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.