• East Asian mathematical journal
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• v.33 no.4
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• pp.381-411
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• 2017

The purpose of this study is to investigate how students' mathematical creativity changes through problem-solving instruction using problem-posing for elementary school students and to explore instructional methods to improve students' mathematical creativity in school curriculum. In this study, nonequivalent control group design was adopted, and the followings are main results. First, problem-solving lessons with problem-posing had a significant effect on students' mathematical creativity, and all three factors of mathematical creativity(fluency, flexibility, originality) were also significant. Second, the lessons showed meaningful results for all upper, middle, and lower groups of pupils according to the level of mathematical creativity. When analyzing the effects of sub-factors of mathematical creativity, there was no significant effect on fluency in the upper and middle groups. Based on the results, we suggest followings: First, there is a need for a systematic guidance plan that combines problem-solving and problem-posing, Second, a long-term lesson plan to help students cultivate novel mathematical problem-solving ability through insights. Third, research on teaching and learning methods that can improve mathematical creativity even for students with relatively high mathematical creativity is necessary. Lastly, various student-centered activities in math classes are important to enhance creativity.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.287-314
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• 2010

The algorithm is a chain of mechanical procedures, capable of solving a problem. In modern mathematics educations, the teaching algorithm is performing an important role, even though contracted than in the past. The conspicuous characteristic of current elementary mathematics textbook's manner of manipulating multiplication algorithm is exceeding converge to 'standard algorithm.' But there are many algorithm other than standard algorithm in calculating multiplication, and this diversity is important with respect to didactical dimension. In this thesis, we have reconstructed the experimental learning and teaching plan of multiplication algorithm unit by making the best use of diversity of multiplication algorithm. It's core contents are as follows. Firstly, It handled various modified algorithms in addition to standard algorithm. Secondly, It did not order children to use standard algorithm exclusively, but encouraged children to select algorithm according to his interest. As stated above, we have performed teaching experiment which is ruled by new lesson design and analysed the effects of teaching experiment. Through this study, we obtained the following results and suggestions. Firstly, the experimental learning and teaching plan was effective on understanding of the place-value principle and the distributive law. The experimental group which was learned through various modified algorithm in addition to standard algorithm displayed higher degree of understanding than the control group. Secondly, as for computational ability, the experimental group did not show better achievement than the control group. It's cause is, in my guess, that we taught the children the various modified algorithm and allowed the children to select a algorithm by preference. The experimental group was more interested in diversity of algorithm and it's application itself than correct computation. Thirdly, the lattice method was not adopted in the majority of present mathematics school textbooks, but ranked high in the children's preference. I suggest that the mathematics school textbooks which will be developed henceforth should accept the lattice method.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.349-368
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• 2023

The purpose of this study is to explore ways for students to connect conceptual and procedural knowledge in mathematical modeling lessons. Accordingly, we selected the greatest common divisor among the learning contents in which elementary school students have difficulties connecting conceptual and procedural knowledge. A mathematical modeling lesson was designed and implemented to solve problems related to the greatest common divisor while connecting conceptual and procedural knowledge. As a result of the analysis, it was found that the mathematical modeling lesson had positive effects on students solving problems by connecting conceptual and procedural knowledge. In addition, through actual class application, a teaching and learning plan was derived to meaningfully connect conceptual and procedural knowledge in mathematical modeling lessons.

• School Mathematics
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• v.14 no.2
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• pp.255-274
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• 2012

The purpose of this study was to investigate the responses of pre-service elementary school teachers to the task that require to apply mathematics knowledge for teaching and from this investigation to draw some conclusions about teacher education. To do the study, task was to develop teaching materials and devise lesson plan for introducing the concept of plain figure 'kite'. For gathering data, 77 pre-service elementary school teachers were selected from the University of Education located in G city. Several conclusions were drawn as follow: first, task for applying MKT is needed to check whether pre-service teachers can apply. Second, assessment is needed to check what kind of MKT do pre-service elementary school teachers have.

• Journal of Educational Research in Mathematics
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• v.26 no.4
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• pp.769-789
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• 2016

Pattern activities are useful to develop functional thinking of young students, but there has been lack of research on how to teach patterns. This study explored teaching methods of geometric patterns for developing functional thinking of elementary school students, and then analyzed the lessons in which such methods were implemented. For this, three classrooms of fourth grades in elementary schools were selected and three teachers taught geometric patterns on the basis of the same lesson plan. The lessons emphasized noticing the commonality of a given pattern, expanding the noti ce for the commonality, and representing the commonality. The results of this study showed that experience of analyzing the structure of a geometric pattern had a significant impact on how the fourth graders reasoned about the generalized rules of the given pattern and represented them in various methods. This paper closes with several implications to teach geometric patterns in a way to foster functional thinking.

• Journal of Elementary Mathematics Education in Korea
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• v.22 no.3
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• pp.267-282
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• 2018

The purpose of this study is to develop and apply a Convergence program for teaching of congruence and symmetry and to investigate the effects of the mathematical creativity and convergence talent. For these purposes, research questions were set up as follows: 1. How is a Convergence program for teaching of congruence and symmetry developed? 2. How does a Convergence program affect the mathematics creativity and convergence talent of fifth grade student in elementary school? The subjects in this study were 16 students in fifth-grade class in elementary school located in Songpa-gu, Seoul. A Convergence program was developed using the integrated unit design process chose the concept of congruence and symmetryas its topic. The developed program consisted of a total 12 class activities plan, lesson plans for 5 activities. Mathematics creativity test, a test on affective domain related with convergence talent measurement were carried out before and after the application of the developed program so as to analyze the its effects. In addition, students' satisfaction for the developed program was investigated by a questionnaire. The results of this study were as follows: First, A convergence program should be developed using the integrated unit design process to avoid focusing on the content of any one subject area. The program for teaching of congruence and symmetry should be considered students' learning style and their preferences for media. Second, the convergence program improved the students' mathematical creativity and convergence talent. Among the sub-factors of mathematical creativity, originality was especially improved by this program. Students thought that the program is good for their creativity. Plus, this program use two subject class, Math and Art, so student do not think about one subject but focus on topic 'congruence and symmetry'. It help students to develop their convergence talent.

• School Mathematics
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• v.18 no.2
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• pp.277-300
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• 2016

In school mathematics, the definition and concept of a differentiation has been dealt with as a formula. Because of this reason, the learners' fundamental knowledge of the concept is insufficient, and furthermore the learners are familiar with solving routine, typical problems than doing non-routine, unfamiliar problems. Preceding studies have been more focused on dealing with the issues of learner's fallacy, textbook construction, teaching methodology rather than conducting the more concrete and efficient research through experiment-based lessons. Considering that most studies have been conducted in such a way so far, this study was to create a lesson plan including teaching resources to guide the understanding of differential coefficients and derivatives. Particularly, on the basis of the theory of Historical Genetic Process Principle, this study was to accomplish the its goal while utilizing a technological device such as GeoGebra. The experiment-based lessons were done and analyzed with 68 first graders in S high school located in G city, using Posttest Only Control Group Design. The methods of the examination consisted of 'learning comprehension' and 'learning satisfaction' using 'SPSS 21.0 Ver' to analyze students' post examination. Ultimately, this study was to suggest teaching methods to increase the understanding of the definition of differentials.

• Education of Primary School Mathematics
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• v.16 no.2
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• pp.123-145
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• 2013

This study was expected to yield the meaningful conclusions from the experimental group who took lessons based on inductive activities using GeoGebra at the beginning of proof learning and the comparison one who took traditional expository lessons based on deductive activities. The purpose of this study is to give some helpful suggestions for teaching proof to mathematically gifted elementary students. To attain the purpose, two research questions are established as follows. 1. Is there a significant difference in proof abilities between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? 2. Is there a significant difference in proof attitudes between the experimental group who took inductive lessons using GeoGebra and comparison one who took traditional expository lessons? To solve the above two research questions, they were divided into two groups, an experimental group of 10 students and a comparison group of 10 students, considering the results of gift and aptitude test, and the computer literacy among 20 elementary students that took lessons at some education institute for the gifted students located in K province after being selected in the mathematics. Special lesson based on the researcher's own lesson plan was treated to the experimental group while explanation-centered class based on the usual 8th grader's textbook was put into the comparison one. Four kinds of tests were used such as previous proof ability test, previous proof attitude test, subsequent proof ability test, and subsequent proof attitude test. One questionnaire survey was used only for experimental group. In the case of attitude toward proof test, the score of questions was calculated by 5-point Likert scale, and in the case of proof ability test was calculated by proper rating standard. The analysis of materials were performed with t-test using the SPSS V.18 statistical program. The following results have been drawn. First, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in proof ability than the comparison group who took traditional proof lessons. Second, experimental group who took proof lessons of inductive activities using GeoGebra as precedent activity before proving had better achievement in the belief and attitude toward proof than the comparison group who took traditional proof lessons. Third, the survey about 'the effect of inductive activities using GeoGebra on the proof' shows that 100% of the students said that the activities were helpful for proof learning and that 60% of the reasons were 'because GeoGebra can help verify processes visually'. That means it gives positive effects on proof learning that students research constant character and make proposition by themselves justifying assumption and conclusion by changing figures through the function of estimation and drag in investigative software GeoGebra. In conclusion, this study may provide helpful suggestions in improving geometry education, through leading students to learn positive and active proof, connecting the learning processes such as induction based on activity using GeoGebra, simple deduction from induction(i.e. creating a proposition to distinguish between assumptions and conclusions), and formal deduction(i.e. proving).

• Communications of Mathematical Education
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• v.20 no.1 s.25
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• pp.33-59
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• 2006

This study is intended to reconsider the meaning of the education for gifted/talented children, the foundation object of science high school by examining the behavior characteristics between gifted students and talented students in open-end mathematical problem solving and to provide the basis for realization of 'meaningful teaming' tailored to the learner's level, the essential of school education. For the study, 8 students (4 gifted students and 4 talented students) were selected out of the 1 st grade students in science high school through the distinction procedure of 3 steps and the behavior characteristics between these two groups were analyzed according to the basis established through the literature survey. As the results of this study, the following were founded. (1) It must be recognized that the constituent members of science high school were not the same excellent group and divided into the two groups, gifted students who showed excellence in overall field of mathematical behavior characteristics and talented students who had excellence in learning ability of mathematics. (2) The behavior characteristics between gifted students and talented students, members of science high school is understood and a curriculum of science high school must include a lesson for improving the creativity as the educational institutions for gifted/talented students, unlike general high school. Based on these results, it is necessary to try to find a support plan that it reduces the case which gifted students are generalized with common talented students by the same curriculum and induces the meaningful loaming to learners, the essential of school education.

• The Mathematical Education
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• v.62 no.1
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• pp.95-115
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• 2023

Even the teachers who agree with the necessity of effective mathematical discussions find it difficult to orchestrate such discussions in the actual lessons. This study focused on analyzing the difficulties 15 elementary school teachers faced in applying "the five practices for orchestrating productive mathematics discussions" to their lessons. Specifically, this study analyzed the process of planning, implementing, and reflecting on the lessons to which three or four teachers as a teacher community applied the five practices. The results of this study showed that the teachers experienced difficulties in selecting and presenting tasks tailored to the student levels and class environment, monitoring all students' solutions, and identifying the core mathematical ideas in student solutions. In addition, this study revealed practical and specific difficulties that had not been described in the previous studies, such as writing a lesson plan for effective use, simultaneously performing multiple teacher roles, and visually sharing student presentations. This study is expected to provide practical tips for elementary school teachers who are eager to promote effective mathematical discussions and to provoke professional discourse for teacher educators through specific examples.