• 과학교육연구지
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• 제45권2호
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• pp.247-256
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• 2021

수학 문제해결에서 시각적 표현은 문제 이해와 해결에 유용한 수학적 표현으로 인식되고 있다. 그렇지만 그 효과는 문제 내용이나 유형, 또는 이용되는 시각적 표현 유형에 따라 다를 수 있다. 본 연구에서는 정형화된 문제와 비정형화된 문제해결에 이용된 시각적 표현의 양상을 살펴보기 위해 초등학교 5학년 학생들을 대상으로 조사연구를 실시하였다. 분석 결과, 정답률에서는 정형화된 문제가 비정형화된 문제보다 높게 나타났다. 정형화된 문제에서는 시각적 표현을 이용하여 문제를 해결하도록 하였음도 불구하고 수식을 이용하여 해결한 비율이 높게 나타났다. 반면에 비정형화된 문제에서는 시각적 표현을 이용하여 해결한 비율이 높게 나타났다. 그렇지만 비정형화된 문제에서 시각적 표현을 이용한 대상자 중에 오답자의 비율도 높게 나타났는데, 이것은 문제 상황을 묘사하는 수준의 시각적 표현에 그친 경우였다. 따라서 다양한 유형의 시각적 표현을 문제해결에 이용할 수 있는 경험을 제공하도록 하고, 시각적 표현으로의 변환 과정에도 주의를 기울일 필요가 있다.

• 한국항공운항학회지
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• 제22권4호
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• pp.42-55
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• 2014

The purpose of this research was to identify expertise in ait traffic control by using cognitive skill analysis for novices and experts in routine and non-routine situations. The result of study was to understand expertise in air traffic control tasks in terms of what cognitive processes are responsible for the expert's high performance levels. The problem solving task was difficult for novices, but performed relatively automatically by experts in a routine situation. The difficulty could indicate the presence of controlled processing. Rather than rules and strategies, novices focused more on environmental factors, which merely increase cognitive load. In a non-routine situation, novices showed that they did not categorize the information consistently and alternative resources were not available for them. Experts, however, performed automatically a task by arranging and organizing information related to problem solving components in contexts without regard to a routine and non-routine situation. Especially experts developed a stable representation and directed alternative resources for air traffic flow and efficiency. Based on the results, cognitive processes of experts could be useful to understand expert performance and analyze the learning process, which imply the necessity of developing expertise systematically.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제3권1호
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• pp.63-77
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• 1999

We introduce what is the meaning of problem and problem solving and also different type of problems and problem-solving strategies were discussed in this paper, with suggestions for teaching both Polya's four-step strategy and specific problem solving strategies. Many real and concrete examples of routine and nonroutine problems in elementary school mathematics are introduced. Especially, we have researched on the actual condition how children in elementary school think about multiplication of fraction for the routine problem. As a result, we have noticed that children have diverse thinking in their own way and also concrete expressions are much better effective than algorithm showing in textbook.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제9권1호
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• pp.25-45
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• 2005

Background Phenomenography suggests that more variation is associated with wider ways of experiencing phenomena. In the discipline of mathematics, broadening the 'lived space' of mathematics learning might enhance students' ability to solve mathematics problems Aims The aim of the present study is to: 1. enhance secondary school students' capabilities for dealing with mathematical problems; and 2. examine if students' conception of mathematics can thereby be broadened. Sample 410 Secondary 1 students from ten schools participated in the study and the reference group consisted of 275 Secondary 1 students. Methods The students were provided with non-routine problems in their normal mathematics classes for one academic year. Their attitudes toward mathematics, their conceptions of mathematics, and their problem-solving performance were measured both at the beginning and at the end of the year. Results and conclusions Hierarchical regression analyses revealed that the problem-solving performance of students receiving non-routine problems improved more than that of other students, but the effect depended on the level of use of the non-routine problems and the academic standards of the students. Thus, use of non-routine mathematical problems that appropriately fits students' ability levels can induce changes in their lived space of mathematics learning and broaden their conceptions of mathematics and of mathematics learning.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권1호
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• pp.39-51
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• 2010

The purpose of this article is to study students' responses to non-routine problems which are presented by using solely numerals or symbolic figures. Such figures have no mathematical meaning but just symbolical meaning. Most students understand geometric figures more concrete objects than numerals because geometric figures such as circles and squares can be visualized by the manipulatives in real life. And since students need not consider (unvisible) any operational structure of numerals when they deal with (visible) figures, problems proposed using figures are considered relatively easier to them than those proposed using numerals. Under this assumption, we analyze students' problem solving processes of numeral problems and figural problems, and then find out when students' difficulties arise in the problem solving process and how they response when they feel difficulties. From this experiment, we will suggest several comments which would be considered in the development and application of both numerical and figural problems.

• 초등상담연구
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• 제7권1호
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• pp.135-163
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• 2008

This study intends to confirm if it is effective in improving the problem behaviors by applying "Logical Consequence" suggested by Adler to the class management. The researcher who is in charge of the 4th grade class of elementary school in G city applied Adlerian logical consequence to her children, observed and examined the effectiveness of reducing the problem behaviors by the qualitative study method of in-depth interview from March to October. The problem behaviors treated in this study includes irrelevant remarks and gossip in school time, no preparation for taking lessons in time, no preparation of a textbook and a supply, no involvement in doing homework, scribbling and poor handwriting on a textbook, teasing a friend (abusive language, joking, violence), indoor running, no involvement in doing a task, being late and no arrangement of indoor shoes. In conclusion, this study indicated that the use of Logical Consequence was relatively effective in improving the problem behaviors and more effective in individual behaviors rather than group's behaviors. While the problem behaviors conducted in a class in the daily routine were effective at the point of the occurred problems, the problem behaviors occurred at the point of time related to a home or the finish of daily routine were ineffective.

• 한국수학교육학회지시리즈A:수학교육
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• 제43권4호
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• pp.399-404
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• 2004

Mathematical creativity is a main topic which is studied within mathematics education. Also it is important in learning school mathematics. It can be important for mathematics teachers to view mathematical creativity as an disposition toward mathematical activity that can be fostered broadly in the general classroom environment. In this article, it is discussed that creativity-enriched mathematics instruction which includes creative problem-solving and problem-posing tasks and activities can be guided more creative approaches to school mathematics via routine problems.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권4호
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• pp.361-380
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• 2010

Some 400 Secondary One (i.e. seventh-grade) students from 10 schools were provided with non-routine mathematical problems in their normal mathematics classes as exercises for one academic year. Their attitudes toward mathematics, their conceptions of mathematics and their problem-solving performance were measured both in the beginning and at the end of the year. Hierarchical regression analyses revealed that the introduction of an appropriate dose of non-routine problems would generate some effects on the students' conceptions of mathematics. A medium dose of non-routine problems (as reported by the teachers) would result in a change of the students' conception of mathematics to perceiving mathematics as less of "a subject of calculables." On the other hand, a high dose would lead students to perceive mathematics as more useful and more as a discipline involving thinking. However, with a low dose of non-routine problems, students found mathematics more "friendly" (free from fear). It is therefore proposed that the use of non-routine mathematical problems to an appropriate extent can induce changes in students' "lived space" of mathematics learning and broaden their conceptions of mathematics and mathematics learning.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권1호
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• pp.51-65
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• 2010

Open-ended problems can foster deeper understanding of mathematical ideas, generating creative thinking and communication in students. High-order thinking tasks such as open-ended problems involve more ambiguity and higher level of personal risks for students than they are normally exposed to in routine problems. To explore the classroom-based factors that could support or inhibit such higher-order processes, this paper also describes two cases of Singapore primary school teachers who have successfully or unsuccessfully implemented an open-ended problem in their mathematics lessons.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.107-124
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• 1999

An approximate Bayes criterion for multivariate Behrens-Fisher problem is proposed and examined. Development of the criterion involves derivation of approximate Bayes factor using the imaginary training sample approach introduced by Speigelhalter and Smith (1982). The criterion is designed to develop a Bayesian test, so that it provides an alternative test to other tests based upon asymptotic sampling theory (such as the tests suggested by Bennett(1951), James(1954) and Yao(1965). For the derived criterion, numerical studies demonstrate routine application and give comparisons with the classical tests.