• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.83-97
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• 2010

The purposes of this study were to explore in depth about 5th graders' mathematical speaking and writing abilities and to investigate differences on those abilities. The study involved 3 5th graders and their speaking and writing abilities in geometry area were analyzed. According to the results of the study, the children had difficulties in selecting and using appropriate mathematical languages to explain mathematical concepts, mathematical ideas, and problem solving steps. The children who participated in the study showed higher ability in speaking than writing.

• Journal of Educational Research in Mathematics
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• v.9 no.2
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• pp.459-471
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• 1999

This study is to develop a mathematics assessment framework based on the mathematics assessment framework and content strands suggested by KEDI, NCTM, NAEP, TIMSS, Oregon State, New Zealand. According to the literature review, there has been more emphasis that students themselves 'communicate' what they 'understood' and how they 'thought' during the situation of 'solving problems'. As a result, communication ability is considered one of the most important factors in assessment situation, which always accompany the abilities of understanding, thinking, problem-solving, etc. In conclusion, the framework related to mathematical knowledge consists of content and behavior domains. The content domain is categorized into 6 content areas of the 7th mathematics curriculum, and the behavior domain is divided into computation, understanding, inference, problem-solving, and communication.

• Journal of Engineering Education Research
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• v.20 no.3
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• pp.32-41
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• 2017

The $4^{th}$ industrial revolution refers to an era where machines capable of outperforming humans are created. In light of the 4th industrial revolution, university students are demanded problem solving abilities, critical thinking abilities, and problem discovering abilities as general and basic abilities. The need for changes in the university level communication education for engineering students remains imperative in this constantly changing social environment. The era where education is conducted only in classrooms is over. This paper discusses the need for diversified education such as the integration of online and offline education, the reinforcement of learning outside of the classroom as well as an education model that transcends formal and informal education such as games and activities that induce self-learning, both intentional and non-intentional learning, and the utilization of mass media and social networking systems. Through providing an education model that assesses and utilizes the data gained from the learning process provided above, this paper widens the perception of future education methods in the 4th industrial revolution.

• The Journal of Korean Association of Computer Education
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• v.13 no.3
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• pp.13-23
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• 2010

The revised 7th education course of information implies that students use variety of information devices to solve the common problems and it also includes the programming education for improving problem-solving abilities. Not only improving problem-solving abilities but also developing thinking skill is expected in programming education. However, traditional programming education is teacher-oriented and focused on language syntax. Accordingly, students have heavy cognitive load and it decrease students' interest of programming. Therefore, in this paper, a instructional method of programming using educational robot is proposed to improve interest of elementary students in concretive operation stage for effectiveness of programming education. Additionally, results of experiments show that proposed robot programming instructional method can be applied in elementary education.

• Journal of Korean Elementary Science Education
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• v.17 no.1
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• pp.47-60
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• 1998

The purpose of this study was to analyze the problem solving strategies of elementary school students and to find out correlations between the functional mental capacity, the perseveration error and the Creature Card Task solving ability. To study this purpose, four categories were selected through pilot test. The sample consisted of 231, the 4th grade students and the 5th grade students in Inchon, Korea and selected 32 students among them. Three instruments were used in this study, Creature Card Task, FIT(Figural Intersection Test) and WCST(Wisconsin Card Sorting Test). Researcher interviewed 32 students about Creature Card Task solving strategies and tests with FIT, WCST. Major findings of the study are as follows: 1. Creature Card Task solving strategies of the selected 4th & 5th grade students were different. Some students solved problems during individual interviews. 2. Creature Card Task solving abilities were significantly correlated with the functional mental capacity and the perseveration error.

• Journal of Gifted/Talented Education
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• v.8 no.2
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• pp.69-89
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• 1998

The purpose of this study is to develop a test which can be used in identification of the gifted students in the area of mathematics. This study was carried out for two years from 1996. Mathematical giftedness is, in this study, regarded as a result of interaction of mathematical thinking ability, mathematical creativity, mathematical task committment, background knowledge. This study presumed that mathematical thinking ability is composed of seven thinking abilities: intuitive insights, ability for information organization, ability for visualization, ability for mathematical abstraction, inferential thinking ability(both inductive and deductive thinking abilities), generalization and application ability, and reflective thinking. This study also presupposed that mathematical creativity is composed of 3 characteristics: fluency, flexibility, originality. The test for mathematical creative problem solving ability was developed for primary, middle, and high school students. The test is composed of two parts: the first part is concentrated more on divergent thinking, while the second part is more on convergent thinking. The major targets of the test were the students whose achievement level in mathematics belong to top 15~20% in each school. The goodness of the test was examined in the aspects of reliability, validity, difficulty, and discrimination power. Cronbach $\alpha$ was in the range of .60~.75, suggesting that the test is fairly reliable. The validity of the test was examined through the correlation among the test results for mathematical creative problem solving ability, I. Q., and academic achievement scores in mathematics and through the correlation between the scores in the first part and the scores in the second part of the test for mathematical creative problem solving ability. The test was found to be very difficult for the subjects. However, the discrimination power of the test was at the acceptable level.

• Journal of The Korean Association For Science Education
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• v.20 no.2
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• pp.329-343
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• 2000

The purpose of this study is to develop the middle school science curriculum to enhance creative problem-solving abilities. The reconstructed curriculum consisted of three big components, that is, scientific knowledge, process skills, and creative thinking skills. Five themes have been selected to incorporate with four areas of the middle school science curriculum, namely, physics, chemistry, biology, earth science. The five themes are structure, change, interaction, energy, and stability. Based upon these five themes, the individual or separated scientific knowledges of learners can be put into the unified knowledges. The process skills were observing, measuring, classifying, communicating, inferring, predicting, variable differentiating controling, data gathering analysis, establishing hypotheses, experiment design, and experimenting. Creative thinking skills include divergent and critical thinking. The finally developed curriculum is presented in the form of matrix.

• Journal of The Korean Association For Science Education
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• v.26 no.4
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• pp.546-558
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• 2006

The purpose of this study was to identify heuristically how abduction was used in a context of solving an earth-environmental problem. Thirty two groups of participants with different institutional backgrounds, i,e., inservice earth science teachers, preservice science teachers, and high school students, solved an open-ended earth-environmental problem and produced group texts in which their ways of solving the problem were written, The inferential processes in the texts were rearranged according to the syllogistic form of abduction and then analyzed iteratively so as to find thinking strategies used in the abductive reasoning. The result showed that abduction was employed in the process of solving the earth-environmental problem and that several thinking strategies were used for inferring rules from which abductive conclusions were drawn. The strategies found included data reconstruction, chained abduction, adapting novel information, model construction and manipulation, causal combination, elimination, case-based analogy, and existential strategy. It was suggested that abductive problems could be used to enhance students' thinking abilities and their understanding of the nature of earth science and earth-environmental problems.

• The Journal of Korean Association of Computer Education
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• v.12 no.3
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• pp.11-22
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• 2009

Scratch, one of the educational programming languages, provides a media-rich programming environment and easy interface to users. It supports Korean language and is utilized usefully in programming classes in elementary and middle schools. However, programming causes cognitive loads to young students. Because the programming process is a complex problem solving procedure that requires logical and abstract thinking abilities. Therefore, we developed a problem based scratch programming teaching and learning model to enhance intrinsic motivation of learners and to maximize the effects of using the scratch, educational programming language. The developed problem based teaching and learning model considered elementary students' characteristics. It was implemented in fifth grade elementary school classes and the educational effects of the model was analysed. The developed model was helpful in enhancing students' problem solving potential and logical thinking abilities.