의 초등학교 수학과 교육과정에서 문제 해결 능력의 향상을 위한 시각적 도구로써 모델 메소드가 적용된다. 그러나 모델 메소드가 실제 싱가포르의 초등학교 수학 교과서에 어떻게 적용되고 있는지 살펴본 연구는 많지 않다. 이에 본 연구에서는 싱가포르의 초등학교 수학과 교육과정에서 모델 메소드와 관련된 내용을 추출하고, 교과서에 적용된 모델 메소드의 특징을 분석하였다. 구체적으로 모델 메소드가 적용된 단원 및 차시의 특징, 수와 연산별 도입 및 적용의 특징을 추출하여 모델 메소드가 어떤 목적으로 어떻게 적용되고 있는지 살펴보았다. 분석 결과, 모델 메소드는 연산이나 문장제와 관련된 단원과 차시에 적용되고, 자연수, 분수, 소수로 적용 범위가 확대된다. 연산의 종류 측면에서 살펴보면 1~2학년에서는 덧셈과 뺄셈에만 적용하고, 3학년 이후에 곱셈과 나눗셈에 확대 적용하여 단계적이고 체계적으로 적용된 모습을 볼 수 있다. 또한 문제 해결 과정의 모든 단계에 명시적으로 적용하고 있다. 이러한 분석 결과를 바탕으로 문제의 구조를 탐색할 수 있는 하나의 모델을 교과서 전체에 일관되고 체계적으로 적용하는 것에 대한 시사점을 논의하였다. A model method has been known as the main characteristic of Singaporean elementary mathematics textbooks. However, little research has been conducted on how the model method is employed in the textbooks. In this study, we extracted contents related to the model method in the Singaporean elementary mathematics curriculum and then analyzed the characteristics of the model method applied to the textbooks. Specifically, this study investigated the units and lessons where the model method was employed, and explored how it was addressed for what purpose according to the numbers and operations. The results of this study showed that the model method was applied to the units and lessons related to operations and word problems, starting from whole numbers through fractions to decimals. The model method was systematically applied to addition, subtraction, multiplication, and division tailored by the grade levels. It was also explicitly applied to all stages of the problem solving process. Based on these results, this study described the implications of using a main model in the textbooks to demonstrate the structure of the given problem consistently and systematically.

한국, 중국, 일본, 미국 초등 수학과 교육과정에서 강조하는 수학적 과정 요소에 대한 분석

방정숙,이지영,이상미,박영은,김수경,최인영,선우진,Pang, JeongSuk,Lee, JiYoung,Lee, SangMi,Park, YoungEun,Kim, SuKyong,Choi, InYoung,SunWoo, Jin 대한수학교육학회 2015 학교수학 Vol.17 No.2

본 연구는 수학적 과정을 중심으로 한국, 중국, 일본, 미국의 초등 수학과 교육과정을 비교 분석한 것이다. 분석 결과 4개국에서 강조하는 수학적 과정을 모두 포괄할 수 있는 10가지의 요소 즉, 개념 원리 법칙 기능의 학습, 수학적 문제해결력, 수학적 추론 능력, 수학적 의사소통 능력, 수학적 표현 능력, 수학적 연결 능력, 수학적 창의력, 수학적 인성, 자기주도적 학습 능력, 긍정적 태도를 추출하였고, 이에 대한 교육과정별 공통점과 차이점을 분석하였다. 이를 토대로 우리나라의 수학과 교육과정 개발과 관련한 시사점을 제안한다. This study analyzed mathematical processes elaborated in the mathematics curricula of Korea, China, Japan, and the US. Ten mathematical processes were extracted: (a) learning of concepts, principles, laws, and skills; (b) problem solving; (c) reasoning; (d) communication; (e) representation; (f) connections; (g) creativity; (h) character-building; (i) self-directed learning; and (j) positive attitude toward mathematics. This study specified the meaning of such processes and their sub-domains, noticing similarities and differences among the curricula. On the basis of the results, this study includes suggestions for the development of next mathematics curriculum in Korea.