• Journal of the Korean School Mathematics Society
• /
• v.18 no.3
• /
• pp.241-258
• /
• 2015

The purpose of this paper is to examine the students' mathematics problem solving process in the intuitive stages. For this, researcher developed the questionnaire which consisted of problems in relation to intuitive and algorithmic problem solving. 73 fifth grade and 66 sixth grade elementary students participated in this study. I got the conclusion as follows: Elementary students' intuitive problem solving ability is very low. The rate of algorithmic problem solving is higher than that of intuitive problem solving in number and operation areas. The rate of intuitive problem solving is higher in figure and measurement areas. Students inclined to solve the problem intuitively in that case there is no clue for algorithmic solution. So, I suggest the development of problems which can be solved in the intuitive stage and the preparation of the methods to experience the insight and intuition.

• Journal of Gifted/Talented Education
• /
• v.21 no.4
• /
• pp.847-860
• /
• 2011

In this study, the instrument of mathematical thinking ability tests were considered, and the differences between gifted and regular high school students in the ability were investigated by the test. The instrument consists of 9 items, and verified its quality due to reliability. Participants were 353 regular and 252 gifted high school students from tenth grade. As a result, not only organizing ability of information but also ability of space perception and visualization and intuitive insight ability could be the characteristics of the mathematical giftedness.

• Journal for History of Mathematics
• /
• v.18 no.2
• /
• pp.23-30
• /
• 2005

Intuition has played an important role in process of invention of mathematics and given understanding of mathematical truth and the direction of solution. So, I review about intuition in history of mathematical philosophy and mathematics because we need systematic research about intuition for search of the methods for enhancement of intuition in mathematics education. According to the research of scholars who emphasize intuitive education, intuition is common feature which everybody hold and is not special feature which particular person hold. In addition, intuition is universal ability that can enhance by proper instruction. So, we have to emphasize the importance of the development of intuition and education which emphasize creative thought via intuition.

• Research in Mathematical Education
• /
• v.10 no.1 s.25
• /
• pp.55-70
• /
• 2006

The purpose of this study was to develop math creative problem solving test in order to identify the mathematically gifted on the basis of their math creative problem solving ability and evaluate the goodness of the test in terms of its reliability and validity of measuring creativity in math problem solving on the basis of fluency in producing valid solutions. Ten open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 open math test items were administered to 2,029 Grade 5 students who were recommended by their teachers as candidates for gifted education programs. Fluency, the number of valid solutions, in each problem was scored by math teachers. Their responses were analyzed by BIGSTEPTS based on Rasch's 1-parameter item-response model. The item analyses revealed that the problems were good in reliability, validity, difficulty, and discrimination power even when creativity was scored with the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creativity of the candidates for math gifted education programs. In addition, it discriminated applicants for two different gifted educational institutions and between male and female students as well.

• Communications of Mathematical Education
• /
• v.25 no.1
• /
• pp.245-259
• /
• 2011

In this study, the instrument of mathematical creative problem solving ability test were considered the differences between Korean and American sixth grade students in mathematical creativity ability and mathematical thinking ability. The instrument consists of 9 items. The participants for the study were 212 Korean and 148 American students. SPSS were carried out to verify the validities and reliability. Reliabilities(Cronbach ${\alpha}$) in mathematical creativity ability is 0.9047 and in mathematical thinking ability is 0.9299 which were satisfied internal validity evaluation on the test items. Internal validity were analyzed by BIGSTEPS based on Rasch's 1-parameter item response model. The results of this study can serve as a foundation for understanding the Korean and American students differences in mathematical creativity ability and mathematical thinking ability. Especially we get the some informations on mathematical creativity ability for American's fifth grade to seventh grade students.

• Journal of Gifted/Talented Education
• /
• v.17 no.1
• /
• pp.1-26
• /
• 2007

The purpose of this study was to develop a math test for identification of the mathematically gifted on the basis of their math creative problem solving ability and to evaluate the goodness of the test. Especially, testing reliability and validity of scoring method on the basis of fluency only for evaluation of math creative problem solving ability was one of the main purposes. Ten closed math problems and 5 open math problems were developed requiring math thinking abilities such as intuitive insight, organization of information, inductive and deductive reasoning, generalization and application, and reflective thinking. The 10 closed math test items of Type I and the 5 open math test items of Type II were administered to 1,032 Grade 7 students who were recommended by their teachers as candidates for gifted education programs. Students' responses were scored by math teachers. Their responses were analyzed by BIGSTEPS and 1 parameter model of item analyses technique. The item analyses revealed that the problems were good in reliability, validity, item difficulty and item discriminating power even when creativity was scored based on the single criteria of fluency. This also confirmed that the open problems which are less-defined, less-structured and non-entrenched were good in measuring math creative problem solving ability of the candidates for math gifted education programs. In addition, it was found that the math creative problem solving tests discriminated applicants for the two different gifted educational institutions.