• The Mathematical Education
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• v.57 no.3
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• pp.311-328
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• 2018

In school mathematics, the concept of an average is not a concept that is limited to a unit of statistics. In particular, high school students will learn about arithmetic mean and geometric mean in the process of learning absolute inequality. In calculus learning, the concept of average is involved when learning the concept of average speed. The arithmetic mean is the same as the procedure used when students mean the test scores. However, the procedure for obtaining the geometric mean differs from the procedure for the arithmetic mean. In addition, if the arithmetic mean and the geometric mean are the discrete quantity, then the mean rate of change or the average speed is different in that it considers continuous quantities. The average concept that students learn in school mathematics differs in the quantitative nature of procedures and objects. Nevertheless, it is not uncommon to find out how students construct various mathematical concepts into mathematical knowledge. This study focuses on this point and conducted the interviews of the students(three) in the second grade of high school. And the expression of students in the process of average concept formation in arithmetic mean, geometric mean, average speed. This study can be meaningful because it suggests practical examples to students about the assertion that various scholars should experience various properties possessed by the average. It is also meaningful that students are able to think about how to construct the mean conceptual properties inherent in terms such as geometric mean and mean speed in arithmetic mean concept through interview data.

• Research in Mathematical Education
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• v.12 no.1
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• pp.49-66
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• 2008

In this paper we present a cognitive developmental analysis of the arithmetic mean concept. This analysis leads us to a hierarchical classification at different levels of understanding of the responses of 227 students to a questionnaire which combines open-ended and multiple-choice questions. The SOLO theoretical framework is used for this analysis and we find five levels of students' responses. These responses confirm different types of difficulties encountered by students regarding their conceptualization of the arithmetic mean. Also we have observed that there are no significant differences between secondary school and university students' responses.

• Journal of Korea Multimedia Society
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• v.20 no.6
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• pp.935-949
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• 2017

The purpose of this study was to analyze the characteristics of virtual manipulatives apps that can be used to teach students struggling to learn mathematics. To achieve this goal, ten general characteristics of 23 virtual manipulatives apps were evaluated. The instructional, interface, and interactive design features of apps were also evaluated on five-point scale ratings of 18 items. In addition, SPSS frequency analysis and the correlation between each feature was analyzed. Frequently presented instructional contents among 23 virtual manipulatives apps were geometry, arithmetic operation, number concept and measurement. The frequently presented level of instructional contents was lower grade elementary school and kindergarten age. The frequently presented instructional type was the simulation. Regarding the design features, instructional design was rated as the highest (mean = 3.7); interactive design (mean = 3.6) and interface design (mean = 3.3) were also rated higher than neural. In addition, as the learning strategy was appropriately presented, it was evaluated that there was less screen linkage and content error.

• Journal of Nuclear Fuel Cycle and Waste Technology(JNFCWT)
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• v.2 no.1
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• pp.77-85
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• 2004

Regulations and guidelines for radioactive waste disposal require detailed information about the characteristics of radioactive waste drums prior to transport to the disposal sites. However, estimation of radionuclide concentrations in the drummed radioactive waste is difficult and unreliable. In order to overcome this difficulty, scaling factor (SF) method has been used to assess the activities of radionuclides, which could not be directly analyzed. A radioactive waste assay system has been operated at Korean nuclear power plant (KORI site) since 1996 and consolidated SF concept has played a dominant role in the determination of radionuclide concentrations. However, SFs are somewhat dispersive and limited in KORI site. Therefore establishment of the assay system using more improved SFs is planned and progressed. In this paper, the scope of research is briefly introduced. For the selection of more reliable activity determination method, the accuracy of predicted SF values for each activity determination method is compared. From the comparison of each activity determination method, it is recommended that SF determination method should be changed from the arithmetic mean to the geometrical mean for more reliable estimation of radionuclide activity. Arithmetic mean method and geometric mean method are compared based on the data set in KORI system. And, this change of SF determination method will prevent an inordinate over-estimation of radionuclide inventory in radwaste drum.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.1
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• pp.49-64
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• 2003

Although assembly sequence planning is an essential task in assembly process planning, it is known as one of the most difficult and time consuming jobs because its complexity is increased geometrically when the number of parts in an assembly is increased. The purpose of this study is to develop a more efficient algorithm for generating assembly sequences automatically. By considering subassemblies, a new heuristic method generates a preferred parallel assembly sequence that can be used in robotic assembly systems. A parallel assembly sequence concept provides a new representation scheme for an assembly in which the assembly sequence precedence information is not required. After an user inputs both the directional mating relation information and the mating condition information, an assembly product is divided into subgroups if the product has cut-vertices. Then, a virtual disassembly process is executed to generate alternate parallel assembly sequences with intermediate assembly stability. Through searching parts relations in the virtual disassembly process, stable subassemblies are extracted from translation-free parts along disassembling directions and this extraction continues until no more subassemblies are existed. Also, the arithmetic mean parallelism formula as a preference criterion is adapted to select the best parallel assembly sequence among others. Finally a preferred parallel assembly sequence is converted to an assembly BOM structure. The results from this study can be utilized for developing CAAPP(Computer-Aided Assembly Process Planning) systems as an efficient assembly sequence planning algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.26 no.4
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• pp.71-82
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• 2001

Using the computer simulation method, we invest19ate the probability distribution of maximum eigenvalue of pair-wise comparison matrix, which has been used as a parameter for measuring the consistency of responses in analytic hierarchy process (AHP). We show that the shape of the distribution of the maximum eigenvalue is different according to the dimension of the matrix. In addition, we cannot find any evidence that the distribution of the Consistency Index is a Normal distribution, which has been claimed in the Previous literature. Accordingly, we suggest using so called K-index calcu1ated based on the concept of cumulative distribution function lather than based on that of arithmetic mean because the probabilistic distribution cannot be assumed to be a Normal distribution. We interpret the simulation results by comparing them with the suggestion of Saaty[11]. Our results show that using Saaty＇s value could be too generous when the dimension of the matrix is 3 and strict over 4. Finally, we propose new criteria for measuring the response consistency in AHP.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.409-419
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• 2014

In school mathematics, the logarithmic function is defined as the inverse function of an exponential function. And the natural logarithm is defined by the integral of the fractional function 1/x. But historically, Napier had already used the concept of logarithm in 1614 before the use of exponential function or integral. The calculation of the logarithm was a hard work. So mathematicians with arithmetic ability made the tables of values of logarithms and people used the tables for the estimation of data. In this paper, we first take a look at the mathematicians and mathematical principles related to the appearance and the developments of the logarithmic tables. And then we deal with the confusions between mathematicians, raised by the estimation data which were known as proportional parts or mean differences in common logarithmic tables.

• Journal of Educational Research in Mathematics
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• v.22 no.1
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• pp.101-115
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• 2012

Analogy, a plausible reasoning on the basis of similarity, is one of the thinking strategy for concept formation, problem solving, and new discovery in many disciplines. Statistics educators argue that analogy can be used as an useful thinking strategy in statistics as well. This study investigated the characteristics of students' analogical thinking in statistics. The mathematically gifted were asked to construct similar problems to a base problem which is a statistical problem having a statistical context. From the analysis of the problems, students' new problems were classified into five types on the basis of the preservation of the statistical context and that of the basic structure of the base problem. From the result, researchers provide some implications. In statistics, the problems, which failed to preserve the statistical context of base problem, have no meaning in statistics. However, the problems which preserved the statistical context can give possibilities for reconceptualization of the statistical concept even though the basic structure of the problem were changed.

• Journal of the Korean Institute of Landscape Architecture
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• v.34 no.5 s.118
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• pp.39-51
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• 2006

This study was carried out to provide guidance to environmental policy makers when deciding which assessment fields (biotic, abiotic, qualitative, functional) should have priority for ecological preservation and to develop an objective and scientific methodology by introducing the engineering concept of the fuzzy integral. The grant of weights was used the eigenvalues calculated by factor analysis, and the converted values of indicators were obtained in multiplying the arithmetic values and eigenvalues. The results of the appropriateness and reliability of assessment fields were examined over 0.6, and the results showed that the design of questionnaire presented no great problems. When the fuzzy integral was calculated to determine the rankings at ${\lambda}$=1, 2, 3, 4, 5, respectively, they were 0.646, 0.630, 0.943, 1.423, and 1.167 for the biotic field, 1.298, 1.400, 0.901, 0.580, and 1.456 for the abiotic field, 0.714, 0.674, 0.346, 0.674, and 1.610 in the qualitative field and 1.000, 0.973, 0.943, 1.024, and 1.008 in the functional field. The sensitivity to ${\lambda}$ value showed that ${\lambda}=4$ was the most suitable. In comparison with ${\lambda}=0$ (the arithmetic mean), the range of change was narrow. Because the range for ${\lambda}=4$ was narrower than my other values, ${\lambda}=4$ was sure to be available in ranking-decision. The fuzzy integral is expected to be a method for analyzing and filtering human thoughts. In the future, in order to overcome linguistic uncertainty and subjectivity, other fuzzy integral models including Sugeno's method, AHP, and so forth should be used.

• Journal of Environmental Health Sciences
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• v.30 no.5 s.81
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• pp.432-439
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• 2004

Korean certification regulation for particulate filtering respirators requires inward leakage (IL) test as European Standards (EN) and the standard levels of regulation are the same as those of EN. This study was conducted to evaluate particulate filtering respirators being commercially used in the market by using IL and assess the characteristics of IL. The study began with discussing the concept of IL, comparison of IL with fit test, and IL measurement method. Three brands of half masks and 10 brands of filtering facepieces (two top class, four 1st class and four 2nd class), total 13 brands respirators, and 10 test panels (subjects) who were classified in 9 facial grids in accordance with face length and lip length, were selected for IL test. IL tests were conducted in the laboratory of 3M Innovation Center which was established by EN standard. As expected ILs of half masks were lower than those of filtering facepiece mask. ILs of half masks and some filtering facepieces were significantly different in manufacturers. ILs of 1st class filtering facepieces were found to be much more than those of 2nd class and thus the result would cause wearers to get confused to select a mask. Four of six brands being no compliance with standards were thought that they should be tested again for certification because of a lot of differences from standards. There were no significant differences among ILs of five exercises. In 6 out of 13 brands lognormal distribution of ILs may be a better fit distribution and in 7 brands both lognormal and normal distributions were rejected. The result indicates that geometric mean may be better than arithmetic mean to establish standard.