• Education of Primary School Mathematics
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• v.8 no.2 s.16
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• pp.61-68
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• 2004

The purpose of this study is to develope and analyze the assessment items which can be used in evaluation of the fraction computation ability for fifth grade students. The item development team consists of three elementary school teachers and three mathematics education expert. The developed items was analyzed item analysis after applying to 135 fifth grade students. As a results of item analysis, it shows meaningful over the level of a standard basis: reliability: 0.80; validity: item 1(1.05), item 2(1.10), item 3(.85), item 4(.90), item 5(1.08); item difficulty: item 1(-.22), item 2(-.41), item 3(.23), item 4(.40), item 5(-.01); item discrimination: item 1(.73), item 2(.73), item 3(.67), item 4(.51), item 5(.56). This means that the test tool could be useful in the evaluation of the fraction computation ability.

• Research in Mathematical Education
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• v.7 no.3
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• pp.163-189
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• 2003

The purpose of this study is to develop a test, which can be used in creative problem solving ability in mathematics of the mathematically gifted and the regular students. This test tool is composed of three categories; fluency (number of responses), flexibility (number of different kinds of responses), and originality (degree of uniqueness of responses) which are the factors of the creativity. After applying to 462 middle school students, this test was analyzed into item analysis. As a results of item analysis, it turned out to be meaningful (reliability: 0.80, validity: item 1(1.05), item 2(1.10), item 3(0.85), item 4(0.90), item 5(1.08), item difficulty: item 1(-0.22), item 2(-0.41), item 3(0.23), item 4(0.40), item 5(-0.01), item discriminating power: item 1(0.73), item 2(0.73), item 3(0.67), item 4(0.51), item 5(0.56), over the level of a standard basis. This means that the test tool was useful in the test process of creative problem solving ability in mathematics

• The Mathematical Education
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• v.46 no.4
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• pp.407-421
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• 2007

The purpose of this study is to identify the item characteristics that are supposed to affect item difficulty and to estimate the regression equations for predicting item difficulty of mathematics in the College Scholastic Ability Test(CSAT). We selected six variables related to item characteristics based on learning theories: contents, cognitive domain, novelty, item type, number of concepts, and the amount of computation. With data of the CSAT mathematics test administered in 2004-2006, item difficulty was regressed on the six variables, the location of an item, and the item writer's judgment on difficulty. The novelty of an item was found to be a statistically insignificant variable in explaining item difficulty. Four regression equations with different sets of independent variables could explain $70%{\sim}80%$ of the item difficulty variance and were validated as predicting item difficulty of the mock CSAT in 2006.

• 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 Educational Research in Mathematics
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• v.14 no.4
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• pp.387-401
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• 2004

The recent international comparative studies such as PISA(Program for International Student Assessment) and TIMSS-R(Third International Mathematics and Science Study-Repeat) provide results of relative mathematics achievement of participating countries. The purpose of this paper is to compare the mathematics results of PISA and TIMSS-R. To make PISA and TIMSS-R results comparable, they were standardized. The close investigation of these standardized results reveals that the two Asian countries(Korea and Japan) and several English speaking countries have the commonality in mathematics achievement. Thus this study looks for patterns and similarities within a group of Asian countries(Korea and Japan) and Western countries(the U.S and Australia) by in-depth analysis of PISA mathematics achievement based on item response theory. As a result, it was noted that Western countries tend to perform well on open constructed items and are likely to perform better when an item involves less formal mathematics. On the other hand, Asian countries perform well when an item involves numeric or algebraic computation related to curriculum-based content, but they are relative poor at an item calls for verbal explanations or interpretations of graphs.

• The Mathematical Education
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• v.61 no.4
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• pp.581-595
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• 2022

The purpose of this study is to specify the procedure for making item models based on ontology models using automatic item generation in the mathematics subject through the CAFA system, and to explore the generated item instances. As an illustration for this, an item model was designed as a part of formative assessment based on the content characteristics, including concepts and calculations, and process characteristics, including application, using the representative values and the measures of dispersion in Mathematics of the 9th grade based on the evaluation criteria achievement standards. The item types generated in one item model were a best answer type, a correct answer type, a combined-response type, an incomplete statement type, a negative type, a true-false type, and a matching type. It was found that HTML, Google Charts, TTS, figures, videos and so on can be used as media. The implications of the use of digital evaluation based on automatic item generation were suggested in the aspects of students, pre-service teachers, general teachers, and special education, and the limitations of this study and future research directions were presented.

• School Mathematics
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• v.9 no.2
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• pp.223-240
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• 2007

The purpose of this study was to investigate the degree to which the middle school mathematics curriculum matched the item difficulty levels of representative mathematics items. The items used in this study were developed for the National Assessment of Educational Achievement. Ranks for difficulty values of the 60 multiple-choice item were calculated via both Classical Test Theory and Item Response Theory and correlated with the rank order of the mathematics content and cognitive domains sequence. There are six content domains; number and operation, algebra, measurement, figure, pattern and function, and probability and statistics. The cognitive domains include computation, understanding, reasoning and problem-solving. Results suggest a congruence between cognitive domain's sequence and item difficulty levels of items based on that sequence. This finding indicates that the linear or hierarchical assumptions concerning the sequence appears to be reasonable. The characteristics of items that were exceptions to this trend were addressed.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.327-343
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• 2006

A general methodology is suggested to solve shelf-space allocation problem of retailers. A multi-item inventory model of breakable items is developed, where items are either complementary or substitute. Demands of the items depend on the amount of stock on the showroom and unit price of the respective items. Also demand of one item decreases (increases) due to the presence of others in case of substitute (complementary) product. For such a model, a Contractive Mapping Genetic Algorithm (CMGA) has been developed and implemented to find the values of different decision variables. These are evaluated to have maximum possible profit out of the proposed system. The system has been illustrated numerically and results for some particular cases are derived. The results are compared with some other heuristic approaches- Simulated Annealing (SA), simple Genetic Algorithm (GA) and Greedy Search Approach (GSA) developed for the present model.

• Journal of the Korean School Mathematics Society
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• v.10 no.1
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• pp.113-127
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• 2007

This study explored the possibility of building a statistical model predicting difficulty of mathematics test items through the analysis of nation-wide scholastic ability test results for the past 5 years. Multiple linear regression analysis was conducted in predicting difficulty of mathematics test items. We adopted three major areas for independent variables: the content area, the behavior area, and the test item format area, each of which was categorized into more detailed sub-areas. For the dependent variable, the proportion of correct answer was used to represent the item difficulty. Statistically significant independent variables were included in the regression model based on the stepwise selection method. Several important factors affecting difficulty of mathematics test items for each area were identified. R-squares for the final regression model were fairly high, implying that the regression equation can be used to predict difficulty of test items at an acceptable level. Lastly, the regression model was cross-validated using independently collected data. We believe that this study will provide basic but very critical information for predicting the proportion of correct answer by showing the factors that should be considered for developing mathematics test items for the college entrance examination or high school classroom test.

• Journal of Fisheries and Marine Sciences Education
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• v.29 no.3
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• pp.757-766
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• 2017

This study investigated not only the existence of differently functioned item due to gender but also domain. In this study, the randomly selected data of TIMSS 2007, which consist of 681 male and 646 women, were analyzed. To detect differently functioned items, this study employed Raju method. For Raju method, three-parameter logistic model was selected. Signed and unsigned area between two item characteristic curve were measured within the real ability range. An item which was detected commonly SA and UA area in Raju method was defined as a differently functioned item. As a result of this study, six items among twenty seven items of mathematics in the TIMSS 2007 were differently functioned item. Five items among those six items, were in favor of boys and one item was in favor of girls. Number, Geometric Shapes and Measures, and Applying were in favor of boys. but Data Display, Reasoning were in favor of girls. The conclusion of this study was summarized as existing differently functioned items in TIMSS 2007 and difference between favorable domain based gender. Finally, it is desirable to consider the differently functioned items by relating those item content for improving the test reliability of TIMSS 2007.