• School Mathematics
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• v.19 no.1
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• pp.59-75
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• 2017

This study analyzed the $6^{th}$ graders' constructions about fraction operations and schemes and figured out the relationships quantitatively between operations and schemes through the written test of 432 students. The results of this study showed that most of students could do partitioning operation well, however, there were many students who had difficulties on iterating operation. There were more students who constructed partitioning operation prior to iterating operation than the opposite. The rate of students who constructed high schemes was lower than that of students who constructed low schemes according to the hierarchy of fraction schemes. Especially, there were many students who construct partitive unit fraction scheme but not partitive fraction scheme, because they could compose unit fraction but not do iterating it. And there were the high correlations between fraction operations and schemes. Given these result, this paper suggests implications about the teaching and learning of fraction.

• Communications of Mathematical Education
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• v.27 no.2
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• pp.135-163
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• 2013

This study dealt with the measurements of the positive psychological experience of high school students in relation to mathematics learning by using PPE-M. The purpose of this study is to compare the positive psychology of the high school students based on the grade and gender variables. Measured data for the purpose of this study examined the difference between the gifted students and the general students through a t-test. In addition, differences were analyzed by grade and gender variables. And One-way ANOVA was conducted to see the difference according to the course variables. The difference between the two groups was meaningful in PPE-M total score. There was meaningful difference in all of 5 areas and 19 factors except for 4 factors (Insight, Honesty, Full with pride, and Achievement). However, there was no difference according to grade levels. The comparison between the gender in the ordinary students shows meaningful difference in 11 factors, not in 12 (Judgment, Insight, Honesty, Prudence, Modesty & Kindness, Gratitude & Happiness, Flow, Superiority feeling, Achievement, High pleasure, Full with pride, and Self-efficacy). Affiliation makes meaningful difference in 22 factors except for Honesty.

• The Mathematical Education
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• v.56 no.1
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• pp.63-80
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• 2017

By analysing the examination papers from third grade high school students, we classified the errors occurred in the problem solving process of high school 'Geometry and Vectors' into several types. There are five main types - (A)Insufficient Content Knowledge, (B)Wrong Method, (C)Logical Invalidity, (D)Unskilled Expression and (E)Interference.. Type A and B lead to an incorrect answer, and type C and D cannot be distinguished by multiple-choice or closed answer questions. Some of these types are classified into subtypes - (B1)Incompletion, (B2)Omitted Condition, (B3)Incorrect Calculation, (C1)Non-reasoning, (C2)Insufficient Reasoning, (C3)Illogical Process, (D1)Arbitrary Symbol, (D2)Using a Character Without Explanation, (D3) Visual Dependence, (D4)Symbol Incorrectly Used, (D5)Ambiguous Expression. Based on the these types of errors, answers of each problem was analysed in detail, and proper ways to correct or prevent these errors were suggested case by case. When problems that were used in the periodical test were given again in descriptive forms, 67% of the students tried to answer, and 14% described flawlessly, despite that the percentage of correct answers were higher than 40% when given in multiple-choice form. 34% of the students who tried to answer have failed to have logical validity. 37% of the students who tried to answer didn't have enough skill to express. In lessons on curves of secondary degree, teachers should be aware of several issues. Students are easily confused between 'focus' and 'vertex', and between 'components of a vector' and 'coordinates of a point'. Students often use an undefined expression when mentioning a parallel translation. When using a character, students have to make sure to define it precisely, to prevent the students from making errors and to make them express in correct ways.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.177-196
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• 2010

The purpose of this study is to find out whether Achievement Tests are fully performing their role as an objective standard that measures student's educational achievement level by analysing the content validity of Achievement Tests developed by KICE and teachers at elementary school. In the study, the content validity of achievement tests were analyzed in the behavioral content objective dimensions. 60 instructional objectives from the Unit one to the Unit six contained in the teachers' guidebook for the elementary third-grade Math subject were analyzed into dimensions of behavior and content. And the Achievement Test developed by KICE and teachers in five elementary schools randomly chosen were collected and analyzed. Then, differences of the proportion between instructional objectives and evaluative objectives in each dimension statistically were verified. The results of the study are as follows : 1. In the dimension of behavior, as analysing and comparing the content validity of achievement tests, there was no significant difference in all domains(knowledge, comprehension, application, analysis, synthesis and evaluation). (p<.05) Therefore, it could be concluded that content validity of the Achievement Test is very high. 2. In the dimension of content, similarly there is no significant difference in all domains between achievement tests by both KICE and teachers. (p<.05) Therefore, the content validity of all tests are very high. In conclusion, it could be concluded that content validity of achievement tests is considerably high in content and behavior dimension. The study suggest the followings : 1. By expanding to the other subjects, there are needs to analyze and verify the content validity of achievement tests. 2. Even the content validity of achievement tests is considerably high however, achievement items are focused on evaluation 3 domains(knowledge, comprehension, application). Therefore evaluation evenly among 6 cognitive domains is required. And further to reduce the deviation of schools, there are needs to active interchange between teachers.

• The Mathematical Education
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• v.55 no.3
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• pp.383-396
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• 2016

This study investigated highschool students' brain waves on functional tasks such as a transition(F task) from equation to graph and the other transition(G task) vice versa. A total of 39 students participated in the study who attended a high school located in Gyunggi province. These students were divided into two groups, HMA and LMA by MASS test revised by Ko, & Yi (2012). The functional tasks for the stroop task to measure EEG were provided from a previous study, Seok(2015). The results indicated two groups on G tasks showed deeper and wider brain waves which demonstrated G tasks were more difficult than F tasks. However, HMA group had an effect of the non-psychological program which had given more chances on G tasks rather than F tasks within Students' Zone of Proximal Development. Also, HMA group's brain waves had more ranges in amplitude and width of waves. These results imply that the characteristics of students' brain waves with math anxiety are consistent to the previous studies.

• The Mathematical Education
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• v.31 no.2
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• pp.109-119
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• 1992

The primary purpose of the present study is to provide the sources to improve the mathematical problem solving performance by analyzing the effects of the belief systems and the misconceptions of the middle school students in solving the problems. To attain the purpose of this study, the reserch is designed to find out the belief systems of the middle school students in solving the mathematical problems, to analyze the effects of the belief systems and the attitude on the process of the problem solving, and to identify the misconceptions which are observed in the problem solving. The sample of 295 students (boys 145, girls 150) was drawn out of 9th grade students from three middle schools selected in the Kangdong district of Seoul. Three kinds of tests were administered in the present study: the tests to investigate (1) the belief systems, (2) the mathematical problem solving performance, and (3) the attitude in solving mathematical problems. The frequencies of each of the test items on belief systems and attitude, and the scores on the problem solving performance test were collected for statistical analyses. The protocals written by all subjects on the paper sheets to investigate the misconceptions were analyzed. The statistical analysis has been tabulated on the scale of 100. On the analysis of written protocals, misconception patterns has been identified. The conclusions drawn from the results obtained in the present study are as follows; First, the belief systems in solving problems is splited almost equally, 52.95% students with the belief vs 47.05% students with lack of the belief in their efforts to tackle the problems. Almost half of them lose their belief in solving the problems as soon as they given. Therefore, it is suggested that they should be motivated with the mathematical problems derived from the daily life which drew their interests, and the individual difference should be taken into account in teaching mathematical problem solving. Second. the students who readily approach the problems are full of confidence. About 56% students of all subjects told that they enjoyed them and studied hard, while about 26% students answered that they studied bard because of the importance of the mathematics. In total, 81.5% students built their confidence by studying hard. Meanwhile, the students who are poor in mathematics are lack of belief. Among are the students accounting for 59.4% who didn't remember how to solve the problems and 21.4% lost their interest in mathematics because of lack of belief. Consequently, the internal factor accounts for 80.8%. Thus, this suggests both of the cognitive and the affective objectives should be emphasized to help them build the belief on mathematical problem solving. Third, the effects of the belief systems in problem solving ability show that the students with high belief demonstrate higher ability despite the lack of the memory of the problem solving than the students who depend upon their memory. This suggests that we develop the mathematical problems which require the diverse problem solving strategies rather than depend upon the simple memory. Fourth, the analysis of the misconceptions shows that the students tend to depend upon the formula or technical computation rather than to approach the problems with efforts to fully understand them This tendency was generally observed in the processes of the problem solving. In conclusion, the students should be taught to clearly understand the mathematical concepts and the problems requiring the diverse strategies should be developed to improve the mathematical abilities.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.369-384
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• 2007

This study examined and compared the level of mathematical anxiety according to the types of students' characteristics based on the former research study showing that there exists a close relationship between characteristics and mathematical anxiety. The subjects of this study are 159 students enrolled in Chungnam Gongju and Kyunggi-do Ahnyang. They were categorized into groups following various standards such as preference index(E-1, S-N, T-F, J-P), ability & disposition, 16 types of characteristics. Then these were tested for types and the level of mathematical anxiety by the factors of mathematical anxiety. The results show that Type E students show the greatest anxiety in learning motivation, and Type N students in the pedagogy of teaching and loaming for the subfactor of mathematical anxiety. Further, Type NT students respond strongly to the pedagogy of teaching and loaming in psychological ability and disposition, which shows that mathematical anxiety and sub-factors of mathematical anxiety are closely somehow related.

• Journal of Digital Convergence
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• v.15 no.6
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• pp.391-398
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• 2017

In this paper, we compared the performance of "Network Intrusion Detection System based on attack feature selection using fuzzy control language"[1] and "Intelligent Intrusion Detection System Model for attack classification using RNN"[2]. In this paper, we compare the intrusion detection performance of two techniques using KDD CUP 99 dataset. The KDD 99 dataset contains data sets for training and test data sets that can detect existing intrusions through training. There are also data that can test whether training data and the types of intrusions that are not present in the test data can be detected. We compared two papers showing good intrusion detection performance in training and test data. In the comparative paper, there is a lack of performance to detect intrusions that exist but have no existing intrusion detection capability. Among the attack types, DoS, Probe, and R2L have high detection rate using fuzzy and U2L has a high detection rate using RNN.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.637-644
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• 1997

Sometimes, the first principal component may come logically from the established knowledge and premises. For example, for the high school students' test scores of Korean, English, Mathematics, Social Study, and Science, it is natural to define the first principal component as the average of all subject scores. In such cases, we need to respect both the background knowledge and the data exploration. The aim of this study is to find the remaining components in principal component analysis of multivariate data when the first principal component is defined a priori by the researcher. Moreover, we study related matrix decomposition and their application to the graphical display.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.553-571
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• 2015

Mathematical, verbal, and spatial abilities are known as three important indicators for the success in the STEM disciplines. In this study, Purdue Spatial Visualization Test-Rotation, College Entrance Scholastic Aptitude Test- Math and Verbal score of engineering freshmen students have been used to find the relationships among these areas. In addition, gender differences in spatial visualization, verbal achievement and mathematical achievement have been investigated, too. In this research, I found that gender difference was highest in spatial visualization ability, followed by verbal achievement and smallest in mathematical achievement. Substantial number of male students possess high level of spatial abilities, but only half of female students were at the same level where their male colleagues were. The correlation between spatial ability and mathematical ability was negligible, contrary to former researches on elementary and middle school students. But the correlation was stronger for female students than male students. The correlation between mathematical achievement and verbal achievement was negative. It reflects the fact that when one section of SAT score is low, score of other sections should be higher to get admitted to college. Gender difference in mathematics was smallest for high achieving spatial ability group. For low spatial ability group gender difference in mathematics achievement has been observed, too. To find the combined contribution of spatial and verbal abilities to mathematics achievement, students were divided into 4 ability groups. Mathematics achievement decreased in the order of (1) high spatial -low verbal group, (2) low spatial - low verbal group, (3) high spatial - high verbal group, (4) low spatial - high verbal group.