• The Mathematical Education
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• v.57 no.2
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• The Mathematical Education
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• v.55 no.1
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• pp.73-89
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• 2016

The purpose of this study was to analyze middle school students' problem posing types and strategies. we analyzed problems posed by 120 middle school students during mathematics class focused on problem posing activities in various aspects. Students' posed problems were classified into five types: not a problem(NP), non-math(NM), impossible(IM), insufficient(IN), sufficient(SU) and each of the posed problems. Students used three kinds of problem posing strategies such as goal manipulation(GM), assumption manipulation(AM), and condition manipulation(CM), and in posing one problem, one or more than two strategies were used. According to the prior studies, problem posing can contributes to the development of students' problem solving ability, creativity, mathematical aptitude, and a broader understanding of mathematical concepts. However, we found that some students had difficulties in posing problems or limited understandings of that. We hope the results of the study contribute to encouraging problem posing activities in mathematics instruction.

• School Mathematics
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• v.12 no.2
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• pp.151-176
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• 2010

This research aims to conduct the teaching experiment based on the constructivism to elementary preservice teachers and report on how they construct and develop the mathematical knowledge on ratio concept. Furthermore, this research aims to examine the significances and difficulties of "constructivist teaching experiment" which are conceived by elementary preservice teachers. As the results of this research, I identified the possibilities and limits of mathematical knowledge construction by elementary preservice teachers in the "constructivist teaching experiment". And the elementary preservice teachers pointed out the significances of "constructivist teaching experiment" such as the experience of prior thinking on the concept to be learned, the deep understanding on the concept, the active participation to the lesson, and the experience of learning process of elementary students. Also they pointed out the difficulties of "constructivist teaching experiment" such as the consumption of much time to carry out the constructivist teaching, the absence of direct feedbacks by teacher, and the adaption on the constructivist lesson.

• Journal of Elementary Mathematics Education in Korea
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• v.14 no.2
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• pp.377-399
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• 2010

Mixed calculations involving fractions and decimals covered in the unit 6-Na in elementary school math class cause students difficulties, leading them make lots of errors. If students fail to understand temporarily or partly what the teacher taught or lose confidence and continue to have difficulty due to a lack of understanding and skills of algorithm, though they properly understand the concept and principle of the learning content, it should be resolved through intensive teaching. For students suffering from this problem, a correct diagnosis and appropriate treatment are required. Therefore, this study developed a feedback program after diagnosing students' errors through evaluating them in order to continuously assist them to fully understand contents regarding mixed calculations involving fractions and decimals.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.655-674
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• 2013

The MEST determined to introduce a vocational ability test for the students in vocational high schools to enhance their job competence skills from 2013 accepting the field voices that current competence test is not proper for vocational high schools whose purpose is job preparation education. The test results can be used as an official certificate in the job settlement process. The purpose of this study is to enhance the students's basic skills for mathematics in vocational high schools and in addition to that, to develop mathematics teaching materials aiming to support students in applying mathematics in real vocational world after their learning mathematics in high schools. It seems that the students in vocational high schools experiencing difficulties in mathematics because of the lack of the basic skills for mathematics demanding for the restructuring the mathematics curriculum aiming for empowering to the maximum of the potential abilities of students in vocational high schools. For this purpose, we extracted essential elements from mathematics curricula ranging from elementary schools to middle schools and vocational high schools what is necessary for students in specialized high schools to enhance the students' abilities in using mathematics in vocational area. Based on above study, we analyzed, organized, and systemized the contents and levels of mathematics. Finally, we proposed in this paper the ways to build programs to enhance the students' essential mathematics skills aiming to level up the students' vocational ability required in real vocational companies.

• The Mathematical Education
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• v.58 no.4
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• pp.545-566
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• 2019

The purpose of this study is to show that research community activities can contribute to the professional development in respect of average concepts and mathematical creativity. In the community, activities were undertaken to transform the existing task into the task that contributes to the manifestation of creativity. In this process, researchers tried to connect the theory with the practice of the class, and the teacher acted as an active learner. The findings show that the teacher who had difficulty in teaching average could overcome difficulties, and also derived the way of task modification and strategies necessary for teaching average. The modified task induced improvements in students' achievement levels, which led to change in teachers' perspective on the relationship between mathematical creativity and learning. Research community activities have been shown to have contributed to improvements with regard to both teaching the average and promoting mathematical creativity.

• The Journal of the Korea Contents Association
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• v.8 no.5
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• pp.268-275
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• 2008

Providing appropriate and cooperative work among learners is an essential factor of a successful educational authoring system. Although from the viewpoint of beginning authors, many authoring functions are employed in existing authoring tool, there has been little research to solve authoring difficulties by companion's assist and to keep pace with learning. Therefore, in this paper, we designed and developed a educational authoring tool using mathematical language and cooperative work among learners, verified the validity. The authoring tool proposed has key features to hide authoring handicaps and keep pace with learning and cooperate with each other by using networked and language-based authoring tool.

• Communications of Mathematical Education
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• v.30 no.4
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• pp.515-530
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• 2016

Recently an extensive study of the mathematicians who have overcome the visually impaired and contribute to the academic in math was published. In the case of Korea, we can find there are mathematicians who have overcome physical disabilities such as cerebral palsy and polio. However there is no example of blind person who majored mathematics to become a mathematic's teacher or professor and have entered any mathematics related professions. This let us to study the reasons that caused difficulties to visually impaired students majoring in mathematics. We also suggest ways that may help blind students to have access to mathematics intuitively. In this study, we propose a tactile mathematics textbooks and teaching manuals utilizing 3D printing which the visually impaired students can touch and feel. We can supply such materials to visually impaired youth, special education teachers and parents in Korea. As a result, visually impaired students will be able to access mathematics easily and can build their confidence in mathematics. We hope that some blind students with mathematical talent do not hesitate to major mathematics and choose career in mathematical professions.

• Journal of the Korean School Mathematics Society
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• v.21 no.4
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• pp.303-326
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• 2018

Fraction has difficulties in learning because of the diversity of meanings, the ways of presenting contents and teaching methods in elementary school mathematics. Therefore, the various strategies of teaching of fraction concept is proposed as an alternative. The problem of equal sharing problem is that children can experience the concept of fractions naturally in the context of everyday distribution. Even before learning formal fractions, children can solve them in various ways based on their own experiences. The purpose of this study is to investigate the degree of problem solving and problem solving strategies for children in 2nd, 4th, and 6th grades in elementary school. As a result of the research, the percentage of correct answers increased as the grade increased, but the grade levels showed a difference depending on the numbers given to the problems. Also, there were differences in the problem solving strategies according to the grade levels. Also, according to the numbers presented in the problem, the percentage of correct answers was high in items that were easy to divide, and the percentage of correct answers was low in items that were difficult to divide. When children solved the problems, they were affected by the strategies they could use immediately according to the number presented in the problem, and their learning experiences were also affected.

• School Mathematics
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• v.16 no.4
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• pp.803-825
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• 2014

From the early stages of learning algebra, literal symbols are used to represent algebraic objects such as variables and parameters. The concept of parameters contains both indeterminacy and fixity resulting in confusion and errors in understanding. The purpose of this research is to compare the beginners of algebra and pre-service teachers who completed secondary mathematics education in terms of understanding this paradoxical nature of parameters. We recruited 35 middle school students in eight grade and 73 pre-service teachers enrolled in a undergraduate course at one university. Using them we conducted a survey on the perception of the nature of parameters asking if one considers parameters suggested in a problem as variables or constants. We analyzed the collected data using the mixed method of qualitative and quantitative approaches. From the analysis results, we identified several difficulties in understanding of parameters from both groups. Especially, our statistical analysis revealed that the proportions of subjects with limited understanding of the concept of parameters do not differ much in two groups. This suggests that learning algebra in secondary mathematics education does not improve the understanding of the nature of parameters significantly.