중학교 수학에서 함수 지도에 관한 연구

노영순(Ro Young Soon) 공주대학교 교육연구소 2009 교육연구 Vol.23 No.-

7차 교육과정에서 함수의 개념을 도입할 때 비례관계로 도입하여 지도하도록 하고 있다. 그러나 현직 교사 중에서 함수의 개념을 대응관계로 도입하고 있는 교사들이 있다. 그렇다면 ‘왜 그들은 교육과정을 따르지 않고 여전히 대응으로 지도하고 있는가? 또, 학생들은 비례관계로 함수의 개념을 도입했을 때 함수의 개념을 잘 이해하는가?’를 조사하고, 함수 개념을 도입할 때 학생들에게 어느 방법이 어떠한 면에서 유익한가? 이 질문에 대하여 학교 현장의 주인공인 교사와 학생을 대상으로 조사ㆍ분석하였다. In the 7th national curriculum, the proportion-related explanation is recommended for math teachers when introducing the concept of function in class. However, there are still a considerable number of current teachers who are dealing it with the concept of correspondence-related. Why do they stick to the concept of correspondence-related instead of following the guided 7th national curriculum? And do the students understand the concept exactly when they are taught with the proportion-related explanation? According to the survey of math teachers, introducing the concept of correspondence-related is more preferred to the proportion-related one that is suggested in the 7th national curriculum in the instruction of the function concept. And another survey that helps estimate the degree of students’ understanding of the function concept for third graders of middle school shows that most students understood it as proportion, formula, a term of algebra or a linear [quadratic, cubic] equation. Furthermore, a large number of students didn’t provide any answers and this means a majority of them don’t have clear idea of the function concept. If so, when introducing the concept of function, which one is more efficient for students to get a full understanding of it? In an attempt to get an answer it, a survey of the math teachers and students was conducted and the result of the investigations and analysis is as follows.

소규모 중학교에서 수준별 이동수업과 소집단 협동학습간의 학업성취도 비교 연구

노영순(Ro Young Soon),도기섭(Do Ki Seop) 공주대학교 교육연구소 2011 교육연구 Vol.25 No.-

본 연구는 소규모 중학교의 수준별 이동수업과 소집단 협동학습간의 학업성취도를 비교ㆍ분석하여 이들 소규모 학교의 입장에서 어떤 수업방법이 더 효과적인가를 알아보고 학업성취도 향상을 위해 적합한 교수ㆍ학습방법에 대한 몇 가지 개선 방안을 제시하고자 한다. 이를 위하여 그동안의 선행연구를 조사 연구하고 수준별 이동수업을 운영하기 위한 기초 자료로 2010년도 1학기 중간고사 수학과 지필평가 성적을 분석하였다. 또한 소집단 협동학습을 위한 학급편성을 위하여 지필평가 성적을 바탕으로 최상위, 상위, 중위, 하위수준의 4등급으로 학생들을 4~5명씩 8개 조로 나누어 1학급 4개 조로 2학급을 구성하였다. 특히 연구 대상학교가 소규모이므로 수학교사가 1명뿐이므로 수준별 이동수업을 위해 보조교사 1명을 채용하여 모두 2명의 수학교사가 수준별 이동수업을 담당하여 본 연구를 수행하였다. 이를 바탕으로 수준별 이동수업과 소규모 협동학습이 상위집단(심화반)과 하위집단(기초반)의 학업성취도에 미치는 영향을 조사였다. 연구의 결과 현실적으로 소규모 학교에서 수학과 수준별 이동수업은 학생들의 수준에 따라 학급을 편성하기가 어렵기 때문에 학생들의 성적 분포에서 양극화와 중간수준의 학생들이 하향 편중될 가능성이 크다고 볼 수 있다. 따라서 소규모 학교에서의 수학 교과 지도는 소집단 협동학습에 의한 지도가 더 적절하고 효과적이라는 제안을 하였다. The purpose of this thesis is to suggest the suitable direction of teaching and learning to improve academic achievement in the small-sized school through the comparison and analysis of a level-centered class and small cooperative learning. In order to accomplish this purpose, it will be selected through two questionaries. 1. Is there a meaningful discrepancy in academic achievement between the level-centered class and small cooperative learning in a discretionary level-based class for high-level students? 2. Is there a meaningful discrepancy in academic achievement between the level-centered class and small cooperative learning in a discretionary level-based class for low-level students? In order to solve these questionaries, academic achievement is compared after testing the high-level students and low-level students in C Middle School of Pyeongtaek, Gyeonggi-do. Each are tested for thirty-two hours over eight weeks. As a result, there is the meaningful discrepancy in academic achievement for both high-level students and low-level students, that shows that small cooperative learning classes have more of a positive effect than the level-centered class in progressing of academic achievement. The results of this study are discussed below. Firstly, it is difficult to divide the diverse classes in consideration of the students’ ability in the small-sized school. So if the level-centered class continues the same as the present, the middle-level students’ score will be concentrated so much in the low that the polarization of the mathematics evaluation score range will be exacerbated. This result demands that teaching and learning strategies be developed to emphasize the needs of our middle school students. Secondly, new teaching materials must be constructed to make the students feel a sense of achievement in attaining their goal which is a proper task for the high-level, middle-level and low-level students rather than inducing the competence of the small cooperative learning among each class. Thirdly, it is necessary to manage a special program for treating a loss of studying as well as considering a suitable role for the students who have no change in achievement because of the chronic heavy loss of studying. In the seventh revised curriculum, it is widely recommended for every school to use a level-centered mathematics class, but there is another choice for flexible selection in school by applying various teaching and learning methods to maximize the study effects considering the school’s circumstances and situations in the seventh revised curriculum. So in the school it is necessary to search constantly for the flexible management and make constant efforts to develop and apply an appropriate class model that is applicable to the school regarding several conditions for both school and students.

數學科 學習不振兒에 대한 段階形 課題學習의 開發 및 適用에 관한 硏究

노영순,김종오 공주대학교 과학교육연구소 2001 과학교육연구 Vol.32 No.1

The underachieved students who don't reach normal step come to lose their interests in mathematics. Also the increasing loss of pre-study cause learning barrier. In order to help the underachieved to increase self-study ability and supplement basic ability for normal class, this study has presented them with step-type assignment materials and helped them to team more actively. So I have examined the effects of achievement, interests, and attitude. I have also tried this study for step-type leveled curriculum of high school beginning in the year of 2002. The conclusions can be got as follows. 1.So as to minimize the loss of pre-study and increase loaming ability caused by personal difference, when developed not graded step-type assignment materials have been applied to the underachieved, meaningful differences have been shown in achievement owing to their improved solving ability. 2.The materials have helped them to team deficient pals voluntarily. They also have been efficient in increasing attitude. However, little meaningful differences have been shown in their interests of mathematics. On the bases of problems and conclusions shown in the proceedings of this study for the underachieved in mathematics, the following suggestion can be got out. 1.After considering the leveling and systematics of mathematics, the contents for the step learning should be reconstructed. Also both the class strategy fitting to cognitive structure and type of the underachieved, and proper opportunity of not-graded assignment study should also be presented. 2.Organizing assignment class should be classified from lower to higher conception gradually. Furthermore abstract and conceptional class should be avoided. Instead the basic law and principle of simple numbers and formula, and generalizing process should be introduced. So problem difficulty should be lowered so that students can study voluntarily. 3.With these things of introducing many lower intuitions and examples, checking their performance, reinforcing, rewarding, and consulting activities, we must teach students so that they have affirmative attitude and confidence in mathematics.

중등학교 수학 교사들의 정보화 기기 활용 실태 및 학습 효과에 대한 의식 조사

노영순 공주대학교 사범대학 과학교육연구소 1999 과학교육연구 Vol.30 No.1

본 연구의 목적은 중등학교 수학과 학습에서 교육정보화를 실현하기 위한 수학교사들의 정보화기기 활용 실태에 대하여 조사하고 이에 따른 학습 효과에 대하여 현장 수학 교사들이 생각하고 있는 의식을 조사 분석하고 그에 대한 문제점을 찾고 그 개선방안을 제시하는 것이다. The purpose of this paper is to investigate (in order to realize the educational information) the actual condition of application of information machineries for learning of mathematics by mathematics teachers in a secondary school. And we find out the point at issue about application of this machineries and presents reform measures after we research and analyze school mathematics teachers' consciousness for learning effect based on this investigation.

Fuzzy Difuntional Relation의 특성화

노영순,이덕호,성열욱 공주대학교 사범대학 과학교육연구소 2000 과학교육연구 Vol.31 No.1

본 눈문에서는 fuzzy difunctional relation 동치조건들을 소개하였고 이를 이용하여 fuzzy difunctional relation과 관련된 일부 결과를 제시하였으며 또한 반군에서의 퍼지합동관계를 α-cut로 특성화 하였다. In this paper, we shall introduce equivalent conditions of the fuzzy difunctional relation, give some results in connection with fuzzy difunctional relations and characterize the fuzzy congruence relation on a semigroup in terms of its α-cut. Also, closed relationship between fuzzy difunctional relations and fuzzy congruence relations will be revealed.

정칙 개 주기성에 관하여

노영순,이덕호,성열욱 공주대학교 사범대학 과학교육연구소 1999 과학교육연구 Vol.30 No.1

변환군에서 정규약개주기성에 대한 몇가지 성질을 조사하고 본 논문의 정리 3과 4를 증명하기 위하여 보조정리 1과 2를 보이고, 공간 X가 콤팩트이고 T가 점열정규약개주기이며 S가 T의 모든 syndetic invariant 부분군에 대하여 약개주기 일 때 T는 equicontinuous가 됨을 보였다.

수행평가방법 중 서술형 평가를 적용한 학습이 학력신장에 미치는 영향 : 고등학교 공통수학을 중심으로

노영순,류춘식 한국학교수학회 2001 韓國學校數學會論文集 Vol.4 No.1

This research is about how the adapted learning of descriptive assessment problems influence on the extension of the ability of the students. As a result, adapted learning of descriptive assessment problems totally led to positive effect, and according to the analyses of behavioral objectives divided into knowledge, comprehension and problem solving, they had more effect on the ability of students' problem solving. Learning attitude of the students were changed into self-centered learning attitude and interest on the subject of mathematics were highly increased since the research had started. If we adapt this research to the learning of mathematics after we develop various problems that can develop creativity, I'm sure that it will be a effective way for both extension of the ability and problem solving ability of the students.

수준별 과제 학습지의 구안과 학습자 자신의 선택에 의한 자기 주도적 학습이 수학과 학업성취에 미치는 영향

노영순,윤희송 한국수학교육학회 2000 수학교육 Vol.39 No.1

국소약개주기성에 관하여

盧永淳 공주대학교 사범대학 과학교육연구소 1993 과학교육연구 Vol.24 No.1

변환군(X,T)에서 위상공간 X의 점 χ에 대하여 만일 U를 χ의 한 근방이라면 xA⊂U를 만족하는 T의 좌 신데틱 부분집합 A가 존재할 때 T를 x애서의 개주기라 한다. 본 논문에서는 개주기성 보다 조건이 강한 국소약개주기성에 관한 몇 가지 성질을 조사하고 다음의 결과를 얻는다. X가 국소 콤팩트 T₂-공간 일 때 다음 (1),(2),(3)은 상호 동치이다. (1) T가 국소약개주기이다. (2) T가 이산국소약개주기이다. (3) T에서의 모든 orbit-closure들의 모임은 X의 star-closed decomposition이다.

[0.Ω]에 의한 位相空間들의 상호관계에 대하여

盧永淳 공주대학교 사범대학 과학교육연구소 1982 과학교육연구 Vol.14 No.1

We see that the toplogical space has an implication with each other, In this paper, we define the ordinal space, [0,Ω],[0,Ω[, and using the special property of this space, we study the relations of each space. In particular, adding the simple spaces, we note this relations by the diagram (of the main classes of toplogical spaces discussed in this paper.) in order to see more easily. 1. Preliminary Definition 1: Let λ be any ordinal number and in [0,λ] use the topology generated by all sets of form {x/x>α} and {x/x<β}. We call this topological space the ordinal space [0,λ]. This space have the sets ]α,β]={x/x>α}λ{x/x<β+1} as a basis for the topology. And we know that [α,β[ is open if and only if α=0 or if α has an immediate predecessor. Let ??, be the first ordinal number larger than ??. When treated as an ordinal number, ?? is denoted by Ωand called the first uncountable ordinal. In stead of λ we use Ω and then get the ordinal space [0,Ω]. The ordinal space[0,Ω[ is subspace of the ordinal space [0,Ω].