• Communications of Mathematical Education
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• v.22 no.4
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• pp.489-503
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• 2008

It is not an easy matter to develop problems which help students understand mathematical concepts correctly and precisely. The aim of this paper is to review the merits and demerits of three problem types (i.e. one answer problems, multiple choice problems and proof problems) and to suggest some points that should be taken into consideration in problem making. First, we presented the merits and demerits of three types of problems by examining actual examples. Second, we discussed some examples of misleading problems and the ways to make desirable ones. Finally, on the basis of our examination and discussion, we suggested some points that should be kept in mind in problem making. The major suggestions are as follows; i) In making one answer problems, we should consider the possibility of sitting a solution by wrong precesses, ii) In formulating multiple choice tests which are layered for their easiness of grading, we should take into account the importance of checking whether the students are fully understanding the concepts, iii) We may depend on the previous research result that multiple choice tests for proof problems can be helpful for the students who have insufficient math background. Besides those suggestions, we made an overall proposal that we should endeavor to find ways to implement the demerits of each problem type and to develop instructive problems that can help students understanding of math.

• The Mathematical Education
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• v.57 no.3
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• pp.197-213
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• 2018

Descriptive problems can be used to grow student's ability of thinking logically and creatively, because it shows if the students had a reasonable way of thinking. Rate of descriptive problems is increasing in middle and high school exams. However, students in middle and high schools are generally used to answering multiple-choice or short-answer questions rather than describing the solving process. The purpose of this paper is to gain a theoretic ground to increase the rate of descriptive problems. In this study, students were to solve some multiple-choice problems, and after a few weeks, to solve the problems of same contents in the form of descriptive problems which requires the students to write the solving process. The difference of the scores were measured for each problems to each students, and students were asked what they think the reason for rise or fall of the score is. The result is as follows: First, average scores of 7 of 8 problems used in this study had fallen when it was in descriptive form, and for 5 of them in the rate of 11.2%~16.8%. Second, the main reason of falling is that the students have actual troubles of describing the solving process. Third, in the case of rising, the main reason was that partial scores were given in the descriptive problems. Last, there seems a possibility gender difference in the reason of falling. From these results, followings are suggested to advance the learning, teaching and evaluation in mathematics education: First, it has to be emphasized enough to describe the solving process when solving a problem. Second, increasing the rate of descriptive problems can be supported as a way to advance the evaluation. Third, descriptive problems have to be easier to solve than multiple-choice ones and it is convenient for the students to describe the solving process. Last, multiple-choice problems have to be carefully reviewed that the possibility of students' choosing incorrect answer with a small mistake is minimal.

• 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 Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.661-667
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• 1997

We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.

• Research in Mathematical Education
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• v.14 no.1
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• pp.1-10
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• 2010

The paper focuses on a type of mathematics competence noted as synthetic. It is needed for success in multiple choice competition problems and it is crucial for the further development of advanced school students. The concept of synthetic competence includes a large fraction of mathematical competences, but also competences and skills related to informatics and linguistics. The general structure of a multiple choice competition is considered as the first level of assessment of the mathematics component of the synthetic competence. As the second level under consideration is the set of complex tasks in a competition test any of which is a bouquet of ideas. Our standpoint on the didactic specifics and goals of the two levels in perspective of the gifted education is briefly presented in the article and some examples are given.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.505-516
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• 2020

This study shows that image deblurring problems can be transformed into the multi-parameter Tikhonov type with multiple right hand sides. Also, this paper proposes the extension of the global generalized cross validation to obtain an appropriate choice of the regularization parameters for this problem. The experimental results of using the preconditioned Gl-CGLS algorithm were analyzed.

• International Journal of Contents
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• v.5 no.1
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• pp.51-55
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• 2009

In this paper, we present a structure of personalized e-Learning system to study for a test formalized by uniform multiple-choice using on/off line mixed estimations as is the case of Driver :s License Test in Korea. Using the system a candidate can study toward the license through the Internet (and/or mobile instruments) within the personalized concept based on IRT(item response theory). The system accurately estimates user's ability parameter and dynamically offers optimal evaluation problems and learning contents according to the estimated ability so that the user can take possession of the license in shorter time. In order to establish the personalized e-Learning concepts, we build up 3 databases and 2 agents in this system. Content DB maintains learning contents for studying toward the license as the shape of objects separated by concept-unit. Item-bank DB manages items with their parameters such as difficulties, discriminations, and guessing factors, which are firmly related to the learning contents in Content DB through the concept of object parameters. User profile DB maintains users' status information, item responses, and ability parameters. With these DB formations, Interface agent processes user ID, password, status information, and various queries generated by learners. In addition, it hooks up user's item response with Selection & Feedback agent. On the other hand, Selection & Feedback agent offers problems and content objects according to the corresponding user's ability parameter, and re-estimates the ability parameter to activate dynamic personalized learning situation and so forth.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.7 no.1
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• pp.253-263
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• 2017

As needs for knowledge on Korean history and the attention of the people are rapidly increasing, various smartphone applications for learning the history have appeared during recent years. These applications provide multiple choice questions to users through their own problem banks. But, since these questions are selected from the fixed set of problems that are stored previously, the learning efficiency of users is inevitably decreased when they use the applications repeatedly. In this paper, we present a question generation system named K-History which generates multiple choice questions in an automatic way using the database on the history of Korea. In addition, we also describe the development of the application Korean History Infinite Challenge as a learning application for Korean history. To develop K-History, we classify typical types of learning problems through various problems based on Korean history learning materials, proposing algorithms to generate problems according to the types found. Through the developed techniques, various learning systems can reduce the cost for creating questions, while increasing the learning efficiency of users.

• 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.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.55-70
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• 2001

Artificial neural network(ANN) models have been widely used for the classification problems in business such as bankruptcy prediction, credit evaluation, etc. Although the application of ANN to classification of consumers＇ choice behavior is a promising research area, there have been only a few researches. In general, most of the researches have reported that the classification performance of the ANN models were better than conventional statistical model Because the survey data on consumer behavior may include much noise and missing data, ANN model will be more robust than conventional statistical models welch need various assumptions. The purpose of this paper is to study the potential of the ANN model for forecasting consumers＇ choice behavior based on survey data. The data was collected by questionnaires to the shoppers of department stores and discount stores. Then the correct classification rates of the ANN models for the training and test sample with that of multiple discriminant analysis(MDA) and logistic regression(Logit) model. The performance of the ANN models were betted than the performance of the MDA and Logit model with respect to correct classification rate. By using input variables identified as significant in the stepwise MDA, the performance of the ANN models were improved.