• Journal of Elementary Mathematics Education in Korea
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• v.15 no.2
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• pp.417-435
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• 2011

Mathematical justification is essential to assert with reason and to communicate. Students learn mathematical justification in 8th grade in Korea. Recently, However, many researchers point out that justification be taught from young age. Lots of studies say that students can deduct and justify mathematically from in the lower grades in elementary school. I conduct questionnaire to know awareness and steps of elementary school students and middle school students. In the case of 9th grades, the rate of students to deduct is highest compared with the other grades. The rease is why 9th grades are taught how to deductive justification. In spite of, however, the other grades are also high of rate to do simple deductive justification. I want to focus on the 6th and 5th grades. They are also high of rate to deduct. It means we don't need to just focus on inducing in elementary school. Most of student needs lots of various experience to mathematical justification.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.405-422
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• 2017

Nim games were divided into three stages : one file, two files and three files game, and inquiry activities were conducted for middle school mathematically gifted students. In the first stage, students easily found a winning strategy through deductive reasoning. In the second stage, students found a winning strategy with deductive reasoning or inductive reasoning, but found an error in inductive reasoning. In the third stage, no students found a winning strategy with deductive reasoning and errors were found in the induction reasoning process. It is found that the tendency to unconditionally generalize the pattern that is formed in the finite number of cases is the cause of the error. As a result of visually presenting the binary boxes to students, students were able to easily identify the pattern of victory and defeat, recognize the winning strategy through game activities, and some students could reach a stage of justifying the winning strategy.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.557-580
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• 2017

The purpose of this study is developing the manifestation process model of group creativity among mathematically gifted students. Therefore, I designed the manifestation process model of group creativity by researching the existing literatures on group creativity and mathematical creativity. The manifestation process model of group creativity was applied to mathematically gifted students' class. By analyzing students' response, the manifestation process model of group creativity was improved and concretized. In conclusion, the process of a combination of contributions was concretized and the major variables on group creativity such as a diversity, conflict, emotionally supportive environment and social comparison were verified. In addition, some reflective processes was discovered from a case study.

• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.169-186
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• 2020

The purpose of this study is to find new material for developing teaching and learning materials for the gifted class of elementary school students by using the rotatable tangram made by modifying the traditional tangram. Rotatable tangram can be justified by gifted students through mathematical communication. However, even gifted class students have some limitations in finding and justifying triangles and rectangles of all sizes unless they go through the 'symbolization' stage at the elementary school level. Therefore, students who need an inquiry process for letters and symbols need to provide supplementary learning materials and additional questions. It is expected that the material of rotatable tangram for the development of teaching and learning materials for elementary school gifted students will contribute to the development of mathematical reasoning and mathematical communication ability.

• Journal of Educational Research in Mathematics
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• v.13 no.2
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• pp.159-178
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• 2003

This study analyzes on the reasoning in the process of justification and mathematical problem solving in our primary mathematics textbooks. In our analyses, we found that the inductive reasoning based on the paradima-tic example whose justification is founnded en a local deductive reasoning is the most important characteristics in our textbooks. We also found that some propositions on the properties of various quadrangles impose a deductive reasoning on primary students, which is very difficult to them. The inductive reasoning based on enumeration is used in a few cases, and analogies based on the similarity between the mathematical structures and the concrete materials are frequntly found. The exposition based en a paradigmatic example, which is the most important characteristics, have a problematic aspect that the level of reasoning is relatively low In Miyazaki's or Semadeni's respects. And some propositions on quadrangles is very difficult in Piagetian respects. As a result of our study, we propose that the level of reasoning in primary mathematics is leveled up by degrees, and the increasing levels are following: empirical justification on a paradigmatic example, construction of conjecture based on the example, examination on the various examples of the conjecture's validity, construction of schema on the generality, basic experiences for the relation of implication.

• Education of Primary School Mathematics
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• v.27 no.3
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• pp.281-301
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• 2024

Many students have experienced difficulties due to the discontinuity in instruction between arithmetic and algebra, and in the field of elementary education, algebra is often treated somewhat implicitly. However, algebra must be learned as algebraic thinking in accordance with the developmental stage at the elementary level through the expansion of numerical systems, principles, and thinking. In this study, algebraic thinking-based classes were developed and conducted for 6th graders in elementary school, and the effect on the ability to solve word-problems in fraction division was analyzed. During the 11 instructional sessions, the students generalized the solution by exploring the relationship between the dividend and the divisor, and further explored generalized representations applicable to all cases. The results of the study confirmed that algebraic thinking-based classes have positive effects on their ability to solve fractional division word-problems. In the problem-solving process, algebraic thinking elements such as symbolization, generalization, reasoning, and justification appeared, with students discovering various mathematical ideas and structures, and using them to solve problems Based on the research results, we induced some implications for early algebraic guidance in elementary school mathematics.

• Journal of Educational Research in Mathematics
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• v.15 no.3
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• pp.353-374
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• 2005

Recently, there have been many changes in researches of mathematics education. There is a growing number of researchers who are interested in empirical researches. According to the these changes, there is also an emphasis on methodology of mathematics education. This means that many researchers try to conduct an research using scientific approach. Therefore, new types of research developing mathematics courses recently has evolved as follows: teaching experiment, hypothetical loaming trajectory, design science, developmental research. The aim of this study is to reflect on developmental research in RME and to induce desirable directions for developing our mathematics courses. In order to attain these purposes, the present paper reflects the philosophy of RME, aim, procedure, data collection, data analysis, and justification of developmental research with illustrating a exemplar Based on these reflections, it is discussed that it needs to construct the mathematics curriculum connecting theory and practice in mathematics education, to report the process of developing mathematics courses faithfully, and to develop real mathematics courses after conducting basic developmental researches in order to take scientific app- roaches for developing mathematics courses.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.205-220
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• 2013

In this research, in order to investigate the principles for the development of mathematics textbook for decision-making based on storytelling, we conceptualized the educational meaning of decision-making and specified the principles and the methods for the textbook based on decision-making. We illustrated the principles and the methods by the cases from the model textbook for the conditional probability that we have developed. We discussed the implication for the future development and implementation of mathematics textbook for decision-making based on storytelling.

• Journal of the Korean School Mathematics Society
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• v.11 no.2
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• pp.201-219
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• 2008

The purpose of this study was to provide useful information for teachers by analyzing various levels of teacher-student communication in elementary mathematics classes and students' mathematical thinking. This study explored mathematical communication of 3 classrooms with regard to questioning, explaining, and the source of mathematical ideas. This study then probed the characteristics of students' mathematical thinking in different standards of communication. The results showed that the higher levels of teacher-student mathematical communication were found with increased frequency of students' mathematical thinking and type. The classroom that had a higher level of Leacher-student mathematical communication was exhibited a higher level of students' mathematical thinking. This highlights the importance of mathematical communication in mathematics c1asses and the necessity of further developing skills of mathematical communication.

• School Mathematics
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• v.15 no.2
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• pp.389-404
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• 2013

Researchers have suggested that students should be experienced in progress of geometric thinking set out in naive and intuitive level and deduced throughout gradual formalization rather than completed mathematics are conveyed to students for students' understanding. This study examined naive and intuitive thinking of students by investigating students' geometric problem solving without diagrams. The students showed these naive thinking: lack of recognition of relation between problem and conditions, use of intuitive judgement depending on diagrams, lacking in understanding of role of specific case, and use of unjustified assumption. This study suggests implication for instruction in geometry.