• Journal of Elementary Mathematics Education in Korea
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• v.10 no.2
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• pp.171-194
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• 2006

As it is not long since the gifted education was implemented in elementary school, it is necessary to accumulate the practical studies on the mathematically gifted education. This paper focused on enhancing creativity by providing the various and divergent thinking activities for mathematically gifted students. For this purpose, I prepared two mathematics problems, and , and let the mathematically gifted 5th grade students solve them. After that, I investigated to analyse their reactions in detail and tried to find the methods for assessing their divergent products. Finally, I found that they could pose various and meaningful calculating equations and also identify the various relations between two numbers. I expect that accumulating these kinds of practical studies will contribute to the developments of gifted education, in particular, instructions, assessments, and curriculum developments for the mathematically gifted students in elementary schools.

• Education of Primary School Mathematics
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• v.12 no.2
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• pp.63-80
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• 2009

In this study, we analyzed teachers' recognitions of the necessity of mathematical descriptive tests and their practices in the elementary schools. We then suggested several examples of improved formats of the mathematical descriptive evaluation. For analyzing teachers' recognitions and practices of mathematical descriptive assessment, we surveyed 104 elementary school teachers in Seoul. We collected the test items from the schools and analyzed them to find how they are practiced in the schools. The results were as follows. First, most elementary school teachers are basically recognizing the direction and the purpose of mathematical descriptive assessment. Second, the ratio of the descriptive test items was very low compared with the teachers' recognition of necessity of including descriptive items in the tests. Third, the teachers usually made the descriptive items with their colleagues using textbooks, test manuals for teachers, and the references that the office of education provided. Fourth, to enhance teachers' understanding of descriptive assessment, systematic training programs for teachers about the descriptive assessment should be continued. Finally, the office of education and research institutes should provide various types of test items and more teacher training programs on descriptive assessments.

• The Mathematical Education
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• v.59 no.4
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• pp.295-312
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• 2020

This study aimed to investigate and compare perceptions of middle and high school mathematics teachers on assessment. For the purpose, we developed and used a survey consisting of two parts(importance/performance on assessment and general opinion on process-based assessment). We gathered data from 188 middle school and 125 high school mathematics teachers in Incheon area. An Importance-Performance Analysis(IPA) method was used for data analysis. As results, middle school mathematics teachers showed higher perception on both importance and performance in almost all area on assessment than high school teachers. In addition, research results based on teaching experience indicated that mathematics teachers having more teaching experience seemed to perceive high importance-high performance and low importance-low performance tasks more than mathematics teachers having less experience. In particular, middle school teachers recognized many low importance-high performance tasks according to their teaching experience. The IPA gave us different results depending on the school size. The larger the school, the more diverse opinions appeared tasks in low importance-high performance. From the general opinion on process-based assessment, the middle school mathematics teachers also seemed to have more positive perspectives and to be more active in assessment than high school mathematics teachers. Finally, we discuss implications for future policy formulation and implementation on process-based assessment.

• Journal of Elementary Mathematics Education in Korea
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• v.18 no.1
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• pp.123-148
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• 2014

The purpose of this study is to figure out the perceptional characteristics of mathematically gifted elementary students by comparing the mathematical reasoning ability and errors between mathematically gifted elementary students and non-gifted students. This research has been targeted at 63 gifted students from 5 elementary schools and 63 non-gifted students from 4 elementary schools. The result of this research is as follows. First, mathematically gifted elementary students have higher inductive reasoning ability compared to non-gifted students. Mathematically gifted elementary students collected proper, accurate, systematic data. Second, mathematically gifted elementary students have higher inductive analogical ability compared to non-gifted students. Mathematically gifted elementary students figure out structural similarity and background better than non-gifted students. Third, mathematically gifted elementary students have higher deductive reasoning ability compared to non-gifted students. Zero error ratio was significantly low for both mathematically gifted elementary students and non-gifted students in deductive reasoning, however, mathematically gifted elementary students presented more general and appropriate data compared to non-gifted students and less reasoning step was achieved. Also, thinking process was well delivered compared to non-gifted students. Fourth, mathematically gifted elementary students committed fewer errors in comparison with non-gifted students. Both mathematically gifted elementary students and non-gifted students made the most mistakes in solving process, however, the number of the errors was less in mathematically gifted elementary students.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.11 no.6
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• pp.67-76
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• 2001

In this paper, we investigate criteria for evaluating cryptographic strength based on randomness testing of the advanced encryption standard candidates, which have conducted by NIST(National Institute of Standards & Technology). It is difficult to prove that a given cryptographic algorithm meets sufficient conditions or requirements for provable security. The statistical testing of random number generators is one of methods to evaluate cryptographic strength and is based on statistical properties of random number generators. We apply randomness testing on several cryptographic algorithms that have not been tested by NIST and find criteria for evaluating cryptographic strength from the results of randomness testing. We investigate two criteria, one is the number of rejected samples and the other is the p-value from p-values of the samples.

• The Mathematical Education
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• v.47 no.4
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• pp.487-503
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• 2008

In this paper, descriptive assessment method for middle school mathematics was evaluated by developing a framework for designing and grading problems for descriptive assessment and analyzing the effectiveness of the problems. The new descriptive assessment problems were developed by reviewing the current 7th National Mathematics Curriculum of Korea and aligned mathematics textbooks to define a set of problem design principles and evaluation framework for the assessment strategy. The developed problems were first pilot tested and then revised based on the feedback from the test. The final version was field tested by 100 students in 7th grade middle school. After the field test, the problems were graded by two middle school math teachers and one math education researcher to determine the overall correlation between graders and also to analyze effectiveness of the evaluation framework of the test. This result of this study is expected to assist in the further development of descriptive problems and grading framework by providing a reference work for teachers to better understand the process and the limitations of executing the new assessment strategy.

• Journal of Gifted/Talented Education
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• v.20 no.1
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• pp.205-229
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• 2010

The R&E(Research and Education) programs in Mathematics, which have the objects to give students mathematically creative experiences and enlarge creativities of the study of mathematics, could not give the experiences as creative researchers because of the following reasons: The students did not participate in the process of choosing the subjects, the evaluation of individual students actually did not existed, and the publications of mathematics papers have been excluded. In this paper, we study on the issues and some suggestions related to these R&E programs to obtain new R&E Model that gives a mathematically creative experience and enlarges creativities of the study of mathematics.

• Communications of Mathematical Education
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• v.14
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• pp.151-162
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• 2001

교육평가는 선발의 기능을 할 뿐 아니라 학습자의 학습상태나 오류경향에 대한 진단을 통해 학습자의 학습에 도움을 주어야 한다. 이르한 측면에서 오류분석은 평가가 지녀야 하는 가장 중요한 기능 중 하나라고 할 수 있다. 인터넷의 대중적 보급과 시간적, 공간적, 기술적 효율성은 평가환경에 대한 새로운 가능성을 제시하고 있다. 인터넷 환경에서의 평가문항은 선다형을 기본으로 하게 되는데, 선다형 평가문항을 통해서는 학습자들의 오류를 직접적으로 관출할 수 없다는 한계가 있다. 그러나 선다형 평가문항을 통한 오류분석이 불가능한 것은 아니다. 본 연구의 목적은 선다형 평가문항에서의 오류분석을 위한 구체적인 방법과 절차를 모색하는 것이다.

• School Mathematics
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• v.9 no.2
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• pp.241-257
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• 2007

The study aims to figure out how to improve existing examination tools to distinguish mathematically gifted children and to clarify procedures and criteria for selecting candidates. Toward this end, it examined correlations between grades of gifted children selected through evaluation by pen-and-pencil tests and their creative problem-solving capability and performance assessment, and analyzed learning activities of the gifted children. According to the analysis, results of pen-and-pencil tests turned out to have low correlations with their creative problem-solving capability and performance assessment, but it was found that their creative problem-solving capability has high correlations with results of performance assessment. The analysis also found that there were some students who participated in a program for gifted children with high marks but had difficulties in adapting themselves to it. It found that there were children who joined the program with low marks but emerged as successive performers later on. In this regard, the existing examination tools to tell the gifted students apart need to be used to the fullest extent, and other diversified tools to evaluate mathematical capabilities that include mathematical creativity need to be further studied and developed. Qualitative studies on affective development of the gifted students and their creative problem-solving processes need to be conducted.

• The Mathematical Education
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• v.38 no.2
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• pp.165-172
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• 1999

$\sub$e/$\^$2/, that were results from those three sources of such imperfection. Especially to eliminate the differences in severity among many raters the randomization procedure of raters sample was very effective in enhancing the reliability of ratings with comparatively small groups of examinees and raters. And we also introduced the new rating methods, i.e. the 2-step diagnostic procedures to check the sizes of the reliability stability of raters and the sore adjustment method to enumerate the optimal mean values in rating the examinees.