• Journal of Information Technology Services
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• v.14 no.1
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• pp.129-143
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• 2015

This study has two goals. The first goal is to investigate whether worked examples are effective in the ill-defined domain with on-line learning and the second goal is to find out which components (conceptual or procedural knowledge) of worked examples are effective factor at the given learning environment. We carried out three experiments in which Korean undergraduate or graduate students were working in three or four conditions of worked examples (CWE, PWE, CPWE, or the control group). While experiment 1 conducted in on-line learning environment did not find any effect and difference among groups and also any logical reason for those results, experiment 2 conducted in completely controlled laboratory setting with less knowledgeable students showed the clear difference among groups by the order CPWE, PWE, and CWE. Experiment 3 in which highly knowledgeable and motivated students were presented the same materials in more controlled on-line learning environment indicated the difference among groups by the order CWE, CPWE, and PWE. The results were discussed within the framework of cognitive load theory.

• Journal of the Korean School Mathematics Society
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• v.17 no.2
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• pp.291-319
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• 2014

The purpose of this study is to investigate students' thinking and understanding through working on Worked-out Examples on numbers and operations, specifically, radical and real numbers and operations in the middle grades. For this purpose, we developed a set of Worked-out Examples; middle school students independently worked on them. Then two students were interviewed. These data were analyzed by using the framework of mathematical proficiency. The data analysis suggested that the students seemed to go through the processes involving a combination of understanding and computation, computation and reasoning, and understanding, computation and reasoning. Also, it appeared that most of the students have difficult solving problems involving with radical and real numbers in related to strategic competence.

• Journal of Veterinary Clinics
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• v.31 no.4
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• pp.288-292
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• 2014

A critical assumption of the standard sample size calculation is that the response (outcome) for an individual patient is completely independent to that for any other patient. However, this assumption no longer holds when there is a lack of statistical independence across subjects seen in cluster randomized designs. In this setting, patients within a cluster are more likely to respond in a similar manner; patient outcomes may correlate strongly within clusters. Thus, direct use of standard sample size formulae for cluster design, ignoring the clustering effect, may result in sample size that are too small, resulting in a study that is under-powered for detecting the desired level of difference between groups. This paper revisit worked examples for sample size calculation provided in a previous paper using nomogram to easy to access. Then we present the concept of cluster design illustrated with worked examples, and introduce design effect that is a factor to inflate the standard sample size estimates.

• Journal of The Korean Association For Science Education
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• v.16 no.3
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• pp.295-302
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• 1996

The purpose of this study was to investigate the effects of training and use of worked-example on chemical problem-solving learning. Schema acquisition and rule automation are the basic components of skilled problem-solving, which are dependent on appropriately focused attention and sufficient cognitive resources. Training and use of worked-example facilitate schema acquisition and rule automation, so improve problem-solving learning. The subjects of this study were 60 high school students. The average age was 17 years old. Then, they were randomly assigned to each groups and the chemical reaction problems used as experimental materials. The independent variables of this study were training and use of worked-examples and dependent variables were time for solution and the number of error. The results of this study were as follows; 1. The worked-example groups spent significantly less time on solution for acquisition problems than the conventional problem groups. 2. The long-acquisition groups spent significantly less time on solution for acquisition problems than the short-acquisition groups. 3. The modified worked-example groups did not spend significantly less time on solution for acquisition problems than the worked-example groups.

• Korean Journal of Cognitive Science
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• v.21 no.4
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• pp.627-653
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• 2010

The present study proposes and examines a new type of multiple-choice math test. In this format, the options are the intermediate derivatives of the math problem solution process rather than the final answers. This idea originates from the studies on the effect of worked-out examples. In these studies, it has been shown that students learn better when they were presented with worked-out examples than when presented with final answers by themselves. In line with these findings, we introduced the intermediate derivatives of the solution process as the options of multiple-choice items so that the test-taker will have a chance to examine the solution process. The test was implemented as a computerized test in which students can solve problems in a short answer format, and then pick a multiple-choice option which appears when requested. The experimental group had multiple-choice options which were intermediate derivatives of the solution process, and the control group had the final answers as the options as in most multiple-choice tests. The participants were 6th graders in elementary school. The posttest results revealed that the average score of the experimental group was higher than that of the control group. The results suggest that tests that use intermediate derivatives of the problem solution process as options can be used as learning tools in the classrooms. Finally, directions for further studies were discussed.

• Korean Journal of Cognitive Science
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• v.1 no.1
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• pp.103-127
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• 1989

Learning systems by using examples have been developed which include ALEX, LP, and LEX.Specially Silver's LP systems suggerts the method to use a seyuence of operators, which was applied to the worked example, to sove a symbolic equation.This paper presents the new learning system, called LRD, in which generalization and discrimination steps are suggerted to solv all the problems similar to the worked example.The system LRD is illustrated by the problem of finding the ranges of transcendentral functions and compared to LP and LEX by the problems discussed in them.

• 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.

• Structural Engineering and Mechanics
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• v.6 no.5
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• pp.517-527
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• 1998

This paper describes an exact method of analysis for natural vibration of diagonal networks by considering an equivalent cyclic periodic structure and adopting the double U-transformation technique. Both a lumped mass system and a distributed mass system are considered to investigate the diagonal networks. The exact solution for the frequency equations and the natural modes of the networks can be derived. As numerical examples, square diagonal cable networks with different meshes are worked out.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.20-28
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• 2007

A fast and robust method of grid generation to multiple functions has been developed for flow analysis in three dimensional space. It is based on the Non-Uniform Rational B-Spline(NURBS) of an approximation method. Many of NURBS intrinsic properties are introduced and much more easily understood. The grid generation method, details of numerical implementation. examples of application, and potential extensions of the current method are illustrated in this paper. The object of this study is to develop the surface grid generation and the grid cluster techniques capable of resolving complex flows with shock waves, expansion waves, shear layers. The knot insert method of Non-Uniform Rational B-Spline seems well worked. In addition, NURBS has been widely utilized to generate grids in the computational fluid dynamics community. Computational examples associated with practical configurations have shown the utilization of the algorithm.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.