• Journal of Educational Research in Mathematics
• /
• v.22 no.3
• /
• pp.331-352
• /
• 2012

The purpose of the study is to verify what cognitive variables have significant effect on proportional problem solving. For this aim, the study classified proportional problem into well-structured, moderately-structured, ill-structured problem by the level of structuredness, then classified the cognitive variables as well into factual algorithm knowledge, conceptual knowledge, knowledge of problem type, quantity change recognition and meta-cognition(meta-regulation and meta-knowledge). Then, it verified what cognitive variables have significant effects on 6th graders' proportional problem solving abilities through multiple regression analysis technique. As a result of the analysis, different cognitive variables effect on solving proportional problem classified by the level of structuredness. Through the results, the study suggest how to teach and assess proportional reasoning and problem solving in elementary mathematics class.

• Education of Primary School Mathematics
• /
• v.15 no.2
• /
• pp.59-75
• /
• 2012

This study aims to find whether the solutions for well-structured problems learned in school can be transferred to the moderately-structured problem and ill-structured problem. For these purpose, research questions were set up as follows: First, what are the patterns of changes in strategies used in solving the mathematics problems with different level of structuredness? Second, From the group using and not using proportion algorithm strategy in solving moderately-structured problem and ill-structured problem, what features were observed when they were solving that problems? Followings are the findings from this study. First, for the lower level of structuredness, the frequency of using multiplicative strategy was increased and frequency of proportion algorithm strategy use was decreased. Second, the students who used multiplicative strategies and proportion algorithm strategies to solve structured and ill-structured problems exhibited qualitative differences in the degree of understanding concept of ratio and proportion. This study has an important meaning in that it provided new direction for transfer and analogical problem solving study in mathematics education.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1994.04a
• /
• pp.236-243
• /
• 1994

In this paper we consider the part-machine cell formation decision of the generalized Group Technology(GT) problem in which multiple process routes can be generated for each part. The existing p-median model and similarity coefficient algorithm can solve only small-sized or well-structured cases. We suggest an assignment method for the cell formation problem. This method uses an assignment model which is a simple linear programming. Numerical examples show that our assignment method provides good separable cells formation even for large-sized and ill-structured problems.

• The Journal of Korean Association of Computer Education
• /
• v.8 no.5
• /
• pp.43-50
• /
• 2005

The purpose of the study was to compare the effects of two instructional methods, which were the instructor-led instruction and the simulation delivery instruction on students' well-structured and ill-structured problem solving performance and motivation. 29 undergraduate students participated in the study and repeated measure design was used. We found significant difference of means in ill-structured problem solving performance and only relevance scale in motivation.

• The Mathematical Education
• /
• v.60 no.2
• /
• pp.133-157
• /
• 2021

Ill-structured problems have drawn attention in that they can enhance problem-solving skills, which are essential in future societies. The purpose of this study is to analyze and evaluate students' spatial reasoning(Intrinsic-Static, Intrinsic-Dynamic, Extrinsic-Static, and Extrinsic-Dynamic reasoning) and problem solving abilities(understanding problems and exploring strategies, executing plans and reflecting, collaborative problem-solving, mathematical modeling) that appear in ill-structured problem-solving. To solve the research questions, two ill-structured problems based on the geometry domain were created and 11 lessons were given. The results are as follows. First, spatial reasoning ability of sixth-graders was mainly distributed at the mid-upper level. Students solved the extrinsic reasoning activities more easily than the intrinsic reasoning activities. Also, more analytical and higher level of spatial reasoning are shown when students applied functions of other mathematical domains, such as computation and measurement. This shows that geometric learning with high connectivity is valuable. Second, the 'problem-solving ability' was mainly distributed at the median level. A number of errors were found in the strategy exploration and the reflection processes. Also, students exchanged there opinion well, but the decision making was not. There were differences in participation and quality of interaction depending on the face-to-face and web-based environment. Furthermore, mathematical modeling element was generally performed successfully.

• Journal of The Korean Association For Science Education
• /
• v.32 no.4
• /
• pp.570-585
• /
• 2012

The Korean national curriculum for secondary school emphasizes scientific problem solving. In line with the national curriculum, many educational studies have been conducted in relation to science education. The objects of these studies were well-defined and well-structured problems. The studies were criticized for overlooking ill-defined and ill-structured problems. Some research has dealt with problem finding in ill-structured problems, which is related to creativity. There is a need for a study of scientific problem finding process in an ill-structured problem situation, because this study will help teachers wanting to teach scientific problem-finding in an ill-structured problem situation. The objective of this study was to conduct an empirical study on the scientific problem finding process in an ill-structured problem situation. One task of scientific problem finding in an ill-structured problem situation was assigned to 92 university students; thereafter, 32 of them participated in the research through interviews. Results indicated that the scientific problem finding process depended on initial clues and tentative solutions. Initial clues were affected by students' experiences, such as major classes, films, and novels. Tentative solutions were influenced by background knowledge of the tasks. Students screened information browsed on the Internet. They applied some standards for selection, particularly emphasized reliability standards, which are supposed to be studied in other contexts. All the students used assumptions to make their problems appear probable, which could be a useful tool to articulate.

• 제어로봇시스템학회:학술대회논문집
• /
• 1992.10b
• /
• pp.575-580
• /
• 1992

Mixed H$_{2}$/H$_{\infty}$ robust control synthesis is considered for finite dimensional linear time-invariant systems under the presence of diagonal structured uncertainties. Such uncertainties arise for instance when there is real perturbation in the nominal model of the state space system or when modeling multiple (unstructured) uncertainty at different locations in the feedback loop. This synthesis problem is reduced to convex optimization problem over a bounded subset of matrices as well as diagonal matrix having certain structure. For computational purpose, this convex optimization problem is further reduced into Generalized Eigenvalue Minimization Problem where a powerful algorithm based on interior point method has been recently developed..

• Journal of Elementary Mathematics Education in Korea
• /
• v.22 no.3
• /
• pp.309-330
• /
• 2018

The purpose of this study is to identify possibility of a mathematical problem posing ability by presenting problem posing tasks with different degrees of structure according to the study of Stoyanova and Ellerton(1996). Also, the results of this study suggest the direction of gifted elementary mathematics education to increase mathematical creativity. The research results showed that mathematical problem posing ability is likely to be a factor in identification of gifted students, and suggested directions for problem posing activities in education for mathematically gifted by investigating the characteristics of original problems. Although there are many criteria that distinguish between gifted and ordinary students, it is most desirable to utilize the measurement of fluency through the well-structured problem posing tasks in terms of efficiency, which is consistent with the findings of Jo Seokhee et al. (2007). It is possible to obtain fairly good reliability and validity in the measurement of fluency. On the other hand, the fact that the problem with depth of solving steps of 3 or more is likely to be a unique problem suggests that students should be encouraged to create multi-steps problems when teaching creative problem posing activities for the gifted. This implies that using multi-steps problems is an alternative method to identify gifted elementary students.

• Journal of The Korean Association For Science Education
• /
• v.28 no.8
• /
• pp.860-869
• /
• 2008

The purpose of this study is to suggest an instructional direction for improving scientific inquiry problem-finding ability of the scientifically-gifted. For this purpose, this study has made an in-depth analysis of the scientific inquiry problems generated by the scientifically-gifted in Problem-Finding Activity in Ill-structured Inquiry Situation (PFAIIS) and Problem-Finding Activity in Well-structured Inquiry Situation (PFAWIS). The results of this study turned out to be as follows: First, most of the problems generated in PFAIIS and PFAWIS could be categorized into seven types (measurement, method, cause, possibility, what, comparison, relationship) according to the inquiry objectives, while the frequency of each type shown in each inquiry objective was a little different. Second, the frequency of scientific concepts stated in inquiry problem was more in PFAWIS than in PFAIIS. But the scientific concepts were shown more diversely in PFAIIS than in PFAWIS. Therefore, results of this study have the following educational implications. First, it is necessary to offer various opportunities of problem-finding activity under ill-structured scientific Inquiry situation. Second, it is needed to emphasize that a new inquiry problem can be found out even during general scientific experiment and frequently to discuss inquiry problems generated during an experiment. Third, it is needed to encourage the scientifically-gifted to generate a scientific inquiry problem based on at least more than seven types.

• Journal of Periodontal and Implant Science
• /
• v.45 no.1
• /
• pp.2-7
• /
• 2015

A fundamental problem in analyzing complex multilevel-structured periodontal data is the violation of independency among the observations, which is an assumption in traditional statistical models (e.g., analysis of variance and ordinary least squares regression). In many cases, aggregation (i.e., mean or sum scores) has been employed to overcome this problem. However, the aggregation approach still exhibits certain limitations, such as a loss of power and detailed information, no cross-level relationship analysis, and the potential for creating an ecological fallacy. In order to handle multilevel-structured data appropriately, mixed effects models have been introduced and employed in dental research using periodontal data. The use of mixed effects models might account for the potential bias due to the violation of the independency assumption as well as provide accurate estimates.