• Research in Mathematical Education
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• v.2 no.1
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• pp.13-19
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• 1998

The What-If-Not strategy as proposed by Brown & Walter (1969) is one of the most effective strategies for problem posing. However, it has focused only on the aspect of algorithms for generating problems. The aim of this strategy and how it is used to accomplish the aim of the challenging phase are not clear. We need to clarify the aim of the What-If-Not strategy and to establish the process of the strategy for accomplishing the aim. The purpose of this article is to offer a new What-If-Not strategy by clarifying the aim of the challenging phase.

• Journal of The Korean Association For Science Education
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• v.24 no.1
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• pp.146-156
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• 2004

The purpose of this study is to look at the use of heuristics when a sixth grader solves a problem. Two research questions have been formulated: The similarities and differences in the use of heuristics when a student solves two problems that are science-knowledge-based and not science-knowledge-based, and the different types of prompts. A male sixth grade student participated in this study. All of the information for the study was collected in three interviews. The interviews began with observing the student's solving problems. The student was asked how and why he solved problem that way. There were some interactions between the researcher and the student during the interview procedures. As results of this study, eight general heuristics were used in both solutions: Check examples for support of an idea: check examples for exceptions to an idea: restate the problem: compare to known examples or patterns: make a hypothesis; check the relevance of other information present; use analogy: and recognize patterns/similarity. There seemed to be more similarities than differences in the type of general heuristic that were used in the two problem solutions. The student was systematic and consistent in his use of the general use of heuristics. Five types of interviewer prompts were detected in the two problem solutions, directional cues, modeling, clarity, problem posing, metacognition and validation.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.14 no.1
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• pp.8-16
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• 2014

We consider the visual barcode recognition problem in a noisy video data setup. Unlike most existing single-frame recognizers that require considerable user effort to acquire clean, motionless and blur-free barcode signals, we eliminate such extra human efforts by proposing a robust video-based barcode recognition algorithm. We deal with a sequence of noisy blurred barcode image frames by posing it as an online filtering problem. In the proposed dynamic recognition model, at each frame we infer the blur level of the frame as well as the digit class label. In contrast to a frame-by-frame based approach with heuristic majority voting scheme, the class labels and frame-wise noise levels are propagated along the frame sequences in our model, and hence we exploit all cues from noisy frames that are potentially useful for predicting the barcode label in a probabilistically reasonable sense. We also suggest a visual barcode tracking approach that efficiently localizes barcode areas in video frames. The effectiveness of the proposed approaches is demonstrated empirically on both synthetic and real data setup.

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

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.663-677
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• 1998

The development of Science and Technology and the social change require new paradigm in Education. In a traditional paradigm, learners have been regarded as a passive being and knowledge could be transmitted to learner. But within this paradigm, it is difficult to confront the social change and to develop problem solving skills in various context. This results in a new, alternative perspective, Constructive paradigm. As an alternative to the traditional settings, Constructive paradigm emphasizes the learner centered instruction. The reform movement in mathematics education including NCTM's standards revolves around this paradigm and the open education movement in our educational system is based on it. Open education values learner's interest, autonomy and internal motivation in learning. However, open education has been misunderstood by most of the teachers. It should be understood as the change of paradigm. In this study, as a way of helping students connect mathematics to their everyday lives and construct meaningful mathematical knowledge and concept, mathematical modelling is suggested. It consists of posing and specifying the real problem, formulation and constructing a mathematical model, analyzing and solving a mathematical problem. interpreting the solution and comparing with reality and communicating results. In this process, technology like computer can be a powerful tool. It can help students explore various problems more easily and concretely.

• Journal of Educational Research in Mathematics
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• v.16 no.4
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• pp.345-366
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• 2006

In this study, we investigated the methods of using the Cabri3D program for education of problem solving in school mathematics. Cabri3D is the program that can represent 3-dimensional figures and explore these in dynamic method. By using this program, we can see mathematical relations in space or mathematical properties in 3-dimensional figures vidually. We conducted classroom activity exploring Cabri3D with 15 pre-service leachers in 2006. In this process, we collected practical examples that can assist four stages of problem solving. Through the analysis of these examples, we concluded that Cabri3D is useful instrument to enhance problem solving ability and suggested it's educational usage as follows. In the stage of understanding the problem, it can be used to serve visual understanding and intuitive belief on the meaning of the problem, mathematical relations or properties in 3-dimensional figures. In the stage of devising a plan, it can be used to extend students's 2-dimensional thinking to 3-dimensional thinking by analogy. In the stage of carrying out the plan, it can be used to help the process to lead deductive thinking. In the stage of looking back at the work, it can be used to assist the process applying present work's result or method to another problem, checking the work, new problem posing.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.401-413
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• 2007

This study was some part of the main program making better the lessons in the classroom in which those should focus on the creative and self-leading method. The purpose of study was to create the model of Problem Based Learning and investigate its efficiency For the purpose, those researchers tried to reform the Myers' PBL model through the pilot experiment and could get the Model of Korean School PBL appropriate to the our classroom situations. Thirty six students from the enriched class in the junior high school 3rd grades was involved in the experiment for 8 weeks. The results showed that the experimental group had statistically significant difference in the real problem solving test and attitude test. Specially, those students also showed that the ability to translate the variety of problem situations mathematically was so excellent and they also had their own technique to generate the understand of problem solving situations, but they aid not show the significant ability to pose the meaningful problem.

• The Mathematical Education
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• v.60 no.4
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• pp.431-449
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• 2021

Elementary mathematics textbooks present contents for enhancing problem solving competency. Still, teachers find teaching problem solving to be challenging. To understand the supports textbooks are suggesting, this study examined tasks from the challenging/thinking and inquiry mathematics. We analyzed 288 mathematical activities based on an analytic framework from the 2015 revised mathematics curriculum. Then, we employed latent class analysis to classify 83 mathematical tasks as a new approach to categorize tasks. As a result, execution of the problem solving process was emphasized across grade levels but understanding of problems was varied by grade levels. In addition, higher grade levels had more opportunities to be engaged in collaborative problem solving and problem posing. We identified three task profiles: 'execution focus', 'collaborative-solution focus', 'multifaceted-solution focus'. In Grade 3, about 80% of tasks were categorized as the execution profile. The multifaceted-solution was about 40% in the thinking/challenging mathematics and the execution profile was about 70% in Inquiry mathematics. The implications for developing mathematics textbooks and designing mathematical tasks are discussed.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.143-157
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• 2016

This study aims to find out the feasibility and effectiveness of mathematical games as a way to provide primary pre-service teachers with doing mathematics. The game had induced the active participation of elementary pre-service teachers. Through transforming the game, the teachers have been able to experience of mathematical problem posing and generating mathematical representation. Based on this, we discuss the role of mathematical games as a method of pre-service teacher education.

• Research in Mathematical Education
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• v.17 no.2
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• pp.119-131
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• 2013

It is the first time that there is a subject, advanced mathematics in the 2009 revised high school curriculum. Therefore it is posing a challenge to the teachers who are teaching it. At the advanced level, it is important for learners to reflect on their mental mathematical activities. This research analysed pre-service secondary teachers' reflective thinking in solving the tasks specific for the teaching and learning of polar coordinates. We report how and through what process mathematical tasks that can create disequilibrium for pre-service secondary teachers enable reflective thinking and expand preservice secondary teachers' thoughts and recognition of defining reflective thinking in looking back on one's problem solving and thinking processes.