초등수학 교육과정 재구성에 대한 현장 실태 조사

김판수,서영서 부산교육대학교 미래교육원 2023 초등교육연구 Vol.38 No.3

본 연구는 초등학교 교사가 수학과 교육과정 재구성을 어떻게 인식하고 실천하고 있는지 그실태를 파악하는 데 목적을 두고 있다. 이를 위해서 A광역시 소속의 초등학교 일반 교사 100명, 그리고 교육대학교 학부에서 수학교육 심화과정을 이수하였거나 또는 수학교육 대학원 석사 과정이상의 학력을 가진 교사 54명을 추가로 포함시켜 총 154명을 연구대상으로 삼았다. 일반 교사집단, 수학교육 심화및전공 집단, 비심화및전공 집단으로 구분하여 일반 교사의 인식을 비롯하여세 집단간 차이와 특성을 파악하고자 하였다. 자료의 분석 결과는 다음과 같다. 첫째, 수학교육 및 수학과 교육과정에 대한 관심은 세 집단 모두 상당히 높은 것으로 나타났다. 또한 수학수업에서 수학과 교육과정을 참조하는 빈도도 모든 집단에서 높게 나타났다. 둘째, 수학 교과서에 있는 특화된 차시인 단원 도입, 단원 평가, 문제해결 차시에 대한 재구성은다양했다. 단원 도입 차시는 대다수가 내용을 생략하거나 압축하는 것으로 나타났으며, 지도서안내대로 수업하는 교사의 비율은 12%에 불과하였다. 그에 비해 단원 평가는 내용을 추가하는반응이 가장 높았고, 문제해결 차시는 지도서 안내대로 지도한다는 반응이 가장 높았다. 셋째, 수학과 교육과정 재구성의 필요성을 묻는 문항에서 ‘그렇다’와 ‘매우 그렇다’에 반응한 교사가 75%로 나타났다. 다수의 교사가 수학과 교육과정 재구성의 필요성을 인식하고 있으나수학과 교육과정을 재구성하는 빈도는 월 1∼2회가 가장 많았다. 넷째, 초등수학과 교육과정을 재구성하는 이유에 대해서 ‘수학 학습에 대한 흥미와 관심을 위해서’가 1순위로 나타났다. 그다음으로 ‘학습 내용의 과다/과소’, 그리고 ‘효과적이라 생각하는나만의 수업 방법 때문에’이라는 것을 선택하였다. 다섯째, 수학과 교육과정을 재구성하는 영역으로는 수와 연산, 도형, 자료와 가능성 순이며 나머지 영역에서는 소수가 반응하였다. 재구성에서 고려하는 가장 큰 요인은 ‘학습에 대한 흥미와관심’으로 영역과 무관하게 가장 높은 비율을 나타내었다. 그다음 요인은 영역별로 차이가 있었다. The purpose of this study is to understand how elementary school teachers recognize and practice mathematics curriculum reconstruction. To this end, 100 general elementary school teachers belonging to A Metropolitan City were selected. In addition, 54 additional teachers who completed an advanced math education course at the University of Education or with a master's degree or higher in mathematics education were selected to study a total of 154 people. It was intended to identify the differences and characteristics between the three groups, that is, general teacher groups, deepening and major groups, and non-deepening and major groups. The analysis results of the data are as follows. First, interest in math education and mathematics curriculum was found to be quite high in all three groups. It was also very high in the general teacher group referring to the curriculum in math classes. Second, the method of reconstructing the introduction of unit, unit evaluation, and problem-solving session, which are specialized in mathematics textbooks, was different. It was found that the majority of the introduction of the unit omitted or compressed the contents. The percentage of teachers teaching according to the guidance of the guide was 12%. On the other hand, the unit evaluation had the highest rate of adding content. On the other hand, the highest percentage of problem-solving was guided according to the guidebook. Third, 75% of teachers responded to ‘yes’ and ‘very yes’ to the question of the necessity of reorganizing the mathematics and curriculum, and the rest were not. In this study, the frequency of teachers reorganizing mathematics and curriculum was the most common once or twice a month. Fourth, the areas that reconstruct the mathematics and curriculum are in the order of numbers and calculations, shapes, data and possibilities, and a small number responded in the rest of the areas. As the first factor considered in the reconstruction, 'interest and interest in learning' showed the highest percentage of responses regardless of the area. Fifth, as for the main reason for reorganizing the elementary mathematics curriculum, ‘for interest and interest in math learning’ was the top priority. Next, ‘excess of learning content' and ‘because of my own teaching method that I think is effective' were selected.

스토리텔링 재구성 수업이 수학적 태도에 미치는 영향

박윤자 ( Yoon Ja Park ),김권욱 ( Kwon Wook Kim ) 부산대학교 과학교육연구소 2015 교사교육연구 Vol.54 No.3

본 연구는 스토리텔링 기반 수학 교과서 4학년 1학기 통계 단원의 스토리텔링을 재구성하여 지도한 후, 학생들의 수학적 태도(흥미도, 태도, 가치)에 미치는 영향을 알아보았다. 이를 위해 H초등학교 4학년 학생을 대상으로 실험반 29명, 비교반 29명을 선정하였다. 그결과 수학 흥미도와 태도 영역에서는 통계적으로 유의한 차이가 나타났지만, 가치 영역에서는 통계적으로 유의한 차이가 나지 않았다. 또한 수학 일기, 학생과 교사의 수업 소감 등에 나타난 정성 평가에서는 수학적태도에 긍정적인 변화를 보였다. 이 연구결과는 스토리 텔링 방식의 수학을 가르치는 선생님들에게 적절한 시사점을 주게 될 것이다. The purpose of this study was to analyze students’attitudes towards mathematics based on lesson plans using storytelling-reconstructed activities for the statistics unit in the 4th grade mathematics textbook. For this, we chose two classes among the 4th grade attending H elementary school, composed 29 students each, one for experiment the other for comparison. The results of this study are summarized as follows: The students’ interest and attitudes towards mathematics showed statistically significant improvement, however there was not any statistically significant difference in terms of mathematical value. The qualitative assessments in mathematical diary, the students’ and teachers’ comments on the class showed an affirmative change in the students’ attitudes towards mathematics. Through these results, this study offers teachers some suggestions to teach mathematics using storytelling- reconstructed activities.

초등교사의 수학과 교육과정 재구성 경험에 대한 연구

김판수,이영주 부산교육대학교 미래교육원 2023 초등교육연구 Vol.38 No.3

본 연구는 수학과 교육과정을 지속적으로 실현하는 초등학교 교사 4인의 교육과정 재구성의경험 사례를 분석하여, 수학과 교육과정 재구성을 통한 교사의 전문성 발달과 교육과정 재구성의방법을 알아보고, 전문성을 가진 교사 양성을 위한 시사점을 얻고자 하였다. 연구 참여 대상은현직 교사 중 수학과 교육과정을 잘 이해하고, 수학과 교육과정 재구성 경험이 풍부한 교사로 선정하였다. 자료 수집은 총 3차로 이루어졌으며, 4인의 사례 연구 결과는 다음과 같다. 첫째, 교과서대로의 수업은 ‘흥미 저하’와 ‘성취 기준 미달’로 귀결되어 교육과정 재구성의필요성을 인식하게 되었다. 그러나 교육과정 재구성을 실천하게 된 계기는 각자 달랐으나 교육과정재구성을 시도하게 된 원동력은 수학 교과의 내용 지식과 수학과 교육과정에 대한 문해력이 높았기때문으로 보인다. 둘째, 교육과정 재구성을 지속시키는 요인은 학생의 긍정적인 피드백과 교사 연구 활동이었다. 전문성을 가진 교사가 중심이 되어 교사 연구회를 운영하고 이를 통해 교사의 전문성을 성장시킨다는 것이 확인되었다. 셋째, 교육과정을 재구성하는 방법은 각기 달랐다. 각 교사가 지향하는 목표는 같으나 그 방식이나 접근에 대한 기본 철학에서는 차이를 나타내 보였고, 그것이 교과서를 재구성하는 방식을 결정하는데 기여한 것으로 보인다. 넷째, 교육과정 재구성의 어려움 조사에서 교사요인으로 시간 부족과 교육과정 재구성에 대한확신 등이 있었다. 그리고 학생들 간의 개인 편차와 개인적 특성과 같은 학생요인도 중요한 어려움으로 나타났으며, 이 요인은 기존 연구에서 발견되지 않았던 것이다. 다섯째, 교육과정 재구성을 활성화를 위해서는 교육환경 구축을 위한 전반적인 지원이 필요하다. 특히 교육과정 문해력을 위한 연수와 교육과정 재구성 사례의 공유와 보급이 요구된다. This study analyzed the experience of reorganizing the curriculum of four elementary school teachers who continuously realize the mathematics curriculum, found out how to develop teachers' professionalism and reorganize the curriculum through mathematics curriculum restructuring, and sought implications for fostering professional teachers. Participants in the study were selected as teachers who understood mathematics and curriculum well among incumbent teachers and had extensive experience in reorganizing mathematics and curriculum. The data collection was conducted in a total of three rounds, and the results of the case study of four people are as follows. First, the textbook-based class resulted in a 'decrease in interest' and 'underachievement standards', and the necessity of reorganizing the curriculum was recognized. However, although the reasons for implementing the curriculum reorganization were different, the driving force behind the attempt to reorganize the curriculum seems to be the high knowledge of the content of the math subject and the literacy in the mathematics and curriculum. Second, the factors that sustain the curriculum restructuring were positive feedback from students and teacher research activities. It was confirmed that teachers with expertise are the main ones who run teacher research groups and grow their professionalism through them. Third, the method of reorganizing the curriculum was different. Each teacher's goal was the same, but there was a difference in the basic philosophy of the method and approach, and it seems to have contributed to determining how to reconstruct textbooks. Fourth, in the survey of difficulties in reorganizing the curriculum, lack of time and confidence in reorganizing the curriculum were confirmed as teacher factors. In addition, student factors such as individual deviations and personal characteristics among students were also found to be important difficulties, which were not found in previous studies. Fifth, in order to revitalize the curriculum restructuring, overall support is needed to establish an educational environment. In particular, training for curriculum literacy and sharing and dissemination of cases of curriculum restructuring are required.

Mathematical model and vector control of a six-phase linear induction motor with the dynamic end effect

Han, Yi,Nie, Ziling,Xu, Jin,Zhu, Junjie,Sun, Jun The Korean Institute of Power Electronics 2020 JOURNAL OF POWER ELECTRONICS Vol.20 No.3

This study investigates a short primary double-side six-phase linear induction motor (LIM) operating in non-periodic transient conditions. The main purpose is to solve the problems arising from the dynamic end effect. The equivalent circuit method is used for intensively studying the transient time-varying law of eddy current and excitation inductance, and the finite element method is adopted for verification. The calculation of eddy current loss leads to an expression of secondary equivalent resistance. Then, a mathematical model is established for the six-phase LIM involving the dynamic end effect. Furthermore, the matrix reconstruction method is adopted for the coupling of windings. Based on the time-varying characteristics of the model, an improved vector control method that can update the velocity-related correction coefficients through on-line calculation is proposed. During the transient process, the slip frequency and the torque current are modified in real-time to achieve the maximum output thrust of the motor. This approach can compensate for the thrust drop caused by the dynamic end effect, thereby improving the control precision. Simulations and experiments show that the related theory and the proposed control method are feasible and effective.

Mathematical Modeling of Acousto-Optical Tomography and its Level Set Simulations

남혜원,David C. Dobson 한국물리학회 2012 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.61 No.3

Acousto-Optical Tomography is modeled by a linear integral equation and an inverse problem involving a diffusion equation in n spatial dimensions, <I>n</I> = 2, 3. Based on measured data, the optical absorption coefficient <I>μ </I>is reconstructed inside of a given domain. We make a two-step mathematical model. First, we solve a linear integral equation. Assuming the energy fluence rate has been recovered from the previous equation, the absorption coefficient <I>μ</I> is then reconstructed by solving an inverse problem. Numerical experiments are presented for the case <I>n</I> = 2. We used the level set method for the numerical experiments. At the end, advantages and disadvantages of those two methods are mentioned.

A mathematical model for the 3d location estimation of 2D echocardiography data

Ahn, Chi Young,Yun, Sangwoon Elsevier 2019 APPLIED MATHEMATICS LETTERS Vol.88 No.-

<P><B>Abstract</B></P> <P>The recovery of 3D left ventricle(LV) shape using 2D echocardiography is very attractable topic in the field of ultrasound imaging. In this paper, we propose a mathematical model to determine the 3D position of LV contours extracted from multiple 2D echocardiography images. We formulate the proposed model as a non-convex constrained minimization problem. To solve it, we propose a proximal alternating minimization algorithm with a solver <I>OPTI</I> for quadratically constrained quadratic program. For validating the proposed model, numerical experiments are performed with real ultrasound data. The experimental results show that the proposed model is promising and available for real echocardiography data.</P>

A study on the 3D position estimation of ventricular borders extracted from 2D echocardiography data

Ahn, Chi Young,Yun, Sangwoon Elsevier 2018 COMPUTERS & MATHEMATICS WITH APPLICATIONS - Vol.75 No.4

<P><B>Abstract</B></P> <P>We study on the reconstruction of 3D left ventricle(LV) using only 2D echocardiography data and information on apical long-axis views. Especially, this paper focuses on determining the 3D position of LV contours extracted from 2D echocardiography images. First we mathematically model the relationship between LV contours on the apical views and their corresponding 3D positions. The relationship is expressed as a linear equation in which the right-hand side is the measured data consisting of all the LV contour points on each view and the coefficient matrix is an unknown matrix that transforms the unknown 3D positions into contour points on their related apical view, with distance and orthogonality conditions on the coefficient matrix and the 3D positions. Next we consider a non-convex constrained minimization problem to determine the coefficient matrix and the 3D positions. To solve this minimization problem, we adopt two block coordinate descent method with a solver in <I>OPTI</I> for quadratically constrained quadratic program. For validating the proposed method, some numerical experiments are performed with synthetic data. The experimental results show that the proposed model is promising and available for real echocardiographydata.</P>

묵사집산법(黙思集算法)에 수록된 퇴타개적문(堆垜開積門)의 현대적 재구성 및 수학교육적 활용 방안

양성현 한국수학사학회 2020 Journal for history of mathematics Vol.33 No.1

Under 2009 Revised Mathematics Curriculum and 2015 Revised Mathematics Curriculum, mathematics teachers can help students inductively express real life problems related to sequences but have difficulties in dealing with problems asking the general terms of the sequences defined inductively due to `Guidelines for Teaching and Learning'. Because most of textbooks mainly deal with the simple calculation for the sums of sequences, students tend to follow them rather than developing their inductive and deductive reasoning through finding patterns in the sequences. In this study, we reconstruct 8 problems to find the sums of sequences in MukSaJipSanBup which is known as one of the oldest mathematics book of Chosun Dynasty, using the terminology and symbols of the current curriculum. Such kind of problems can be given in textbooks and used for teaching and learning. Using problems in mathematical books of Chosun Dynasty with suitable modifications for teaching and learning is a good method which not only help students feel the usefulness of mathematics but also learn the cultural value of our traditional mathematics and have the pride for it. 2009 개정 수학과 교육과정과 2015 개정 수학과 교육과정에서는 교수 · 학습상의 유의점에서 수열과관련된 실생활 문제를 귀납적으로 표현할 수는 있지만 귀납적으로 정의된 수열의 일반항을 구하는문제를 다루지 않도록 명시하고 있다. 이로 인하여 대부분의 교과서들이 수열을 통해 다양한 규칙성을찾아 귀납적 · 연역적 추론 능력을 기르기 보다는 대수적 계산 능력에 치중토록 구성되었다. 따라서‘수열의 합’에서 ‘ Σ 의 뜻과 성질’을 학습한 후 ‘여러 가지 수열의 합’에서 ‘자연수의 거듭제곱의 합’ 을 학습할 때, 실생활에 대한 수열의 실용적 측면이 상당히 약화되었다. 이에 본 연구에서는 현존하는 조선 산학서 중 가장 오래된 것으로 여겨지는 묵사집산법(黙思集算法)에 수록된 퇴타개적문(堆垜開積門) 10문항 중 ‘수열의 합’과 관련된 8문항을 교육과정의 용어와 기호를 사용하여 교과서와교수학습 상황에서 활용할 수 있도록 현대적으로 재구성하였다. 실용적인 측면이 강했던 조선시대산학서의 사례들을 교수학습 과정에서 소개하고 활용하는 것은 학생들로 하여금 수학의 실용성을느끼게 해줄 수 있을 뿐만 아니라 우리 전통 수학에 대한 문화적 가치와 자긍심을 일깨워줄 수 있다.

Research on Novel 3D Modelling Methodology for Animation Design based on Computer Graphics Theory and Mathematical Analysis with Kinect Implementation

Honglin Huang 보안공학연구지원센터 2015 International Journal of Multimedia and Ubiquitous Vol.10 No.10

At present, the 3D object model technique is being applied in the simulation, virtual reality, 3D film industry and culture protection, and many other fields which can be widely applied. However, the existing 3D reconstruction technology is based on the complex and often expensive sensors. Therefore, we conduct research on computer graphics theory and mathematical modelling based 3D reconstruction methodology with Kinect. We firstly introduce the basic concepts and application of Kinect system which serves as the preliminary of our research. Then, we conduct mathematical modelling for our proposed system with theoretical analysis. Later, experiment and numerical simulation is conducted for verifying the robustness and effectiveness of our proposed approach. The visualized and numerical simulation result indicates that our method outperforms and holds better accuracy compared with other popular adopted algorithms. In the future, we plan to combine more optimization techniques to polish and modify our approach.

비와 비율 지도에 대한 연구 -교과서 재구성을 중심으로-

김수현,나귀수 대한수학교육학회 2008 수학교육학연구 Vol.18 No.3

In this research, we reconstructed the textbook on the concept of rate and ratio, which is based on the review on the previous researches and the analysis on the elementary textbook of the 7th mathematics curriculum. We conducted the teaching experiment using the reconstructed textbook, which is to identify the students' conception of rate and ratio and the appropriateness and limit of the reconstructed textbook. As the results of this study, we identify that the changed sequence of instruction (that is, ratio → percent and value of rate→ rate) was very proper to help students understand the concept of rate and ratio. The relative comparison and absolute comparison and the additive thinking and multiplicative thinking included in the reconstructed textbook were identified very helpful to students' understanding. Meanwhile some contexts given in the reconstructed textbook were identified to cause the students' cognitive confusions. 본 연구에서는 비와 비율의 교수・학습과 관련된 선행 연구를 고찰하고, 현행 초등학교 교과서의 문제점을 분석하였다. 선행 연구 고찰과 현행 교과서의 문제점 분석을 토대로 교과서를 새롭게 재구성하였으며, 재구성된 교과서를 활용하여 실제 교수・학습을 실시하고 그 과정에서 나타난 재구성 교과서의 적절성과 한계, 학생들의 비와 비율 개념화 과정 등을 확인하였다. 현행 교과서와 다르게, 본 연구의 재구성 교과서에서는 비율, 백분율과 비의 값, 비로 지도 순서를 바꾸었으며, 이는 적절한 것으로 확인되었다. 또한 재구성 교과서에서는 상대 비교와 절대 비교, 가법적 사고와 승법적 사고 등을 다루었으며, 이는 학생들의 비와 비율 개념 이해에 도움을 주는 것으로 확인되었다. 한편, 재구성 교과서에 제시된 다양한 맥락들 중에서 일부 맥락은 학생들의 인지적 혼란을 야기하는 것으로 확인되었다.