• Education of Primary School Mathematics
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• v.7 no.2
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• pp.117-129
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• 2003

The purpose of this study is to analyze the interaction patterns and the commonly accepted norms of reaching a consensus among small-group children when solving open-ended problems. In conclusion, open-ended problems have various strategies or different acceptable answers, so they give children learning opportunities to compare the answers and to participate in communication. And more valuable interaction patterns come from 'measuring','classifying' problems and open-ended problems with implicit solution. Therefore, teachers might as well consider the relation between problems and interaction patterns when they pose open-ended problems in a small-group study setting. They are expected to empower children to have sociomathematical norms of reaching a consensus un der indirect and supportive guidance.

• Research in Mathematical Education
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• v.8 no.3
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• pp.123-144
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• 2004

There is a tradition of advocating the 'two basics' (basic knowledge and basic skills) in Chinese mathematics education. The direct consequence is that Chinese students are able to produce excellent performance in the international mathematics examinations and outstanding results in the international mathematics competitions. In this article, we will present why and how Chinese teachers teach the 'two basics,' and how combine the pupil's creativity with their 'two basics.' Open ended problem solving is a way to meet the goal. The following topics will be concerned: Culture background; the speed of computation; 'make perfect' ; Efficiency in classroom; Balance between 'two basics' and personal development. In Particular, Chinese mathematics educators pay more attentions to the link between open ended problem solving and the 'two basics' principal.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.723-744
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• 2010

The aim of this study was to find the effects of open-ended problems on mathematical creativity and brain function. In this study, one class of first grade students were allocated randomly into two groups. Each group solved different problems. The experimental group solved the open-ended problems and the comparison group solved the closed-problems. Mathematical creativity was tested by the paper test. And Brain function was tested by an EEG(electroencephalogram) tester. The results of this study are as follows. Firstly, this study analyzed how the open-ended problems are effective on mathematical creativity. This analysis showed that it had a meaningful influence on the mathematical creativity(p=0.46). Accordingly, we could find out that open-ended problems make the student connect the mathematical concept and idea and think variously. Secondly, this study analyzed the effect of open-ended problems on brain function. This analysis showed that it did not have a meaningful influence on the brain function(p=.073) statistically but the experimental group's evaluation was higher than comparison groups' at the post-test. It also had a meaningful influence on the brain attention quotient(left) (p=.007), attention quotient(right) (p=.023) and emotion tendency quotient(p=.025). As a result of such tests, we could find out that open-ended problems are effective on brain function, especially on the attention ability. With the use of the open-ended problems, students could show quick understanding and response. An emotion tendency is also developed in the process. Because various answers are accepted, the students gain an internal reward at the process of finding an answer. Putting the above results together, we could find that open-ended problem is effective on mathematical creativity and brain function.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.19-38
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• 2011

The purpose of this study was to analyze the responses and the behavioral characteristics between mathematically promising students and normal students in solving open-ended problems. For this study, 55 mathematically promising students were selected from the Science Education Institute for the Gifted at Seoul National University of Education as well as 100 normal students from three 6th grade classes of a regular elementary school. The students were given 50 minutes to complete a written test consisting of five open-ended problems. A post-test interview was also conducted and added to the results of the written test. The conclusions of this study were summarized as follows: First, analysis and grouping problems are the most suitable in an open-ended problem study to stimulate the creativity of mathematically promising students. Second, open-ended problems are helpful for mathematically promising students' generative learning. The mathematically promising students had a tendency to find a variety of creative methods when solving open-ended problems. Third, mathematically promising students need to improve their ability to make-up new conditions and change the conditions to solve the problems. Fourth, various topics and subjects can be integrated into the classes for mathematically promising students. Fifth, the quality of students' former education and its effect on their ability to solve open-ended problems must be taken into consideration. Finally, a creative thinking class can be introduce to the general class. A number of normal students had creativity score similar to those of the mathematically promising students, suggesting that the introduction of a more challenging mathematics curriculum similar to that of the mathematically promising students into the general curriculum may be needed and possible.

• The Mathematical Education
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• v.44 no.2 s.109
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• pp.307-323
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• 2005

The purpose of this study was to develop a program to cultivate mathematical creativity based on open-ended problem and to investigate its effect. The major features of this innovative program are (a) breaking up fixations, (b) multiple answers, (c) various strategies, (d) problem posing, (e) exploring strategies, (f) selecting and estimating, (g) active exploration through open-ended problems. 20 units for 7th grade mathematics were developed. This study hypothesizes that experimental students may develop more divergent thinking abilities than their traditional counterparts. The participants were 7th grade students attending middle schools in Seoul. Instruments were pre and post tests to measure mainly divergent thinking skills through open-ended problems. The results indicated that the experimental students achieved better than the comparison students on overall and each component of fluency, flexibility, and originality of divergent thinking skills, when deleting the effect of covariance of the pretest. The developed program can be a useful resource for teachers to use in enhancing their students' creative thinking skills. Further this open-ended approach can be served as a model to implement in classes. This study suggests that further investigations are needed in order to examine effects on affective domains such as motivation and task perseverance which are also considered as important factors of creativity.

• The Mathematical Education
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• v.46 no.2 s.117
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• pp.207-226
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• 2007

The purpose of this study was to design and develop the processes of tasks and assessment rubrics of open-ended tasks, and those for the 5th graders of elementary school mathematics. 7 tasks were finally developed, and 'problem understanding', 'problem solving process', 'communication' were selected as the criteria for assessment rubrics. The result was that the ability of mathematical power covering problem understanding ability, problem solving ability and mathematical communication ability was low. Specifically, problem understanding ability was the highest, problem solving ability was middle, and mathematical communication ability was the lowest.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.4
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• pp.965-975
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• 1994

Opening the tip of a PHC pile, under a constant driving energy, can result in an increment of penetration depth due to the decrement of driving resistance. Therefore, the bearing capacity of an open-ended PHC pile may become larger than that of a closed-ended PHC pile by virtue of the increased embedded length. However, two main problems can be caused by opening the end of PHC pile. First problem is the variation of bearing capacity by opening the pile tip, and the second one is whether the tip of an open-ended PHC pile will be failured by a high pressure developed by the soil plug. In this study, model pile tests in calibration chamber were performed to investigate the practicability of open-ended PHC pile in view of both the pile bearing capacity and the possible failure of the pile tip. According to the test results, the total bearing capacity of open-ended piles approaches the total bearing capacity of closed-ended piles with the increase of the penetration depth. The failure of pile tip could be occurred in the region of 0.8~1.1 times as the inside diameter from the pile tip.

• Survey Research
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• v.18 no.4
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• pp.127-147
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• 2017

Despite the importance of questionnaires, little survey methodology research on questionnaire design has been conducted in Korea. The purpose of this study was to explore whether two questionnaire forms (close-ended vs. open-ended questions) about 'the most important problem in Korea' elicited similar responses. During the 2016 Korean General Social Survey (KGSS), a random half of respondents were asked the open-ended question form and the remaining half were asked the close-ended question form. While the economy is the most mentioned response (35% vs. 33.2%) to both close-ended and open-ended question forms, there is similarity in the order of highly mentioned responses if we consider that 'politics' is not provided as one of response categories in the close-ended question form. The order of second to fourth response category is crime (24.4%), education (15.4%), and poverty (6.3%) to the closed-ended question form, and politics (10.8%), crime (9.5%), and education (7.6%) to the open-ended question form. Also, the characteristics of respondents who responded with the economy as being the most important are slightly different between the two halves in terms of age, household income, and satisfaction with economic condition. Our findings suggest that we need to be careful when we adopt questions developed in other countries and to consider using survey experiments in pre-testing questionnaire items.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.3
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• pp.907-935
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• 2010

The purpose of this study was to investigate the effects of using open-ended problems in ability-level activities in mathematics instruction and to draw some informative conclusions in order to improve the practice of teaching and learning mathematics in the elementary school. To fulfill the purpose, the research questions were established as follows: 1. Is there any difference between the academic achievements of the experimental group(doing ability-level activities using open-ended problems) and the control group(doing general ability-level activities)? 2. Which sub-group(grouped by achievement score in pretest) get affected most by ability-level activities using open-ended problem in the experimental group? 3. What kinds of responses do students show in their ability-level activities using open-ended problems? By applying t-test and analysing the response, the conclusions were drawn as follows: First, using open-ended problems in ability-level activities has positive effects on the academic achievement of the experiment group. The mean of posttest scores of the experiment group was statistically meaningfully higher(p<.05). Second, using open-ended problems in ability-level activities affect most to the achievement of lower sub-group in the experiment group. The mean of posttest scores of lower sub-group in the experiment group was statistically meaningfully higher than that of control group(p<.05). Third, students showed various and creative response in their ability-level activities using open-ended problems.

• Journal of the Korean School Mathematics Society
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• v.10 no.2
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• pp.221-235
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• 2007

Open problems can provide experiences for students to yield originative and various products in their level, because it is open with respect to its departure situation, goal situation, or solving method. Teachers need to pose and utilize open problems in forms of solution-finding or proving problems. For this we first have to specify which resource and method to use by concrete examples. In this article, we exemplify a method and procedure of posing an open problem by the two cases in which we pose open problems by reorganizing given closed problems. And we analyze students' responses for the two posed open problems. On the basis of these, we reflect implications for mathematical education of open problems.