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이봉주,이세형,Lee, Bongju,Lee, Se Hyung The Korean School Mathematics Society 2021 韓國學校數學會論文集 Vol.24 No.1
이 연구에서는 학습자가 수학 텍스트를 반복하여 읽을 때 나타나는 수학 학습 과정이 어떻게 변하는지를 조사하였다. 또한 수학 학습 방법으로써 반복 읽기의 효과를 점검하고 보다 효율적인 반복 읽기 교수·학습 전략에 대한 시사점을 모색하였다. 반복 읽기 수학 학습에는 국립대학교 수학교육과에 재학 중인 예비 수학교사 8명이 참가하였다. 예비 수학교사는 각각 4개의 그룹으로 구성되어 그룹에 따라 서로 다른 4개의 주기로 총 3회 반복 읽기를 시행하였다. 수학 학습 자료 읽기 과정에서 나타나는 예비 수학교사의 시선의 움직임을 추적하고 심박수를 측정하였다. 수집한 자료를 회차별 총 읽기 시간, 슬라이드별 총 읽기 시간, 각 회차와 슬라이드별 총 읽기 시간의 변화 추세, 슬라이드 읽기 순서, 회차별 심박수 변화 추세 등의 다섯 가지 측면에서 분석하였다. 첫 번째 읽기에서는 참가자의 대부분이 비슷한 양상을 보였으나, 두 번째와 세 번째 읽기에서는 개별 학습자에 따른 읽기 패턴의 변화가 보다 다양하게 드러났다. 또한, 첫 번째 읽기에서 반복 주기와 무관하게 가장 많은 시간이 소요되었고, 이후 반복적 읽기 시간에서는 개인별로 차이가 나타났다. 연구 결과에서 도출한 가장 중요한 결론은 반복 읽기를 통한 자기 주도적 수학 학습은 주기와 관계없이 효과적이라는 것이다. 추가적으로 반복 읽기 교수·학습 전략의 효율성을 증진시키기 위한 네 가지 전략을 제안하였다. This study aimed to investigate how the learners' mathematics learning processes change with repeatedly reading mathematical text. As a way to teach and learn mathematics, we also wanted to examine the effect of repeated reading and to explore the implications for a more efficient teaching and learning strategy. To help us with this study, we mainly used eye tracking and heart rate (HR) measurement. There were four cycles in a cycle of repeated reading, and the number of repeated readings for all cycles was fixed to three times. Eight prospective mathematics teachers in the Department of Mathematics Education of a National University in South Korea participated. Data were analyzed in five aspects: (1) the total reading time per round, the total reading time per slide; (2) the change trends of total reading time per round and slide; (3) the order of slides read; (4) the change trends of HR per round. We found that most participants read in a similar pattern in the first reading, but the second and third reading patterns appeared more diverse for each learner. Also, the first reading required the most time regardless of the repeat cycle, and the time it took to repeatedly read afterward varied depending on the individual. Based on the findings of this study, the most primary conclusion is that self-directed mathematics learning by using repeated reading is effective regardless of cycle. In addition, we suggested four strategies to improve the efficiency of this teaching and learning method.
교수 질 프로필(IQP)에 기반한 중학교 2학년 수학과 교수의 질 분석
이봉주,한인기,서보억,Lee, Bongju,Han, Inki,Suh, Boeuk 영남수학회 2018 East Asian mathematical journal Vol.34 No.2
This study was conducted as a part of the project to evaluate the quality of mathematics instruction in the national curriculum system. The purpose of this study is to measure the consistency between teaching goals of mathematics curriculum, contents presentation of textbooks, and testing including adequacy of each element in mathematics instruction for 8th grade. To do this, we used MIQP (instructional quality profile for Mathematics) developed basing on the instructional quality profile (IQP) in the previous research of the project. First, the quality of textbooks' content presentation for 8th grade was found that the desirable levels in number and operation area and geometric area was relatively less compared to other areas, but it was generally good. Second, it was found that the quality of mathematics testing for 8th grade was good in terms of consistency with the curriculum's teaching goals, consistency with the content presentation of textbooks, and adequacy of testing. However, regional differences in the quality of testing showed that there were some deficiencies in regions outside the metropolitan.
Sfard의 구상화(Reification) 이론에 근거한 중·고등학생의 이차방정식 근의 공식 개념 형성 수준 분석
장현석 ( Chang Hyun Suk ),이봉주 ( Lee Bongju ) 한국수학교육학회 2018 수학교육 Vol.57 No.3
In this paper, we applied Sfard's reification theory to analyze the secondary students’ level of conceptualization with regard to the formula of quadratic equation. Through the generation and development of mathematical concepts from a historical perspective, Sfard classified the formulation process into three stages of interiorization, condensation, and reification, and proposed levels of formulation. Based on this theory, we constructed a test tool reflecting the reversibility of the nature of manipulation of Piaget’s theory as a criterion of content judgement in order to grasp students’ conceptualization level of the formula of quadratic equation. By applying this tool, we analyzed the conceptualization level of the formula of quadratic equation of the 9<sup>th</sup> and 10<sup>th</sup> graders. The main results are as follows. First, approximately 45% of 9<sup>th</sup> graders can not memorize the formula of quadratic equation, or even if they memorize, they do not have the ability of accurate calculation to apply for it. Second, high school curriculum requires for students to use the formula of the quadratic equation, but about 60% of 10<sup>th</sup> graders have not reached at the level of reification that they can use the formula of quadratic equation. Third, as a result of imaginarily correcting the error of the previous concept, there was a change in the levels of 9<sup>th</sup> graders, and there was no change in 10<sup>th</sup> graders.
수학 성취도가 낮은 학생의 보충 지도 과정에서 블렌디드 e-러닝과 개별화 교수체제의 효과 비교 분석
송다겸 ( Song Dagyeom ),이봉주 ( Lee Bongju ) 한국수학교육학회 2017 수학교육 Vol.56 No.2
The purpose of this study is to compare and analyze the impact on low-achievers in mathematics who studied mathematics using Blended e-learning and Personalized system of instruction after school. Blended e-learning is defined as the management of e-learning using the e-study run by the education office in local. Personalized system of instruction was proceeded as follows; (1) all students are given a syllabicated learning task and a study guide, (2) students study the material autonomously according to their own pace for a certain period of time, (3) the teacher strengthens the students` motivation through grading and feedback after students study a subject and solve the evaluation problem. The learning materials for Personalized system of instruction are re-edited the offline education contents provided by the blended e-learning to the level of students. The 118 7th grade students from the D middle school participated in this study. The results were verified by achievement tests before and after the study, as well as survey regarding their attitude toward mathematics. The results are as follows. First, Blended e-learning has more positive impacts than Personalized system of instruction in mathematics achievement. Second, there was no difference in mathematics achievement according to their self-directed learning between Blended e-learning and Personalized system of instruction. Third, both types utilizing Blended e-learning and Personalized system of instruction have positive effect on attitude toward mathematics, and there is not their difference between two methods of teaching and learning mathematics.
수학교사의 요구를 반영한 창의성과 인성 교육 전문성 신장 내용요소 탐색1)
김현아 ( Kim Hyun-ah ),이봉주 ( Lee Bongju ) 한국수학교육학회 2016 수학교육 Vol.55 No.4
This study was to explore the factors that mathematics teachers actually need to improve their students` creativity and character to pursue education in the direction of the revised curriculum. We first temporarily extracted the elements to reinforce mathematics teachers` professionalism for creativity and character education through literature review, and then conducted the modified delphi technique and interview by targeting secondary school mathematics teachers. Based on the discussion of previous studies, we divided into five areas for mathematics teachers` professional development of creativity and character education: 1. understanding of creativity and character education, 2. creating an environment, 3. understanding curriculum for creativity and character education, 4. instructional design and apply for creativity and character education, 5. evaluating for creativity and character education. Actually content elements highly required by mathematics teachers were reset 17 items. The results of this study are expected to be used as the basis for teachers` professional development of creativity and character education in mathematics education.
고밀도 평판형 유도결합 BCl<sub>3</sub>/SF<sub>6</sub> 플라즈마를 이용한 GaAs/AlGaAs와 InGaP 반도체의 선택적 식각에 관한 연구
유승열,류현우,임완태,이제원,조관식,전민현,송한정,이봉주,고종수,고정상,Yoo Seungryul,Ryu Hyunwoo,Lim Wantae,Lee Jewon,Cho Guan Sik,Jeon Minhyon,Song Hanjung,Lee BongJu,Ko Jong Soo,Go Jeung Sang,Pearton S. J. 한국재료학회 2005 한국재료학회지 Vol.15 No.3
We investigated selective dry etching of GaAs over AlGaAs and InGaP in high density planar inductively coupled $BCl_3/SF_6$ plasmas. The process parameters were ICP source power (0-500 W), RE chuck power (0-30W) and gas composition $(60-100\%\;BCl_3\;in\;BCl_3/SF_6)$. The process results were characterized in terms of etch rate, selectivities of GaAs over AlGaAs and InGaP, surface morphology, surface roughness and residues after etching. $BCl_3/SF_6$ selective etching of GaAs showed quite good results in this study. Selectivities of GaAs $(GaAs:AlGaAs\~36:1,\;GaAs:InGaP\~45:1)$ were superior at $18BCl_3/2SF_6$, 20 W RF chuck power, 300 W ICP source power and 7.5 mTorr. Addition of $(5-15\%)SF_6\;to\;BCl_3$ produced relatively high selectivities of GaAs over AlGaAs and InGaP during etching due to decrease of etch rates of AlGaAs and InGaP (boiling points of etch products: $AlF_3\~1300^{\circ}C,\;InF_3>1200^{\circ}C$ at atmosphere) at the condition. SEM and AFM data showed slightly sloped sidewall and somewhat rough surface$(RMS\~9nm)$. XPS study on the surface of processed GaAs proved a very clean surface after dry etching. It shows that planar inductively coupled $BCl_3/SF_6$ plasmas could be a good candidate for selective dry etching of GaAs over AlGaAs and InGaP.