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

• Research in Mathematical Education
• /
• v.10 no.3 s.27
• /
• pp.151-167
• /
• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U. S. researchers. We examine the approach by illustrating its three aspects: 1) Open process (there is more than one way to arrive at the solution to a problem; 2) Open-ended problems (a problem can have several of many correct answers), and 3) What the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U. S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

• School Mathematics
• /
• v.19 no.1
• /
• pp.153-170
• /
• 2017

This study conducted an analysis of types of reasoning shown in students' solving a problem and processes of students' reasoning according to type of problem by posing an open-ended problem where students' reasoning activity is expected to be vigorous and a multiple-choice problem with which students are familiar. And it examined teacher's role of promoting the reasoning in solving an open-ended problem. Students showed more various types of reasoning in solving an open-ended problem compared with multiple-choice problem, and showed a process of extending the reasoning as chains of reasoning are performed. Abduction, a type of students' probable reasoning, was active in the open-ended problem, accordingly teacher played a role of encouragement, prompt and guidance. Teachers posed a problem after varying it from previous problem type to open-ended problem in teaching and evaluation, and played a role of helping students' reasoning become more vigorous by proper questioning when students had difficulty reasoning.

• The Mathematical Education
• /
• v.43 no.3
• /
• pp.275-289
• /
• 2004

The purpose of the study is to investigate how children and preservice teachers would make a progress in solving the open-problems related to area. In knowledge-based information age, information inquiry, information construction, and problem solving are required. At the level of elementary school mathematics, area is mainly focused on the shape of polygon such as square, rectangle. However, the shape which we need to figure out at some point would not be always polygon-shape. With this perspective, many open-problems are introduced to children as well as preservice teacher. Then their responses are analyzed in terms of their logical thinking and their understanding of area. In order to make students improve their critical thinking and problem solving ability in real situation, the use of open problems could be one of the valuable methods to apply.

• Proceedings of the Korea Society of Mathematical Education Conference
• /
• 2006.10a
• /
• pp.45-62
• /
• 2006

The open approach to teaching school mathematics in the United States is an outcome of the collaboration of Japanese and U.S. researchers. We examine the approach by illustrating its three aspects: open process (there is more than one way to arrive at the solution to a problem; 2) open-ended problems (a problem can have several of many correct answers), and 3) what the Japanese call 'from problem to problem' or problem formulation (students draw on their own thinking to formulate new problems). Using our understanding of the Japanese open approach to teaching mathematics, we adapt selected methods to teach mathematics more effectively in the United States. Much of this approach is new to U.S. mathematics teachers, in that it has teachers working together in groups on lesson plans, and through a series of discussions and revisions, results in a greatly improved, effective plan. It also has teachers actively observing individual students or groups of students as they work on a problem, and then later comparing and discussing the students' work.

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

• Research in Mathematical Education
• /
• v.14 no.1
• /
• pp.51-65
• /
• 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 Home Economics Association
• /
• v.39 no.7
• /
• pp.37-58
• /
• 2001

The Purpose of this study was to examine the direct or indirect effects of psychological family environment self-control, and friends characteristics of middle school students on their problem behaviors. Data were corrected from 520 senior students of middle school (266 boys and 254 girls) who reside in Inchon. The level of problem behaviors was directly influenced positively by closeness with friends and negatively by self-control and open communication with mothers. And the level of problem behaviors was indirectly influenced positively by intrafamily conflicts and negatively by self-control, parental monitoring and open communication with parents. Self-control was the most powerful predicator of problem behaviors of middle school students. Self-control was directly influenced positively by open communication with fathers and negatively by intrafamily conflicts. Closeness with friends was directly influenced positively by parental monitoring and negatively by self-control and open communication with mothers.

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

• Journal of the Korea Society of Computer and Information
• /
• v.21 no.12
• /
• pp.1-10
• /
• 2016

In this paper, we attempt to prevent certain cases by tracing a history and making genogram about open source software and its modification using similarity of source code. There are many areas which use open source software actively and widely, and open source software contributes their development. However, there are many unconscious cases like ignoring license or intellectual properties infringe which can lead litigation. To prevent such situation, we analyze source code similarity using program dependence graph which resembles subgraph isomorphism problem, a typical NP-complete problem. To solve subgraph isomorphism problem, we utilized harmony search of metaheuristic algorithm and compared its result with a genetic algorithm. For the future works, we represent open source software as program dependence graph and analyze their similarity.