• The Mathematical Education
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• v.52 no.2
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• pp.217-230
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• 2013

This study attempts to propose the construction of textbook contents of fraction division and to suggest a method to strengthen the connection among problem context, manipulation activities and symbols by proposing an algorithm of dividing fractions based on problem contexts. As showing the suitable algorithm to problem context, it is able to understand meaningfully that the algorithm of fractions division is that of multiplication of a reciprocal. It also shows how to deal with remainder in the division of fractions. The results of this study are expected to make a meaningful contribution to textbook development for primary students.

• Communications of Mathematical Education
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• v.36 no.3
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• pp.313-334
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• 2022

The purpose of this study is to analyze the changes in mathematical learning through applying STEAM education according to social needs for out-of-school youth. For this purpose, we developed a teaching and learning model and program for mathematics and music STEAM education, and we implemented and analyzed the changes of affective area and problem-solving strategies. The analysis results of characteristic in affective area are as follows: first, the activity-oriented class of mathematics and music STEAM education aroused interest in mathematics. Second, providing opportunities for mathematics and music STEAM education instilled a positive perception of the value of mathematics and STEAM education. Third, the autonomous communication-oriented learning environment of mathematics and music STEAM education improved confidence and motivation to learn in mathematics. The analysis results of the characteristic in problem-solving strategy are as follows: first, through the STEAM education with mathematics and music, a conceptual understanding of internally and externally dividing points was formed, and a given problem was expressed and solved in a formula. Second, the functional correspondence relationship was understood, and the given problem was described and solved with symbols associated with the function. The suggestions of the study are as follows: first, based on the teaching and learning model and results of this study, various STEAM education programs for out-of-school youth should be developed and expanded to foster future competencies and provide new changes for out-of-school youth. Second, it can be used for research on the development of teaching and learning materials for convergence elective subjects in the high school credit system by referring to the mathematics and music convergence STEAM program of this study. As the subjects and fields of STEAM education are diversified and organized, students in need of receiving educational opportunities will be reduced, and there will be a world where the name of out-of-school youth and alternative education will not be necessary. Therefore, it is expected that development of teaching and learning programs created by interest in education of out-of-school youth will be used as an innovative idea in school education to achieve a virtuous cycle.

• Journal of the Korean School Mathematics Society
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• v.15 no.1
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• pp.53-80
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• 2012

This study was designed to find the characteristics of mathematical errors and discourse in simultaneous equations and inequalities for migrant students from North Korea. 5 sample students participated, who attended in an alternative school for the migrant students from North Korea at the study in Seoul, Korea. A total of 8 lesson units were performed as an extra curriculum activity once a week during the 1st semester, 2011. The results indicated that students showed technical errors, encoding errors, misunderstood symbols, misinterpreted language, and misunderstood Chines characters of Koreans and the discourse levels improved from the zero level to the third level, but the scenes of the third level did not constantly happen. Nevertheless, the components of discourse, explanation & justification, were activated and as a result, evaluation & elaboration increased in ERE pattern on communication.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.1-19
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• 2012

Kant defines mathematical cognition as the cognition by reason from the construction of concepts. In this paper, I inquire the meaning and the characteristics of the construction of concepts based on Kant's theory on the sensibility and the understanding. To construct a concept is to exhibit or represent the object which corresponds to the concept in pure intuition apriori. The construction of a mathematical concept includes a dynamic synthesis of the pure imagination to produce a schema of a concept rather than its image. Kant's transcendental explanation on the sensibility and the understanding can be regarded as an epistemological theory that supports the necessity of arithmetic and geometry as common core in human education. And his views on mathematical cognition implies that we should pay more attention to how to have students get deeper understanding of a mathematical concept through the construction of it beyond mere abstraction from sensible experience and how to guide students to cultivate the habit of mind to refer to given figures or symbols as schemata of mathematical concepts rather than mere images of them.

• Journal of Educational Research in Mathematics
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• v.20 no.3
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• pp.275-292
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• 2010

In this study, we discussed the way to teach algebra earlier through investigating to research trends of Early Algebra and researching about nature of subject involving algebra. There is a strong view that arithmetic and algebra have analogous forms and that algebra is on extension to arithmetic. Nevertheless, it is also possible to present a perspective that the fundamental goal and role of symbols and letters are difference between arithmetic and algebra. And, we could recognize that geometry was starting point of algebra trough historical perspectives. To consider these, we extracted some of possible directions to approaches to teach algebra earlier. To access to teaching algebra earlier, following ways are possible. (1) To consider informal strategy of young children. (2) Arithmetic reasoning considered of the algebraic relation. (3) Starting to algebraic reasoning in the context of geometrical problem situation. (4) To present young students to tool of letters and formular.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.10
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• pp.4231-4245
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• 2020

Non-orthogonal multiple access (NOMA) is widely studied in both academia and industry due to its high spectral efficiency over orthogonal multiple access (OMA). To effectively improve spectrum efficiency, an amplify-and-forward (AF) cooperative NOMA system is proposed as well as a novel detection scheme is proposed, in which we first perform successive interference cancellation (SIC) twice at U1 for the two signals received from two time slots to remove interference from symbol 2, then two new signals apply max ratio combining (MRC). In addition, a closed-form upper bound approximation for the ergodic capacity of our proposed system is derived. Monte-Carlo simulations and numerical analysis illustrate that our proposed system has better ergodic capacity performance than the conventional cooperative NOMA system with decode-forward (DF) relay, the conventional cooperative NOMA system with AF relay and the proposed AF cooperative NOMA system in [16]. In addition, we can see that ergodic capacity of all NOMA cooperative systems increase with the increase of transmit SNR. Finally, simulations display that power allocation coefficients have little effect on ergodic capacity of all NOMA cooperative systems. This is due to this fact that ergodic capacity of two symbols can be complementary with changing of power allocation coefficients.

• Journal of Korean Society of Transportation
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• v.34 no.3
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• pp.248-262
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• 2016

The study documents the analysis on characters and symbols shown in the pavement markings in the perspective of mathematics educators. The purpose of this study is to propose a pavement marking method that can enhance readability from the driver's eye position. To this end, this study analyzed the figure of the pavement markings that can be actually recognized by the projective geometry perspective. As a result, it proposed alternatives to the current pavement markings by introducing the concept of the compression ratio. Results of the study are as follows. First, the rule was established to obtain the compression ratio. If the observation of two viewing angles are x and y, then the compression ratio S is ${\sin}y/{\cos}\(\frac{x-y}{2}\)$. Second, we presented two alternatives to the pavement marking method for the displayed information. One is a method for improving the pavement markings in terms of the compression ratio, the other is a method by varying vertical length of the pavement markings while holding its width constant. Based on the outcomes from this study, a mathematical analysis can be further studied for the perception of speed according to the types of pavement marking line.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• 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.

• Education of Primary School Mathematics
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• v.19 no.1
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• pp.1-18
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• 2016

Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.