중고등학생의 대수적 추론 문제해결능력과 문제해결과정 분석

김성경,현은정,김지연,Kim, Seong Kyeong,Hyun, Eun Jung,Kim, Ji Yeon 영남수학회 2015 East Asian mathematical journal Vol.31 No.2

The purpose of this study is to suggest how to go about teaching and learning secondary school algebra by analyzing problem-solving ability and problem-solving process through algebraic reasoning. In doing this, 393 students' data were thoroughly analyzed after setting up the exam questions and analytic standards. As with the test conducted with technical school students, the students scored low achievement in the algebraic reasoning test and even worse the majority tried to answer the questions by substituting arbitrary numbers. The students with high problem-solving abilities tended to utilize conceptual strategies as well as procedural strategies, whereas those with low problem-solving abilities were more keen on utilizing procedural strategies. All the subject groups mentioned above frequently utilized equations in solving the questions, and when that utilization failed they were left with the unanswered questions. When solving algebraic reasoning questions, students need to be guided to utilize both strategies based on the questions.

함수 영역 문제해결 협력학습 과정에서 문제 유형에 따른 중학생의 인지부하 분석

김성경 ( Kim Seong-kyeong ),김지연 ( Kim Ji Youn ),이선지 ( Lee Sun Ji ),이봉주 ( Lee Bongju ) 한국수학교육학회 2018 수학교육 Vol.57 No.2

From the assumption that an individual’s working memory capacity is limited, the cognitive load theory is concerned with providing adequate instructional design so as to avoid overloading the learner’s working memory. Based on the cognitive load theory, this study aimed to provide implications for effective problem-based collaborative teaching and learning design by analyzing the level of middle school students’ cognitive load which is perceived according to the problem types(short answer type, narrative type, project) in the process of collaborative problem solving in middle school function part. To do this, this study analyzed whether there is a relevant difference in the level of cognitive load for the problem type according to the math achievement level and gender in the process of cooperative problem solving. As a result, there was a relevant difference in the task burden and task difficulty perceived according to the types of problems in both first and second graders in middle schools students. and there was no significant difference in the cognitive effort. In addition, the efficacy of task performance differed between first and second graders. The significance of this study is as follows: in the process of collaborative problem solving learning, which is most frequently used in school classrooms, it examined students' cognitive load according to problem types in various aspects of grade, achievement level, and gender.

고등학생들은 왜 수학을 공부하는가?

김성경 ( Seong-kyeong Kim ),우연경 ( Yeon-kyoung Woo ),최영인 ( Young-in Choi ) 경북대학교 중등교육연구소 2020 중등교육연구 Vol.68 No.4

본 연구에서는 수학과 교육과정 실행에서 중요한 참여 주체인 학습자의 응답을 통해 학습자들이 인식하는 수학 학습의 목적을 확인하고자 하였다. 고등학교 3학년 학생 229명의 개방형 문항에 대한 617개의 응답(1-3순위)을 분석하였고, 수학 성취 수준에 따른 응답률 차이도 확인하였다. 분석 결과, 고등학생들이 수학을 공부하는 이유는 9개의 대범주와 15개의 하위 범주로 구분되었다. 가장 많이 제시된 응답은 ‘미래를 위한 유용성’으로 나타났다. 다음으로는 ‘외부의 압력’, ‘일상을 위한 유용성’, ‘흥미’와 ‘사고력’이 뒤를 이어 높은 응답률을 보였다. 상위 성취집단과 하위 성취집단 간 수학 학습 목적 인식을 비교한 결과에서도 차이가 나타나 해당 결과의 함의를 논의하였다. 본 연구를 통해 수학과 교육과정의 실행 측면에서 학습자들이 교과 목적을 얼마나 인식하고 있는지를 확인하였고, 수학교육 목적의 항존적 부분과 가변적 부분에 대한 추가적 논의가 필요함을 제안하였다. This study attempted to confirm the purpose of mathematics education recognized by learners. We classified the purpose category by analyzing 617 responses from 229 high school students. Furthermore, we analyzed whether the purpose of mathematics education appears differently depending on the level of mathematics achievement. The results showed that the reasons why high school students study math were divided into 9 broad categories and 15 specific categories. The most frequently suggested response was ‘instrumentality for the future’. Next, 'external pressure' , 'usefulness for everyday' , 'interest' and 'thinking power' were followed. The results of comparing the difference in recognition of the purpose of mathematics education between the upper and lower achievement groups were discussed. Finally, it was suggested that discussion on the purpose of subject education is necessary.

MQI를 이용한 예비교사와 현직교사의 수학수업의 질 분석1)

김성경 ( Kim Seong-kyeong ) 한국수학교육학회 2016 수학교육 Vol.55 No.4

This study analyzed the quality of mathematics classes with observations using the instrument, MQI(Mathematical Quality of Instruction). Class recordings and interviews were conducted on 2 pre-service teachers and 4 in-service teachers. This study recorded and analyzed 3 or 4 classes for each mathematics teacher by using revised MQI. There were a total of 8 raters: 2 or 3 raters analyzed each class. MQI has four dimensions: Richness of the Mathematics, Working with Students and Mathematic, Errors and Imprecision, Student Participation in Meaning-Making and Reasoning. In the dimension of `Richness of Mathematics`, all teachers had good scores of `explanations of teacher` but had lower scores of `linking and connections`, `multiple procedures or solution methods` and `developing mathematical generalizations.` In the dimension of `Working with Students and Mathematics`, two in-service teachers who have worked and having more experience had higher scores than others. In the dimension of `Errors and Imprecision`, all teachers had high scores. In the dimension of `Student Participation in Meaning-Making and Reasoning`, two pre-service teachers had contrast and also two in-service teachers who hadn`t worked not long had contrast. Implications were deducted from finding to improving quality of mathematics classes.

수학 교과 역량의 구현 양상 분석: <확률과 통계> 교과서를 중심으로

김성경 ( Seong-kyeong Kim ) 경북대학교 중등교육연구소 2021 중등교육연구 Vol.69 No.1

본 연구에서는 2015 개정 교육과정에서 강조한 교과 역량이 9종의 고등학교 <확률과 통계> 교과서에 어떻게 구현되어 있는지 분석하였다. 교사들은 수업 설계 과정에서 교과서를 중요한 도구로 활용하므로 교과서 분석을 통해 교과 역량의 구현 양상을 확인할 수 있기 때문이다. 이에 수학 교과 역량을 반영한 과제의 제시 방식을 살펴보고, 과제에 반영된 수학 교과 역량과 하위요소의 분포 및 특성을 분석하였다. 주요 연구 결과를 바탕으로 도출한 결론은 첫째, <확률과 통계> 교과서에서 역량을 반영한 과제의 제시 방식을 분석한 결과, 교과서는 과제와 관련된 교과 역량의 명칭만 제시할 뿐, 교과서와 교사용지도서 모두 어떤 방법으로 과제를 지도함으로써 목표한 교과 역량을 함양할 수 있는지에 대한 구체적인 설명은 빈약하였다. 둘째, <확률과 통계> 교과서는 여섯 가지 교과 역량 중 ‘정보 처리’, ‘태도 및 실천’을 반영한 과제를 빈약하게 다루고 있었다. 셋째, <확률과 통계> 교과서는 교과 역량 중 문제 해결, 추론, 창의·융합을 반영한 과제는 많이 제시하고 있으나, 이 역량들의 일부 하위요소는 대부분의 교과서에서 다루어지지 않았다. This study analyzed how the mathematical competencies emphasized in the 2015 revised curriculum were implemented in < Probability and Statistics > textbooks. Since teachers use textbooks as an important tool in the course of instruction design, analysis of textbooks can confirm the implementation of subject competency. Specifically, the method of presenting tasks reflecting the mathematical competencies was investigated, and the distribution and characteristics of the mathematical competencies and sub-elements reflected in the task were analyzed. The conclusions drawn based on the main research results are as follows. First, textbooks of < Probability and Statistics > only presented the name of the mathematical competencies related to the task. In both textbooks and teacher's guides, specific explanations on how to teach assignments to cultivate targeted competencies were poor. Second, textbooks of < Probability and Statistics > poorly dealt with tasks reflecting 'information processing' and 'attitude and practice' among the six mathematical competencies. Third, textbooks of < Probability and Statistics > presented many tasks that reflect ‘problem solving’, ‘reasoning’, and ‘creativity and integration’, but some sub-elements of these competencies are not covered in most textbooks.

초등학교 6학년 학생들의 수학적 정당화의 필요성에 대한 인식과 수학적 정당화 수준

김희진 ( Hui Jin Kim ),김성경 ( Seong Kyeong Kim ),권종겸 ( Seong Kyeong Kim ) 한국수학교육학회 2014 수학교육 Vol.53 No.4

초등학생과 중학생의 수감각 문제해결 방법에 대한 분석

김지연 ( Ji Youn Kim ),현은정 ( Eun Jeong Hyun ),김성경 ( Seong Kyeong Kim ) 한국수학교육학회 2015 수학교육논문집 Vol.29 No.1

수학교육에서 학생들의 수감각 발달을 강조하고 있지만 이에 대한 연구는 부족한 실정이며 초등학생에 국한된 경우가 많다. 이에 본 연구는 초등학생과 중학생을 대상으로 수감각 문제를 해결하는 방법을 분석함으로써, 수감각 지도방향에 대한 시사점을 제공하고자 하였다. 이를 위해 본 연구에서는 문제를 해결하는 방법으로 수감각을 활용하는 방법과 알고리즘을 활용하는 방법으로 분류하고, 검사지를 이용하여 학생들의 반응을 분석하였다. 그 결과 중학생들이 초등학생들에 비해 수감각 검사 점수가 높았으며, 문제해결 방법 중 수감각을 활용하는 비율도 높았다. 또한 성취도가 높은 학생들은 수감각과 알고리즘을 모두 활용하였으나 성취도가 낮은 학생들은 알고리즘을 활용하여 문제를 해결하려고 하는 경향이 강했다. 그리고 성취도가 높은 학생들은 초등학생에 비해 중학생이 상대적으로 수감각을 더많이 활용하였으나, 성취도가 낮은 학생들끼리는 차이가 없었다. 마지막으로 수감각 구성 요소별로 수감각을 활용하는 비율에 차이가 있는 것으로 나타났다. Mathematics education emphasizes on nurturing number sense, but researches on this have been scarce, and most of them has been confined to elementary level students. This thesis, therefore, tried to analyze how elementary students solve mathematics sense problems in order to give some insight into how to teach number sense. For this, this thesis categorized into two ways of using number sense and algorithm as problem solving, and analyzed students` responses using test sheets. Accordingly, middle school students showed higher score on the number sense test and higher rates of using number sense than elementary students. In addition, students showing higher achievement used both number sense and algorithm, but those of lower achievement were more likely to use only algorithm. Plus, among students showing higher achievement, middle school students used more number sense than elementary school students, but there was not meaningful difference among those showing lower achievement. Lastly, It was shown that there was difference in the rate using number sense according to the number sense components.