• Journal of Elementary Mathematics Education in Korea
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• v.9 no.1
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• pp.39-64
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• 2005

The purpose of this study is to transform questions in the 7th curriculum to open-ended problems and exam students' attitude towards open-ended problems. Research questions in this thesis are as follows: First, to transform questions in the 7th curriculum to open-ended problems and apply to a class in the fourth grade D elementary school. Second, to find how students respond to learning mathematics with open-ended problems. As a result of this study, the following are identified. First, the students showed positive reactions towards learning mathematics with open-ended problems. Those experience with open-ended problems make student solve mathematics problems with interest and confidence. Second, both good and bad students in the math class show interest and concentration toward open-ended problem. But a few students show less interest towards those problems. Third, through discussion about problem-solving with open-ended problems, students take part in math class actively and show respect one another. Fourth, especially students show more interest and confidence towards the open-ended problems transformed from mathematics textbook and like the constructive open-ended problems.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.215-227
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• 2006

After reviewing China's appearance and research on the Math open-ended problems, together with the application of those problems in mathematics test of Shanghai Senior Middle School Entrance Exams (SSMSEE) since 1999, this paper points out the difficulty in establishing an evaluation system for such problem. Through comparative study, the paper gives an operational definition of open-ended problem, and it attempts to establish an evaluation system and non-systematic competence targets that are appropriate to Math open-ended problems. Meanwhile, it describes the performance feature of those targets. By applying the standard international grading system of difficulty, it discusses the elements of difficulty in Math open-ended problems, and puts forward an evaluation as well as a level-of-difficulty forecasting system that is appropriate to the Middle School Entrance Exam.

• The Mathematical Education
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• v.55 no.2
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• pp.209-232
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• 2016

This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.

• Research in Mathematical Education
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• v.14 no.1
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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.

• The Mathematical Education
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• v.47 no.4
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• pp.421-436
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• 2008

Mathematics assessment doesn't mean examining in the traditional sense of written examination. Mathematics assessment has to give the various information of grade and development of students as well as teaching of teachers. To achieve this purpose of assessment, we have to search the methods of assessment. This paper is aimed to develop the open-ended problems that are the alternative to traditional test, apply them to classroom and analyze the result of assessment. 4-types open-ended problems are developed by criteria of development. It is open process problem, open result problem, problem posing problem, open decision problem. 6 grade elementary students who are picked in 2 schools participated in assessment using open-ended problems. Scoring depends on the fluency, flexibility, originality The result are as follows; The rate of fluency is 2.14, The rate of flexibility is 1.30, and The rate of originality is 0.11 Furthermore, the rate of originality is very low. Problem posing problem is the highest in the flexibility and open result problem is the highest in the flexibility. Between general mathematical problem solving ability and fluency, flexibility have the positive correlation. And Pearson correlational coefficient of between general mathematical problem solving ability and fluency is 0.437 and that of between general mathematical problem solving ability and flexibility is 0.573. So I conclude that open ended problems are useful and effective in mathematics assessment.

• 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.

• Communications of Mathematical Education
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• v.35 no.3
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• pp.277-293
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• 2021

The purpose of this study was to find out how problem solving learning with open-ended mathematics problems for elementary school students affects their mathematical creativity and mathematical attitudes. To this end, 9 problem solving lessons with open-ended mathematics problems were conducted for 6th grade elementary school students in Seoul, The results were analyzed by using I-STATistics program to pre-and post- t-test. As a result of the study, problem solving learning with open-ended problems was effective in increasing mathematical creativity, especially in increasing flexibility and originality, which are sub-elements of creativity. In addition, problem solving learning with open-ended problems has helped improve mathematical attitudes and has been particularly effective in improving recognition needs and motivation among subfactors. In problem solving learning with open-ended problems, students were able to share various responses and expand their thoughts. Based on the results of the study, the researchers proposed that it is necessary to continue the development of quality materials and teacher training to utilize mathematical problem solving with open-ended problems at school sites.

• 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.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 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.