• The Mathematical Education
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• v.46 no.4
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• pp.371-388
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• 2007

This is a case study trying to understand from the view of affordance which certain three middle school students perceive an activation of previous knowledge in the course of problem solving when they solve algebra word problems with a previous knowledge. The results of this study showed that at first, every subjects perceived the text as affordance which explaining superficial similarities, that is, a working(painting)situation rather than problem structure and then activated the related solution knowledge on the ground of the experience of previous problem solving which is similar to current situation. The subject's applying process for solving knowledge could be arranged largely into two types. The first type is a numeral information connected with the described problem situation or a symbolic representation of mathematical meaning which are the transformed solution applied process with a suitable solution formula to the current problem. This process achieved by constructing a virtual mental model that indicating mathematical situation about the problem when the solver read the problem integrating symbolized information from the described text. The second type is a case that those subjects symbolizing a formal mathematical concept which is not connected with the problem situation about the described numeral information from the applied problem or the text of mathematical meaning, which process is the case to perceive superficial phrases or words that described from the problem as affordance and then applied previously used algorithmatical formula as it was. In conclusion, on the ground of the results of this case study, it is guessed that many students put only algorithmatical knowledge in their memories through previous experiences of problem solving, and the memories are connected with the particular phrases described from the problems. And it is also recognizable when the reflection process which is the last step of problem solving carried out in the process of understanding the problem and making a plan showed the most successful in problem solving.

• Educational Technology International
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• v.11 no.1
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• pp.93-117
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• 2010

The purpose of this study was to develop the problem solving instruction facilitating novice learner to represent the problem. For the purpose, we mainly focused on three aspects of problem solving. First, learner should represent the targeted problem and its solutions for problem solving. Second, from crucial notions of cognitive load theory, learner's mental load should be optimized for problem representation. Third, for optimizing students' mental load, experts may support making their thinking more visible and mapping from their intuition to expert practice. We drew the design principles as follows. First, since providing worked examples for the targeted problem has been considered to minimize analogical errors as well as reduce cognitive load in problem representation at line of problem solving and instructional research, it is needed to elaborate the way of designing. The worked example alternatively corresponds to expert schema that consists of domain knowledge as well as strategies for expert-like problem representation and solution. Thus, it may help learner to represent what the problem is and how to solve it in problem space. Second, principle can be that expert should scaffold learner's self-explanations. Because the students are unable to elicit the rationale from worked example, the expert's triggering scaffold may be critical in that process. The unexplained and incomplete parts of the example should be completed not by expert's scaffold but by themselves. Critical portion of the expert's scaffold is to explain about how to apply and represent the given problem, since students' initial representations may be reached at superficial or passive pattern of example elaboration. Finally, learner's mental model on the designated problem domain should be externalized or visualized for one's reflection as well as expert's scaffolding activities. The visualization helps learner to identify one's partial or incorrect model. The correct model of learner could be constructed by expert's help.

• The Mathematical Education
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• v.50 no.1
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• pp.1-12
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• 2011

It is the aim of this paper to study the target problem solving process in reference to the base problem. We observed closely how students solve the target problem in reference to the base problem. The students couldn't solve the target problem, although they succeed to find the base problem. This comes from failing to discover the structural similarity between the target problem and the base problem. Especially it is important to cognize the proper corresponding of primary components between the base problem and target problem. And there is sometimes a part component of the target problem equivalent to the base problem and the target problem can't be solved without the insight into this fact. Consequently, finding the base problem fail to reach solving the target problem without the insight into their structural similarity. We have to make efforts to have an insight into the structural similarity between the target problem and the base problem to solve the target problem.

• Journal of Engineering Education Research
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• v.18 no.3
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• pp.39-45
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• 2015

Many methods have been suggested for a creative problem solving approach. TRIZ approach is ranked top in its practical application because it is originated from the real patent analysis. This approach is assumed to be generic which can be applied to any types of problems regardless of problem type and its domain. The objective of this study is to propose a creative problem solving approach using TRIZ's contradiction analysis, then introduce a case study of applying this approach to a creative design coursework. Main topic covers a creative problem solving approach, a problem definition using TRIZ contradiction analysis, finding invention principles, and problem solving from the generic approach. For the course project, Roborobo tool is adopted to implement the design concept. This coursework helps students finding a general problem solving approach, and applying a generic solution for their specific problem domain.

• Research in Mathematical Education
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• v.10 no.3 s.27
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• pp.151-167
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• 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
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• v.3 no.1
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• pp.1-23
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• 2001

In this paper, contents related to problem solving in 7th elementary mathematics curriculum analyzed in five aspects: problem solving stages, problem solving strategies, problems, problem posing, and assessment on problem solving abilities. From the results and processes of analysis, following conclusions are obtained: First, it is difficult to say the contents related to problem solving in 7th elementary mathematics curriculum are prepared organically. Second, it is difficult to say that contents related to problem solving in 7th elementary mathematics curriculum reflect results of recent researches.

• Journal of The Korean Association For Science Education
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• v.24 no.4
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• pp.774-784
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• 2004

In the previous study, six factors which could disturb students' problem solving in an everyday context were identified and discussed. In this study, teaching materials to help students overcome those disturbing factors for successful problem solving in an everyday context were developed and applied to twenty-nine grade 10 students, and the effects of teaching materials were analyzed. According to the analysis of the correlation between the performance in everyday context problem solving and the benefit from the teaching materials, it was found that students who received the help from the teaching materials showed better performance with statistical significance. And students noted that teaching materials were helpful for them to solve the physics problems. Analyzing the overall performance of students in solving the everyday context problem, students in the experimental group showed better performance than the control group and this performance difference was larger among low-score students in school science testing. However, these differences were not statistically significant because the sample size was small. And, based on the analysis of interviews with students, it was also found that some students who showed low performance might not receive help from the teaching materials because the materials were too complex to be read easily, or because the basic concepts needed to solve the problem were not understood. Therefore, the results obtained from the interviews will be used to design more effective teaching for problem solving in an everyday context.

• Educational Technology International
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• v.13 no.2
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• pp.283-312
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• 2012

Problem-solving ability is one of the most important learning outcomes for students to compete and accomplish in a knowledge-based society. It has been empirically proven that visualization plays a central role in problem-solving. The best performing problem-solver might have a strong visualization tendency. However, there is little research as to what factors of visualization tendency primarily related to problem-solving ability according to phases of problem-solving. The purpose of this study is to identify the relationship between visualization tendency and problem-solving ability, to determine which factors of visualization tendency influence problem-solving ability in each phase of problem-solving, and to examine different problem-solving ability from the perspective of the levels of visualization tendency. This study has found out that visualization tendency has a significant correlation with problem-solving ability. Especially, Generative Visualization and Spatial-Motor Visualization as sub-visualization tendency were more strongly related to each phase of problem-solving. It indicates that visualization tendency to generate and operate mental processing can be considered a major cognitive skill to improve problem-solving ability. Furthermore, students who have high visualization tendency also have significantly higher problem-solving ability than students with low visualization tendency. It shows that the levels of visualization tendency can predict variables related to students' problem-solving ability.

• Journal of Korean Institute of Industrial Engineers
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• v.9 no.2
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• pp.3-8
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• 1983

The multiple choice knapsack problem is modified. To solve this modified multiple choice knapsack problem, Lagrangian relaxation is used, and to take advantage of the special structure of subproblems obtained by decomposing this relaxed Lagrangian problem, a modified ranking algorithm is used. The K best rank order solutions obtained from each subproblem as a result of applying modified ranking algorithm are used to formulate restricted problems of the original problem. The optimality for the original problem of solutions obtained from the restricted problems is judged from the upper bound and lower bounds calculated iteratively from the relaxed problem and restricted problems, respectively.

• Journal of the Korean Society of Earth Science Education
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• v.7 no.1
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• pp.133-143
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• 2014

The purpose of this study was to examine the effect of scientific discussion classes focusing problem finding on the primary school students' scientific creative problem solving ability, science process skills and attitude toward science class. To verify this research problem, the subject of this study was fifth-grade students selected from four classes of M elementary school located in Busan city. For four months, the experimental group of 51 students was taught using the "scientific discussion classes focusing problem finding". The control group also of 53 students was taught in normal classes which used a text-book. All students were given pre and post test to verify the effects of scientific discussion classes focusing problem finding on the primary school students' scientific creative problem solving ability, science process skills and attitude toward science class. The results from this study are as the following. First, the scientific discussion classes focusing problem finding were effective in scientific creative problem solving ability among the primary school students. It is possibly because in the process where one student compare his/her own thoughts with the others' ones and discuss them. Second, the scientific discussion classes focusing problem finding were effective in science process skills among the primary school students. Third, the scientific discussion classes focusing problem finding were effective in attitude toward science class. In conclusion, the scientific discussion classes focusing problem finding had positive effects on improvement of primary school students' scientific creative problem solving ability, science process skills and also could lead to a change in students' cognition about science class to a positive way. Therefore, the scientific discussion class focusing problem finding is hopefully to be provided as an effective instructive strategy of science class in school in the future.