• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.2
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• pp.33-44
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• 1990

An efficient algorithm is developed for the linear programming relaxation of generalized multiple choice knaspack problem. The generalized multiple choice knaspack problem is an extension of the multiple choice knaspack problem whose relaxed LP problem has been studied extensively. In the worst case, the computational coimplexity of the proposed algorithm is of order 0(n. $n_{max}$)$^{2}$), where n is the total number of variables and $n_{max}$ denotes the cardinality of the largest multiple choice set. The algorithm can be easily embedded in a branch-and-bound procedure for the generalized multiple choice knapsack problem. A numerical example is presented and computational aspects are discussed.sed.

• The Mathematical Education
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• v.43 no.2
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• pp.151-162
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• 2004

For the past several years, performance assessment has been widely used by mathematics teachers. The superiority of performance assessment items compare to multiple choice items has been discussed by many researchers, however these discussions tend to be lack of empirical data. Thus, this study aims to examine the effectiveness of tree response items in comparison with multiple choice items. Using the information function in Item Response Theory(IRT), item information of free response items and multiple choice items from the Third International Mathematics and Science Study-Repeat(TIMSS-R) were obtained and compared. Test informations of the whole mathematics area as well as each content area of mathematics were computed. On average, tree response items yielded more information than multiple choice items, especially in measurement and data interpretation. This study also revealed that free response items estimated students' mathematics ability more accurately than multiple choice items with smaller number of items.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.3
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• pp.365-375
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• 1996

We consider an extension of the multiple choice linear knapsack problem and develop a fast algorithm of order $O(r_{max}n^2)$ by exploiting some new properties, where $r_{max}$ is the largest multiple choice number and n is the total number of variables. The proposed algorithm has convenient structures for the post-optimization in changes of the right-hand-side and multiple choice numbers. A numerical example is presented.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.519-527
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• 1995

By finding some new properties, we develop an O($r_{max}n^2$) algorithm for the generalized multiple choice linear knapsack problem where $r_{max}$ is the largest multiple choice number and n is the total number of variables. The proposed algorithm can easily be embedded in a branch-and-bound procedure due to its convenient structure for the post-optimization in changes of the right-hand-side and multiple choice numbers. A numerical example is presented.

• 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.

• Journal of Korean Elementary Science Education
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• v.23 no.4
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• pp.332-343
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• 2004

Multiple choice items have been widely used. However the difficulties in understanding and solving the items have not been known well. The purpose of this study is to analyze the difficulties and errors in the process of solving multiple choice items. Twelve multiple choice items were developed based on the Unit 5 Separation of Mixtures in the 4th grade. Four items which students had hardly given the correct answer were selected and six students were chosen for interview. Interview results were analyzed with regard to the errors in the process of solving the multiple choice items. The findings of this study are as follows: I) The students who misread and misunderstand the questions choose the incorrect answers. 2) Most of the students activate daily knowledge in the process of problem solving. 3) The students who have misconception with the daily knowledge or have no experiences choose incorrect answers, while students who activate both daily knowledge and school knowledge choose correct answer. 4) The students of high level commit errors mainly in the latter part of problem solving process, but the students of low level do from early.

• Journal of The Korean Association For Science Education
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• v.31 no.6
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• pp.887-900
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• 2011

Teachers use explanations to communicate important scientific ideas to students. Consequently, all biology teachers should be evaluated to determine how effective they are at constructing and communicating biological explanations. Open response questions are required to detect pre-service biology teachers' abilities to communicate robust and accurate scientific explanations. Nevertheless, multiple-choice questions are typically preferred by educators because of the common drawbacks of using open-response instruments, such as scoring time, inter-rater scoring disagreements, and delayed feedback to test takers. This study aims to measure pre-service biology teachers' competence in building scientific explanations and to investigate how accurately multiple-choice questions predict the results of open-response questions. One hundred twenty four pre-service biology teachers participated in the study and were administered 20 multiple-choice items and three open-response items designed to measure the accuracy and quality of their explanations of evolutionary change. The results demonstrated that pre-service teachers displayed higher competence when tested with multiple choice items than when tested with open response items. Moreover, scores derived from multiple-choice items poorly predicted the scores derived from open-response items. Multiple-choice items were also found to be poor measures of the consistency, purity and abundance of conceptual elements in teachers' evolutionary explanations. Additionally, many teachers held mixed-models composed of both scientific and naive ideas, which were difficult to detect using multiple-choice formats. Overall, the study indicates that multiple-choice formats are poorly suited to measuring several aspects of biology teachers' knowledge of evolution, including their ability to generate scientific explanations. This study suggests that open-response items should be used in teacher education programs to assess pre-service teachers' explanatory competency prior to being permitted to teach science to children.

• Journal of The Korean Association For Science Education
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• v.18 no.4
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• pp.643-650
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• 1998

In order to assess students' higher mental abilities, such as scientific inquiry thinking skills, the essay type items would be more adequate than the multiple choice itmes. However, due to the present condition in which a huge number of students take the examination at the same time, it is inevitable to use the multiple choice type. For this reason, it is necessary to develop a new type of multiple choice items which can reduce the disadvantages of the traditional multiple choice type and can achieve a similar level of validity as subjective type assessment. The three-tier multiple choice test items which can be used for a large sample of students and especially for scientific inquiry thinking abilities, are proposed and examined. The three-tier multiple choice test items asked firstly conclusion or the results of calculation or experimental apparatus, secondly the processes of calculation or of developing conclusion, thirdly asking relevant scientific concepts. For the item analysis, 1 point was given to the correct answer, while 0 point was given to the wrong one. The data were processed through the computer program developed in Turbo C 2.0 language with an IBM compatable personal computer. The average score in the sub-items asking for scientific concepts was lower than that in the sub-items asking for results or processes. The score of guessing by chance in the three-tier multiple choice items was only 0.13%, so that the probability of making correct answers by just guessing would be extremely low. The three-tier multiple choice items, even if they are objective items, are thought to assess thinking skills of the scientific inquiry meaningfully excluding the possibility of guessing by chance.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.31-41
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• 1992

An extension of generalized linear multiple choice knapsack problem [1] is presented and an algorithm of order 0([n .n$_{max}$]$_{2}$) is developed by exploiting its extended properties, where n and n$_{max}$ denote the total number of variables and the cardinality of the largest multiple choice set, respectively. A numerical example is presented and computational aspects are discussed.sed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.45
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• pp.291-299
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• 1998

We present a variant for the generalized continuous multiple-choice knapsack problem[1], which additionally has the well-known generalized lower bound constraints. The presented problem is characterized by some variables which only belong to the simple upper bound constraints and the others which are partitioned into both the continuous multiple-choice constraints and the generalized lower bound constraints. By exploiting some extended structural properties, an efficient algorithm of order Ο($n^2$1og n) is developed, where n is the total number of variables. A numerical example is presented.