• Journal of the Korean School Mathematics Society
• /
• v.17 no.2
• /
• pp.291-319
• /
• 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 Information Technology Services
• /
• v.14 no.1
• /
• pp.129-143
• /
• 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.

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

• Structural Engineering and Mechanics
• /
• v.6 no.5
• /
• pp.517-527
• /
• 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 the Korean Society for Aeronautical & Space Sciences
• /
• v.33 no.10
• /
• pp.26-34
• /
• 2005

In this paper, a novel moving least squares interface welding method is proposed to carry out the coupled analysis of whole model composed of independently modeled finite element substructures with nodal mismatching interfaces. To verify the validity, and efficiency of the proposed interface welding method, various numerical examples are worked out including patch tests, convergence tests, and examples of coupled analyses of the structural systems with mismatching substructures. From the numerical tests, it is confirmed that one can efficiently carry out the coupled analysis of whole model composed of mismatching finite element substructures through the proposed method without any remeshing or any additional unknown.

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

• Language and Information
• /
• v.9 no.1
• /
• pp.51-68
• /
• 2005

This paper proposes an informational approach to the dative alternation in English following up on the Stochastic Optimality- Theoretic (OT) model by Bresnan and Nikitina (2003). While Bresnan and Nikitina's stochastic OT model resolves the crucial problem of 'gradience' unavoidably implicated in variation phenomena by applying the notion of probability to linguistic problems, it fails to account for the details of the unusually alternating examples, which normally would not alternate. More importantly, it fails to capture the focus effect involved in the alternation. This paper has worked out all the problematic examples by modifying the Bresnan and Nikitina model. This new account captures not only the unusual behavior of the less-alternating verbs and idioms but also the special focus effect of the common alternating verbs.

• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.61-74
• /
• 2014

This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.

• The Journal of the Acoustical Society of Korea
• /
• v.15 no.2E
• /
• pp.33-38
• /
• 1996

This paper provides an approach for representing an optimum vector quantizer by a scalar nonlinear gain-plus-additive noise model. The validity and accuracy of this analytic model is confirmed by comparing the calcuated model quantization errors with actual simulation of the optimum Linde-Buzo-Gray(LBG) vector quantizer. Using this model we frm MSE measure of an M-band filter bank codec in terms of the equivalent scalar quantizatin model and find the optimum FIR filter coefficients for each channel in the M-band structure for a given bit rate, given filter length, and given input signal correlation model. Specific design examples are worked out for 4-tap filters in the two-band paraunitary case. These theoretical results are confirmed by extensive Monte Carlo simulation.

• Proceedings of the Korea Concrete Institute Conference
• /
• 2004.05a
• /
• pp.466-471
• /
• 2004

Efficient numerical finite element analysis of creeping concrete structures requires the use Kelvin or Maxwell chain model, which is most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Bazant and Xi, but only for the case of a continuous retardation spectrum based on Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published microplane model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context. the Maxwell chain is more effective than Kelvin chain. because of the kinematic constraint of the microplanes used in M4. Determination of the continuous relaxation spectrum for Maxwell chain. based on the solidification theory, is outlined and numerical examples are presented.