• School Mathematics
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• v.17 no.3
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• pp.407-421
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• 2015

Linear system is a basic subject matter of school mathematics courses. Even though elimination is a useful method to solve linear systems, its fundamental principles were not discussed pedagogically. The purpose of this study is to help the development of mathematical content knowledge on linear systems conceptions. To do this, various representations and translations among them were considered, and in particular, the basic principles for elimination method are analyzed geometrically. Rectangular representation is used to solve word problem treated in numbers of things in elementary mathematics and it is useful as a pre-stage to introduce elimination. Slopes and intercepts of lines associated linear equations are used to obtain the Cramer's formula and this solving method was showing the connection between algebraic and geometric procedures. Strategy deleting variables of linear systems by elementary operations is explored and associated with the movements of lines in the family of lines passing through a fixed point. The development of mathematical content knowledge is expected to enhance pedagogical content knowledges.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.67-88
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• 2020

This study analyzed the characteristics of prospective teachers' Horizon Content Knowledge(HCK) related to understandings of an inverse function symbol. This study aimed to deduce implications of developing HCK in terms of the means which would enhance mathematics teachers' professional development. In order to achieve the aim, this study identified features of HCK by examining the previous literature on HCK, which has conformed Ball & Bass(2009) and exploring the research in AMT, including Zazkis & Leikin(2010) which has emphasized cultivating AMT through university mathematics education. In addition, a questionnaire was developed regarding the features of HCK and taken by 57 prospective teachers. By analyzing the data obtained from the written responses the participants presented, this study delineated the specific characteristics of the teachers' HCK with regard to an inverse function symbol. Additionally, several issues in the teacher education for improving HCK were discussed, and the results of this research could inspire designing and implementing a teacher education program relevant to HCK.

• School Mathematics
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• v.16 no.1
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• pp.111-133
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• 2014

This study aims to explore mathematical belief system and core belief factors to be found. The mathematical belief system becomes an auto regulation device for students' using mathematical knowledge in mathematical situations and provides them with the context to perceive and understand mathematics. They have individual mathematical beliefs for each of mathematics subject, mathematical problem solving, mathematical teaching and learning and self-concept, and these beliefs of students construct mathematical belief system according to mutual relationships among the mathematical beliefs. Using correlation analysis and multiple regression, mathematical belief system was structuralized and core belief factors were found. Mathematical belief system is structuralized and, as a result the core belief factors that are psychological centrality of high school students' mathematical belief system are found to be persistence, challenge, confidence and enjoyment. These core belief factors are formed on the basis of personal experiences and they are personal primitive beliefs that cannot be changed with ease and cannot be shared with other people but they are related with many other beliefs influencing them.

• Communications of Mathematical Education
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• v.34 no.3
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• pp.355-372
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• 2020

The concept of infinite series is an important subject of major mathematics curriculum in college. For several centuries it has provided learners not only counter-intuitive obstacles but also central role of analysis study. As the understanding in concept on infinite series became foundation of development of calculus in history of mathematics, it is essential to present students to study higher mathematics. Most students having concept of infinite sum have no difficulty in mathematical contents such as convergence test of infinite series. But they have difficulty in organizing concept of infinite series of partial sum. Thus, in this study we try to analyze construct the concept of infinite series in terms of APOS theory and genetic decomposition. By checking to construct concept of infinite series, we try to get an useful educational implication on teaching of infinite series.

• School Mathematics
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• v.12 no.1
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• pp.45-60
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• 2010

In school mathematics, gakdo(korean, ie angular measure in english) lost effectiveness as a term, on the other hand, an expression gak-ui-kugi(korean, ie size of angle in english) is prevalent these days. So it is necessary to accept this expression. It is necessary to specify in textbook that the size of angle rely on the degree of gap between two edges regardless of the length of edges. The content of curriculum manual and the content of textbooks must be reconciled. Random units for measuring the size of angle are not contained in textbooks. It can be possible, but it is not carried out actually. So, it is necessary not to require it in curriculum manual considering this circumstance. In curriculum manual, it is necessary to specify the role of 1-right angle as a standard unit, and situations to use it must be presented in textbooks. In cut-paste method of finding the sum of the size of three angles in a triangle and the sum of the size of four angles in a quadrilateral, keeping a straight angle and one rotation in mind, an explanation is based upon a premise that students know how to express the $180{^{\circ}}$ and $360{^{\circ}}$ in figure as a result. It is a leap of logic.

• Communications of Mathematical Education
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• v.32 no.4
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• pp.477-493
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• 2018

The six core competencies included in the mathematics curriculum Revised in 2015 are problem solving, reasoning, communication, attitude and practice, creativity and convergence, information processing. In particular, the creativity and convergence competency is very important for students' enhancing much higher mathematical thinking. Based on the creativity and convergence competency, this study selected the five elements of the creativity and convergence competency such as productive thinking element, creative thinking element, the element of solving problems in diverse ways, and mathematical connection element, non-mathematical connection element. And also this study selected the content(chapter) of the graph in the seventh grade mathematics textbook. By the subject of the ten kinds of textbook, this study examined how the five elements of the creativity and convergence competency were shown in each textbook.

• The Mathematical Education
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• v.61 no.4
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• pp.581-595
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• 2022

The purpose of this study is to specify the procedure for making item models based on ontology models using automatic item generation in the mathematics subject through the CAFA system, and to explore the generated item instances. As an illustration for this, an item model was designed as a part of formative assessment based on the content characteristics, including concepts and calculations, and process characteristics, including application, using the representative values and the measures of dispersion in Mathematics of the 9th grade based on the evaluation criteria achievement standards. The item types generated in one item model were a best answer type, a correct answer type, a combined-response type, an incomplete statement type, a negative type, a true-false type, and a matching type. It was found that HTML, Google Charts, TTS, figures, videos and so on can be used as media. The implications of the use of digital evaluation based on automatic item generation were suggested in the aspects of students, pre-service teachers, general teachers, and special education, and the limitations of this study and future research directions were presented.

• The Mathematical Education
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• v.60 no.2
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• pp.209-228
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• 2021

The purpose of this study is developed the Item Feature Analysis (IFA) frameworks for curriculum-based assessments, focusing on Math competency and representation in secondary schools and implemented the IFA in National Assessment of Educational Achievement. To conduct the study, previous studies were analyzed, and feasibility studies were conducted twice. As a result of the study, we structured the IFA framework based on the 2015 revised mathematics curriculum in Korea and developed a method to analyze the characteristics of the math items. The results of structuring the framework for math included two categories: math competency in the content aspects, and representation type in the formal aspects. Specifically, 12 features of math competency and 8 features of representation type were identified, and an item feature analysis framework composed of these features was developed. The math competency was developed based on the subject competency of 2015 national curriculum. Math assessments in high schools, which have been changed to the competency-based assessments, had more frequency of the feature of math competency compared to middle schools. In this study, implemented the IFA in National Assessment of Educational Achievement and explored the way of ensuring the validity. These have been proved as critical applications for ensuring the validity of curriculum-based student assessment as well as building a tool for assessment.

• Communications of Mathematical Education
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• v.37 no.2
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• pp.199-212
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• 2023

The purpose of this study is to find out whether there is a difference in achievement between blocked practice and interleaved practice according to the difference in domain and type of learning content in mathematics subject, and through this result, it is to confirm whether the effect of interleaved practice in mathematics learning is due to the 'Discriminative-contrast Hypothesis' or the 'Distributed-practice Hypothesis'. Although interleaved practice is more effective than blocked practice, previous studies have not shown consistent results regarding the cause. Therefore, in this study, 103 first-year middle school students were randomly assigned to blocked practice, interleaved practice, remote blocked practice, and remote interleaved practice groups had learning activities over 4 times. The results reveals that the effect of interleaved practice appeared in similar types in the same domain, but the effect of interleaved practice did not appear in different types in different domain. In addition, through this result, it was confirmed that the effect of interleaved practice was due to the 'Discriminative-contrast hypothesis' rather than the 'Distributed-practice hypothesis'. Further research topics were suggested after the issues on the research method and the findings were discussed.

• Journal of the Korean School Mathematics Society
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• v.9 no.4
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• pp.557-573
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• 2006

The purpose of this study is to examine the usefulness of teaching Maple in College Mathematics Education. The subject are 60 students of college of science in H university and C university located in Daejeon. They were divided into two parts; an experimental group (group I, group II, each of 20 students) and a control group (group III of 20 students). The group I and II are provided calculus lecture in class as well as Maple lab, while group III are lectured only in class. In order to know the effectiveness of using Maple, a test is designed in the way that group I is allowed to use both pencil and Maple, while group II and III are restricted to use only pencil. The result of this study is as follows. i) According to the performance of testing exam, there is no significant difference between three groups (p>.05) when they are allowed to use only pencil. ii) The achievement of group I is much higher than that of group II and III (p<.05) when they were provided both pencil and Maple. iii) Lot of students in group I who fail to solve with pencil can succeed in solving problems using Maple.