• 한국과학교육학회지
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• 제8권1호
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• pp.43-55
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• 1988

This study intended to find the differences between expert's and novice's thinking processes when they solve physics problems. Five physics professors and twenty sophomore students in a physics department were participated in the study. The researcher investigated their thinking processes in solving three physics problems on NEWTON's law of motion. The researcher accepted so called "Thinking Aloud" method. The thinking processes were recorded and transfered into protocols. The protocols were analysised by problem solving process coding system which was developed by the researcher on the basis of Larkin's problem solving process model. The results were as follows: (1) There was no difference of time required in solving physics problem of low difficulty between expert and novices; but, it takes 1.5 times longer for novices than experts in solving physics problems which difficulties are high and average. (2) Novices used working forward strategy and working backward strategy at the similiar rate in solving physics problems which difficulties were average and low. while Novices mo mostly used working backward strategy in solving physic problems which difficulty was high. Experts mostly used working forward strategy in solving physics problems whose difficulties was average and low, however experts used working forward strategy and working backward strategy at the similiar rate in solving physics problem which difficulty was high. (3) Novices usually wrote only a few information on the diagram of figure they drawn, on the other hand experts usually wrote almost all the information which are necessary for solving the problems. (4) Experts spent much time in understand the problem and evaluation stage than novices did, however experts spent less time in plan stage than novices did. (5) Physics problems are solved in sequence of understanding the problem, plan, carrying out the plan, and evaluation steps regardless of problem difficulty.

• 대한지구과학교육학회지
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• 제5권1호
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• pp.8-19
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• 2012

The purpose of this study is to: analyze the characteristics on ill-structured problem-solving process; examine the type of memories used in their monitoring. The data were primary collected from observation and secondary the semi-structured in-depth interviews based on analysis of observation results with two students who belong to science school and a guidance. The findings of this study revealed that the ill-structured problems possess multiple representations and the upper level's problem have several sub-problems. And multiple steps simultaneously exist in particular stage of problem-solving process that is not single sequential but complex flow and have high frequency of discussion step. Type of memories used in ill-structured problems include idiosyncratic memories which is related in personal histories such as school performance, problem-related memories, abstract rules and intuition.

• 한국학교수학회논문집
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• 제18권3호
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• pp.241-258
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• 2015

본 연구의 목적은 직관적 수준에서 초등학생들의 수학 문제해결 과정을 분석하는 것이다. 이를 위해 수와 연산, 도형 및 측정 영역을 대상으로, 알고리즘에 의한 해결에서부터 직관적 판단에 의해 해결이 가능한 8문제로 구성된 검사 도구를 제작하여 조사연구를 실시하였다. 직관적 수준에 따른 결과 분석에서는 본 연구에서 설정한 분석틀을 따랐다. 분석 결과, 직관적 수준에서 해결 가능한 문제에 대한 정답률이 전반적으로 낮게 나타났다. 내용 영역별로 살펴보면, 수와 연산 영역에서는 알고리즘 수준에 의한 정답률이 높았지만, 도형 및 측정 영역에서는 직관적 수준에 의한 정답률이 높았다. 결과 분석을 통해 알고리즘 적용에 필요한 요소가 문제에 제시되지 않은 경우에 학생들은 문제 구조에 대한 통찰을 통해 답을 하려는 경향을 가지고 있다는 것을 알 수 있었다. 이에 통찰을 통해 직관적으로 해결할 수 있는 다양한 문제의 개발과 직관적 원리에 의한 교육 방안을 마련할 필요성을 제기하였다.

• 대한수학교육학회지:학교수학
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• 제5권3호
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• pp.361-384
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• 2003

본 연구는 연립일차방정식에 관한 문장제에서 IDEAL 문제 해결 모형을 바탕으로 "구조-표현"을 강조한 교수-학습을 실시하였을 때 학생들의 문제해결 과정을 탐구하였다. 연구 결과, 구조-표현을 강조한 학급의 학생들이 이를 강조하지 않은 학급의 학생들보다 문제해결 능력이 향상되었으며, 동치문제, 동형문제, 유사문제를 더 정확하게 구별하였다. 또한, 구조-표현을 강조한 학급의 학생들이 그렇지 않은 학급의 학생들보다 문맥에 대한 이해 및 불완전한 정보 추출에서의 오류, 미지수간의 내적 관계에 대한 수학적 기호표현으로의 불완전한 전이 오류, 적절하지 않은 방정식 생성 오류의 발생 빈도가 적었다. 그리고, IDEAL 문제 해결 모형의 문제의 확인 단계(I)와 문제의 정의 단계(D)에서 학생들이 문제 해결 계획을 수립하기 위해 문제를 읽고 이해하여 문제를 해결하는 과정을 중점적으로 분석한 결과, 직접 변환 모델과 구조 도식 모델이 나타났다.

• 한국수학교육학회지시리즈A:수학교육
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• 제31권2호
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• pp.109-119
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• 1992

The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• 한국과학교육학회지
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• 제14권1호
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• pp.85-102
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• 1994

The purpose of this study was to analyze students' physics problem solving processes and to find the patterns of their problem spaces when high school and university students solved the physics problems. A total of 51 students in a high school and in two universities participated in this study. Their thinking processes in solving 5 physics problems on electric circuit were recorded by using 'thinking aloud' method and were transferal into protocols. 'The protocols were analyzed by the coding system of problem solving process. One of the major theoretical contributions of the computer simulation approach to problem solving is the idea of problem space. Such a concept of problem space was applied to physics problems on electric circuit in this study, and students' protocols were analyzed by the basic problem spaces which were made up from the item analysis by the researcher. The results are as follows: 1) On the average 4.0 test items among 5 ones were solved successfully by all subjects, and all of the items were solved correctly by only 19 persons among all of them. 2) In regard to the general steps of problem solving process, there was little difference for each item between the good solvers and the poor ones. But according to the degree of difficulty of task there was a good deal of difference. For a complex problem all of 4 steps were used by most of students, but for a simple one only 3 steps except evaluating step were used by most of them. 3) It was found in this study that most of students used mainly the microscopic approach, that is, a method of applying Ohm's law on electric circuit simply and immediately, not using the properties of electric circuits. And also it was observed that most of students used the soloing tom below, that is, a solving path in which they were the first to calculate physical Quantities of circuit elements, before they caught hold of the meaning of the given problem regardless of the degree of difficulty.

• 한국초등수학교육학회지
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• 제20권1호
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• pp.55-69
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• 2016

본 연구는 통계적 문제해결 과정의 관점에서, 우리나라 초등 수학교과서의 통계 영역 지도 방식을 분석하였다. 그 결과 통계적 문제 해결의 4단계 중에서 자료 분석단계에 대한 집중도가 심한 것으로 드러났고, 문제 설정과 자료 수집, 결과 해석단계의 비중이 매우 저조한 것으로 분석되었다. 이를 토대로 초등 수학교과서의 통계 영역 교과서 개발과 관련된 시사점을 논의하였다.

• 융합보안논문지
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• 제13권2호
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• pp.175-183
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• 2013

본 연구는 전문대학 신입생의 비판적 사고성향과 문제해결과정의 정도를 파악한 후 이들 간의 상관성과 문제해결과정에 미치는 영향을 파악하고자 수행하였다. 연구대상은 전문대학에 재학 중인 1학년 215명이었고 자료수집은 구조화된 설문지를 이용하여 2012년 11월 20일에서 12월 5일까지 수집하였고 SPSS 18.0으로 분석하였다. 연구결과, 전문대학 신입생의 비판적 사고성향은 연령, 대인관계에서 유의한 차이가 있었고, 문제해결과정은 연령, 대인관계, 전공만족도에서 유의한 차이가 있었다. 전문대학 신입생의 비판적 사고성향과 문제해결과정간의 관계는 통계적으로 유의한 양의 상관관계(r=.605, P<.001)를 나타냈다. 전문대학 신입생의 문제해결과정에 영향을 미치는 요인은 비판적 사고성향과 전공 만족도로 문제해결과정을 38% 설명하였다. 본 연구는 전문대학생의 비판적 사고성향이 문제해결에 미치는 영향에 대한 실증연구를 표준적인 방법론에 의거 체계적으로 수행하여 비판적 사고성향과 전공만족도를 높일 수 있는 합리적인 교수학습 전략 및 교육과정 개발 방향을 제시하였다는 점에서 그 의의를 찾을 수 있다.

• 대한화학회지
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• 제46권4호
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• pp.353-363
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• 2002

이 연구의 목적은 일반고와 과학고 학생들의 정신용량과 풀이 방법에 따른 산화 환원 반응식 완결 과정의 특성을 분석하여 산화 환원 단원의 교수학습 지도에 시사점을 얻고자 하는데 있다. 일반고 학생 79명과 과학고 학생 57명을 대상으로 하여 정신요량 검사, 산화 환원 반응식 완결 검사를 실시하였으며, 문항 유형별로 학생들의 문제 풀이 실패 유형과 성공 유형을 추출하여 분석틀을 개발하고 개발한 분석틀에 의하여 정신용량과 풀이 방법에 따라 실패 사례와 성공 사례를 분석하여 나타나는 특징을 알아보았다. 일반고 학생들과 과학고 학생들 모두 산화 환원 개념 이해 정도가 낮을수록 미정계수법을 많이 선택하였으며 미정계수법을 선택한 학생들은 정신용량이 클수록 문제 풀이의 성공률이 높았다. 또한, 산화 환원 개념 이해 정도가 높은 학생들은 산화수법이나 이온 자법을 더 많이 선택하였고 정신용량에 관계없이 문제 풀이의 성공률이 높게 나타났다. 학생들의 풀이 과정을 분석한 결과 성공 유형은 산화 환원의 개념 이해 정도가 높고 풀이 방법에 관계없이 풀이 단계 수를 줄이 학생들이었다. 실패 유형은 물이 방법에 따라 다르게 나타났다. 미정계수법을 선택한 학생들의 실패 유형은 계산 과정 중 틀린 경우, 미정방정식을 잘못 세운 경우 문제 풀이 과정중 고려해야 할 변인을 모두 고려하지 못한 경우 풀이 과정이 복잡하여 중단한 경우였다. 산화수법을 선택한 학생들의 실패 유형은 산화수를 잘못 결정한 경우 질량균형 또는 전하균형을 고려하지 않은 경우였다.