• School Mathematics
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• v.4 no.4
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• pp.565-580
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• 2002

연구자들은 학생들에게 문제해결 전략을 지도하는 것이 학생들의 문제해결력을 신장시켜 준다는 보고하고 있다. 이와 같은 연구결과를 배경으로 수학 교과서를 통하여 문제해결 전략을 지도하려는 시도들이 미국을 비롯하여 한국에서도 있어 왔다. 본 논문은 문제해결 전략을 교과서에 제시할 수 있는 가능한 세 가지 모델들을 논의하고, 미국과 한국의 수학교과서에서 문제해결 전략을 제시하는 방법을 분석하였다. 한 가지 모델은 문제해결 전략에 한 단원을 할애하는 것이다. 두 번째 모델은 각 수학내용을 지도하는 단원에 문제해결 전략의 지도를 위한 하위단원을 할당하는 것이다. 마지막, 세 번째 모델은 문제해결 전략 지도를 위한 특정 단원이나 하위 단원을 설정하는 것이 아니라 가능한 많은 쪽에 전략을 제시하는 것이다. 위에 언급한 세 가지 가능한 모델을 바탕으로 미국과 한국의 초등학교 수학교과서에서 문제해결 전략을 제시하는 양상을 비교하였다. 이 비교를 위하여 각 학년별로 제시되는 모든 전략들을 교과서와 교사용 지도서를 토대로 추출하였다. 각 교과서에서 전략을 제시한 양식을 비교한 결과 다음과 같은 결론을 얻게 되었다. 한국의 수학교과서는 전형적으로 첫 번째 모델의 양식으로 문제해결전략을 제시하고 있었다. 각 단원마다 별개의 문제해결 전략이 제시되었다. 또한, 학년별 지도 전략을 살펴보면 학년별로 연계성이 있게 전략이 제시 되었다기 보다는 학년별로 다른 다양한 전자의 지도에 중점을 둔 듯하다. 미국의 수학교과서는 두 번째 모델과 세 번째 모델의 중간적인 양식으로 문제해결 전략을 제시하고 있다. 즉, 각 단원마다 문제해결 전략 지도를 위한 하위 단원을 지정하였으며 필요한 경우에는 본 단원의 주 학습요소와 관련된 문제해결 전략은 단원 중에도 제시되고 있었다. 따라서, 차기 수학교과서 개정시기에는 세 번째 모델을 그 모형으로 삼아 문제해결 전략들을 제시하는 방안을 강구해야 할 것으로 기대된다.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.419-443
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• 2018

The purpose of this study was to analyze the problem solving strategies of ordinary students, gifted students, pre-service teachers, and in-service teachers with the 'chicken and pig problem,' which has multiple strategies to obtain the solution. For this study, 98 students in the 6th grade elementary schools, 96 gifted students in a gifted institution, 72 pre-service teachers, and 60 in-service teachers were selected. The researcher presented the "chicken and pig" problem and requested them the solution strategies as many as possible for 30 minutes in a free atmosphere. As a result of the study, the gifted students used relatively various and efficient strategies compared to the ordinary students, and there was a difference in the most used strategies among the groups. In addition, the percentage of respondents who suggested four or more strategies was 1% for the ordinary students, 54% for the gifted students, 42% for the pre-service teachers, and 43% for the in-service teachers. As suggestions, the researcher asserted that various kinds of high-quality mathematical problems and solving experiences should be provided to students and teachers and have students develop multi-strategy problems. As a follow-up study, the researcher suggested that multi-strategy mathematical problems should be applied to classroom teaching in a collaborative learning environment and reflected them in teacher training program.

• Proceedings of The KACE
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• 2018.08a
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• pp.59-62
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• 2018

모순이라는 관점에서 문제를 창의적으로 해결하고자 한 나비 모형은 모순의 유형을 나누어 정의하고 유형별 문제 해결 목표와 추상적 해결 전략을 정의하여 논리적 접근을 가능하게 하였다. 본 연구에서는 모순 문제와 문제에 대한 시간 및 구성요소들의 특성을 이용하여 모순 유형을 결정하고 주어진 문제의 문제 해결 목표와 추상적 해결 전략, 나비 다이어그램을 제시하는 프로그램을 개발한다. 또한 모순 유형 중에서 추상적 해결 전략으로 두 가지 매개 모순을 모두 만족시켜야 하는 문제의 구체적 해결 전략을 개발하기 위하여 시간과 구성요소의 분할과 결합 전략에 대한 알고리즘을 설계한다. 본 연구는 나비 모형을 기반으로 모순 문제의 구체적인 해결 전략을 자동적으로 찾을 수 있도록 돕는다. 궁극적으로는 나비 모형을 기반으로 컴퓨터가 스스로 모순 문제를 해결할 수 있는 알고리즘을 개발한다.

• Journal of Engineering Education Research
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• v.8 no.2
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• pp.64-83
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• 2005

The purpose of this study is to investigate the correlations between technological problem solving strategies and variables related with self-regulation of students in engineering college. The subjects for this study are 120 students from engineering college. After using the problem solving strategy task and self-regulation questionnaire, they were classified into two groups, upper 25% group and bottom 25% group. The data was analyzed using the SPSS 10.0 for windows. The statistical technique used for data analysis was Pearson's correlation coefficient and t-test. The major conclusions of this study are as follows. Frist, there is positive correlation between strategies of design and self-efficacy & planning. Second, there is positive correlation between strategies of trouble shooting and self-monitoring, planning and effort. Third, especially self-efficacy, one of the self-regulation subvariables, directly affects on technological problem solving strategies.

• Journal of the Korean School Mathematics Society
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• v.16 no.1
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• pp.113-139
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• 2013

The purpose of this study is to provide informations about cause of failures when students solve word problems by analyzing what errors students made in solving word problems and types of error and features of error according to problem solving strategy. The results of this study can be summarized as follows: First, $5^{th}$ grade students preferred the expressions, estimate and verify, finding rules in order when solving word problems. But the majority of students couldn't use simplifying. Second, the types of error encountered according to the problem solving strategy on problem based learning are as follows; In the case of 'expression', the most common error when using expression was the error of question understanding. The second most common was the error of concept principle, followed by the error of solving procedure. In 'estimate and verify' strategy, there was a low proportion of errors and students understood estimate and verify well. When students use 'drawing diagram', they made errors because they misunderstood the problems, made mistakes in calculations and in transforming key-words of data into expressions. In 'making table' strategy, there were a lot of errors in question understanding because students misunderstood the relationship between information. Finally, we suggest that problem solving ability can be developed through an analysis of error types according to the problem strategy and a correct teaching about these error types.

• Journal of The Korean Association For Science Education
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• v.21 no.2
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• pp.289-298
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• 2001

The effect of the instructional approach that asked students to check their problem-solving processes through a paired think-aloud problem solving after presenting molecular-level pictures and a four stage-problem solving strategy was investigated. Four high school classes (N = 191) were randomly assigned to St group (using Strategy individually), SL group (Solver Listener), St-SL group (using Strategy-Solver Listener), and control group. Although the test scores of the St-SL group on strategy performing ability were significantly higher than those of the control group, there was not significant difference for the scores in the multiple-choice algorithmic problems. Regarding the subcategories of strategy performing ability test, students' ability of understanding given of problems and deriving the proper physical quantity was improved, but their ability of setting up subgoals and reviewing their solving process was very low. The preference to the strategy of the St-SL group was more positive than that of the St group.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.433-452
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• 2009

This study investigated the teaching strategies of two exemplary American teachers regarding word problems and their impact on students' ability to both understanding and solving word problems. The teachers commonly explained the background details of the background of the word problems. The explanation motivated the students' mathematical problem solving, helped students understand the word problems clearly, and helped students use various solving strategies. Emphasizing communication, the teachers also provided comfortable atmosphere for students to discuss mathematical ideas with another. The teachers' continuous questions became the energy for students to plan various problem solving strategies and reflect the solutions. Also, this research suggested a complementary model for Polya's problem solving strategies.

• Communications of Mathematical Education
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• v.15
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• pp.153-159
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• 2003

수학 학습의 목표를 수학적 사고력의 신장이라는 측면에서 보았을 때 이를 위하여 문제에 대한 다양한 해법을 찾는 활동은 중요하다. 문제에 대한 다양한 접근은 문제해결의 전략을 학습시키고 사고의 유연성을 길러줄 수 있는 방법이 된다. 문제에 대한 다양한 해법을 찾는 과정에서 이미 알고 있는 지식이 어떻게 응용되는지를 알게 된다. 특히 기하 문제에 대한 다양한 접근은 문제해결의 전략을 학습시킬 수 있는 좋은 예가 된다. 본고에서는 문제해결을 통한 수학적 일반성을 발견하기 위한 방법으로서 문제에 대한 다양한 해법을 연역과 귀납에 의하여 일반화하는 과정을 탐색하고자 한다. 특히 수학 문제에 대한 다양한 해법을 찾는 것은 문제해결 전략으로서 뿐만 아니라 창의적 사고의 신장 측면에서 시사점을 던져준다.

• The Korean Journal of Elementary Counseling
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• v.8 no.1
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• pp.123-139
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• 2009

The purpose of this study was to verify the effects of a conflict resolution program on conflict resolution strategies and friendship quality of children. The subjects of this study were higher-grader students of elementary school. Out of the students, 18 were into the experimental group, while the rest were into the control-group. The experimental design was the pretest-posttest control group design, and the 50-minutes conflict resolution program was treated for the experimental group twice per week (a total of 11 sessions). The scale of conflict resolution strategies presented by Ha Ji Wean (2005) and the scale of friendship quality of children presented by Rhee Un Hai and Koh Yun Joo (1999) were used as the measurement tools in this study. In order to supply the limitations of quantitative data, the journals of group participation of each session and the participation reports after the completion of the program were qualitatively analyzed. The results of hypotheses verification were as follows; First, conflict resolution strategies conflict was significant difference in enhancement of the compromising-integrating strategy and the obliging strategy, and reduction of the dominating strategy. Second, friendship quality was significant difference in enhancement of the friendship positive function, and friendship satisfaction, and in reduction of the friendship negative aspect, The results of the study confirmed that the conflict resolution program affected both conflict resolution strategies and the friendship quality of children.

• Journal of Elementary Mathematics Education in Korea
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• v.1 no.1
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• pp.67-86
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• 1997

The purposes of this paper are to show problem-solving strategies and their typical problems to suggest specific ways to teach strategies to promote problem-solving abilities. (1) Problem-solving strategies can be divided into general strategies and specific strategies. General strategies refer to procedural teaching-learning activities based on Polya's 4 step problem-solving. Specific strategies refer to Lenchner's 12 problem solving strategies and their characteristics which are helpful to the substantial solution of specific problems. (2) Concerning to problem-solving strategies teaching, the followings are suggested. First, the sequence of strategy teaching should be from easy to difficult ones, from short to long ones. Second problems for strategy training should be simple and good enough to serve as examples of the strategies. Repetition with similar problems are needed. Third, analysis and comparison of various strategies, and extension and adaptation of the strategies to complicate problems are needed. Fourth, procedures of strategies teaching are the follows: Have students make their own strategies focused on the solution process; Have students solve the problems with expectation of the solving methods; Have students compare and reflect on their solving methods; And assess problem - solving processes.