• Journal of Elementary Mathematics Education in Korea
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• v.3 no.1
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• pp.21-39
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• 1999

In this paper, we first exam the relation between Piaget's theory of cognitive development and cognitive constructivism. With it's outcome We find three principles of constructivist teaching-learning methods for primary mathematics These are as follows 1) active learning based on self-regulatory process 2) empirical learning by self initiated activities 3) individual learning derived from present cognitive structure and fits of new experiences. Finally we introduce several examples for classroom practice applied the above principles in primary mathematics.

• School Mathematics
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• v.14 no.1
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• pp.109-134
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• 2012

The purpose of this study is to develop authentic assessment model and example tools of mathematics teaching and learning. By reviewing literature researches, we set up the definition of authentic assessment in mathematics education, checked the criterian of authentic assessment tasks and mathematical activities. We searched various assessment models of mathematics teaching and learning, project assessment proceeding model, and criterian of project assessment, and checked various project tasks of the authentic assessment. And we developed authentic assessment model and example tools of mathematics teaching and learning. The model is applied project tasks in the form of being integrated with class to high school students, with high school mathematics especially. Furthermore, we carried the test of content validity for a validity of developed tasks for experts in studies of mathematics education. The result is that authentic assessment model and example tools of mathematics teaching and learning has an significance in mathematics education and can be used to judge whether students are doing 'real' mathematics or not, keeping the applicability in the form of being integrated with class.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.05a
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• pp.81-84
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• 2006

• School Mathematics
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• v.7 no.2
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• pp.169-192
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• 2005

The purpose of this study is to provide the conformity for developing project-based teaching$\cdot$learning materials for the mathematically gifted students. And this study presents development procedural model in order to improve the effectiveness, analyze its practical usage and examine the verification of the developed materials. It made the following results regarding the development of project-based teaching$\cdot$learning materials for gifted children in mathematics. First, it is necessary to provide appropriate teaching$\cdot$learning model to develop the materials, and the materials should be restructured to be available to other level students. Second, it is suggested to develop a prototype in order to develop teaching$\cdot$learning materials for gifted children in mathematics, further the prototype needs to be restructured until it satisfies theoretical frame. Third, an introduction should be made before the activity to perform the projects effectively. Fourth, a teacher's guidance should introduce children's examples corresponding to the objectives of learning, the examples of topics examined by students, and teacher's manual and attention for teaching. This study has a point of presenting the detailed guidelines with regards to development of teaching$\cdot$learning materials for gifted students in mathematics. This study has a point of presenting the detailed guidees with regards to development of teaching$\cdot$learning materials for gifted students in mathematics.

• School Mathematics
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• v.11 no.2
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• pp.243-260
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• 2009

In this paper, we have designed a teaching unit for the learning mathematising of secondary pre-service teachers by exploring generalized fibonacci sequences. First, we have found useful formulas for general terms of generalized fibonacci sequences which are expressed as combinatoric notations. Second, by using these formulas and CAS graphing calculator, we can help secondary pre-service teachers to conjecture and discuss the limit of the sequence given by the rations of two adjacent terms of an m-step fibonacci sequence. These processes can remind secondary pre-service teachers of a series of some mathematical principles.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.163-180
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• 2019

This study introduces a development of calculus contents which makes to understand the main concepts of calculus in a short period of time and to enhance problem solving and computational thinking for complex problems encountered in the real world for college freshmen with diverse backgrounds. As a concrete measure, we developed 'Teaching and Learning' contents and Python-based code for Calculus I and II which was used in actual classroom. In other words, the entire process of teaching and learning, action plan, and evaluation method for calculus class with Python based coding are reported and shared. In anytime and anywhere, our students were able to freely practice and effectively exercise calculus problems. By using the given code, students could gain meaningful understanding of calculus contents and were able to expand their computational thinking skills. In addition, we share a way that it motivated student activities, and evaluated students fairly based on data which they generated, but still instructor's work load is less than before. Therefore, it can be a teaching and learning model for college mathematics which shows a possibility to cover calculus concepts and computational thinking at once in a innovative way for the 21st century.

• School Mathematics
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• v.12 no.4
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• pp.493-506
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• 2010

In this study, we conducted classroom activities that are exploring and explaining visualized materials for problem solving of school mathematics with pre-service teachers in 2007~2009. After finishing these classroom activities, pre-service teachers recorded an afternote that includes changes of their thinking about mathematics and mathematics education through these activities in this study. We collected various opinions of pre-service mathematics teachers. From the analysis these data, we searched educational effects of our classroom activities. Through conducting the practice like these classroom activities of our study, pre-service mathematics teachers will have an opportunity of a practical training that supports the teaching of mathematical problem-solving. Moreover their PCK will be enhanced. Also, They will learn a good way to realize the aim of school mathematics curriculum.

• School Mathematics
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• v.11 no.1
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• pp.55-70
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• 2009

The purpose of this study is to implement Lakatos method in the teaching and learning of geometry for middle school students. In his landmark book , Lakatos suggested the following instructional approach: an initial conjecture was produced, attempts were made to prove the conjecture, the proofs were repeatedly refuted by counterexamples, and finally more improved conjectures and refined proofs were suggested. In the study, students were selected from the high achieving students who participated in the special mathematics and science program offered by the city council of Seoul. The students were given a contradictory geometric proposition, and expected to find the cause of the fallacy. The students successfully identified the fallacy following the Lakatos method. In this process they also set up a primitive conjecture and this conjecture was justified by the proof and refutation method. Some implications were drawn from the result of the study.

• Communications of Mathematical Education
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• v.28 no.4
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• pp.431-455
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• 2014

The purpose of this study was to suggest methods to apply generalizability theory to mathematics teacher evaluation using classroom observations in Korea by analysing mathematics teachers in the U.S. using the instructional quality of assessment instrument as an illustrative example. The subjects were 96 teachers participating in Year 3 and Year 4 from the Middle-school Mathematics and the Institutional Setting of Teaching (MIST) project funded by the National Science Foundation since 2007. The MIST project investigates the following question: What does it takes to support mathematics teachers' development of ambitious and equitable instructional practices on a large scale (MIST, 2007). This study examined data based on both the univariate generalizability analysis using GENOVA program and the multivariate generalizability analysis using mGENOVA program. Specifically, this study determined the relative effects of each error source and investigated optimal measuring conditions to obtain the suitable generalizability coefficients. The methodology applied in this study can be utilized to find effective optimal measurement conditions for the mathematics teacher evaluation for professional development in Korea. Finally, this study discussed limitations of the results and suggested directions for future research.

• Journal of Science Education
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• v.43 no.1
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• pp.17-42
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• 2019

This study, as an attempt to integrate mathematics and information for convergence education, was conducted to develop teaching-learning materials on mathematics education combined with coding education, which has recently been emphasized. We chose the subject of digital signature for coding education, and used SageMath as a coding program. In this study, we overview mathematics used in the elliptic curve digital signature algorithm, one of the many methods for digital signature, and developed the teaching-learning materials on the algorithm for mathematics education integrated with information education based on coding. The elliptic curve digital signature algorithm utilized in transactions of Bitcoin, which many people recently are interested in, is a good example, showing students that mathematics is applied to problem-solving in the real world and provides an optimal environment for implementation by coding. Accordingly, we expect that a class on algorithm will provide a specific teaching-learning program to achieve the goal of integrated mathematics education. By comprehensively considering the opinions of mathematicians, mathematics teachers and mathematics education experts, we expect that the teaching-learning program will be realized as a meaningful class in science high schools, high school's math clubs, and 'number theory' class in colleges.