• The Mathematical Education
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• v.47 no.2
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• pp.155-168
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• 2008

The theory of representation, which has been an important topic of epistemology, has long history of study. But it has diverse meaning according to the fields of argument. In this paper the author set the meaning of mathematical representation as the interrelation of internal and external representations. With this concept, the following items were studied. 1. Survey on the concepts of mathematical representations. 2. Investigation of pedagogical significance of the mathematical representations, taking into account the characteristics of school mathematics. 3. Recommendation of principles for teaching representation to cope with the problems that are related with cause of disliking each domain of the secondary school mathematics. This study is expected to enable the development of teaching methods to help students strengthening their ability to comprehend mathematical sentences.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Journal for History of Mathematics
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• v.10 no.1
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• pp.12-18
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• 1997

수학의 각 분야 중에서 선형성을 가지는 부분은 그 이론이 가장 정연하게 처리되나 이것이 선형대수학이라는 학문으로 형성된 것은 최근의 일이며, 더욱이 선형대수는 그 광범위한 응용성으로 인하여 더욱 중요시되게 되었다. 선형대수의 교육적 의의는 함수의 특수한 경우인 선형변환을 다룸으로서 선형성을 지닌 수학의 구조를 쉽게 파악할 수 있다는 것이며 더욱이 해석기하 등에도 쉽게 응용할 수 있게 된다. 본 논문에서는 타인, 쌍곡선, 포물선인 이차곡선을 행렬을 이용하여 표현하고, 좌표축의 회전이동과 평행이동을 통하여 행렬을 대각화하고, 고유치의 부호에 의하여 이차곡선의 변환과 분류를 다루었으며 더불어 곡선의 개형을 알아보았다.

• School Mathematics
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• v.13 no.3
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• pp.405-422
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• 2011

In this study, we consider the meaning of one-to-one correspondence through theoretical background under operation of matrix. On algebraic point of view, its significance is 'through one-to-one correspondence from a set with given structure, become a methods in order to induce an algebraic system in to a new set.' That is a key idea making isomorphic structure. Such process experiences necessity of mathematical fact, as well as the deep understanding of one-to-one correspon -dence. Also that becomes a base for develop a various mathematical concepts, such as matrix, exponential laws, symmetric difference, permutation and so on. This study help teachers and students to understand of mathematical concepts meaningfully and to facilitate teacher's professional development.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.397-413
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• 2018

The purpose of this study is to analyze the level of statistical literacy among fifth and sixth graders in the data presentation task based on the speculative data generation process. For the research, the data presentation tasks based on the speculative data generation process was designed and statistical literacy standards for evaluating the student's level was presented based on prior studies. It is meaningful that the stepwise presentation of the students' statistical literacy and analysis of their developmental patterns can help them to find their current position and reach a higher level of performance. In this study, the standard of statistical literacy level was clarified based on the previous research, and a new perspective was presented about the data presentation instruction in the statistical education by analyzing the students' responses by each level.

• Education of Primary School Mathematics
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• v.21 no.4
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• pp.445-459
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• 2018

The purpose of this study is to provide a method to help elementary school students learn ratio-related concepts effectively through visual representations. This study was conducted to identify the differences in the composition of ratio-related concepts between Korean and Singaporean textbooks, reconstruct a unit of proportional expressions and distributions by using visual representations and confirm the differences in performance between an experimental and a comparison group of 6th grade students. While the experimental group mathematics lessons is from the reconstructed textbook, the comparison group lessons is from an existing textbook that does not include any reconstructive representations. A t-test of mean was applied to determine the differences between the experimental and comparison group. Analysis revealed significant differences in the mean between the experimental group and the comparison group, and the intermediate level group showed more improvement compared to the higher and lower level groups. An implication of this study is that the application of visual representations can assist students' understanding of ratio-related concepts.

• Education of Primary School Mathematics
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• v.10 no.1 s.19
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• pp.1-13
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• 2007

For the last 30 years many researches were conducted to supply a lot of information on brain that were worth using in teaching and learning. They have showed that students received information through multi-path, and used familiar learning sense to present the received informations. However, nowadays only visual materials are mainly used in mathematics classroom. The purpose of this research is aimed to investigate implications of which learning senses are dominated to learn mathematics. Learning sense were catagorized to visual, auditory, and kinesthetic sense according to Politano & Paquin's classification. We surveyed student's learning senses using questionares. Subjects were composed of 141 elementary students, 117 middle school students, 145 high school students,, and 99 college students. T-test were used to investigate whether there are differences in student's learning senses according to grade levels or not.

• Journal of Elementary Mathematics Education in Korea
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• v.16 no.1
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• pp.145-166
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• 2012

The objective of this study is to analyze the cases related to the lingual and non-lingual metaphors used in the math class at elementary school and consider the values of metaphors as a teaching method for the subject of mathematics. Throughout this study, teachers' gestures are analyzed as lingual and non-lingual metaphors shown between teachers and students in the class for the topic of the inverse proportion in quartic equations for direct and inverse proportions in Chapter 7 for the first semester of the 6th grade at elementary school in terms of the amended curriculum for the year of 2007. According to the results of the analysis, it can be concluded that there are mechanical and hypothetical movement metaphors in the mathematical metaphors observed in this study. Also, in terms of gestures, iconic, metaphoric and deixis gestures are found. Such metaphors seem to be evenly distributed throughout the math class and expressed in various forms. Based on the results of the analysis, the educational meaning given by the utilization of metaphors is considered for the math class.

• The KIPS Transactions:PartA
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• v.12A no.5 s.95
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• pp.385-390
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• 2005

Set constraints logic language is a language that adopts `set theory` in programming. In this paper, we introduce the procedure for solving set constraints proposed by A. Dovier and show how the procedure can be implemented in logic language Prolog. The procedure is represented in `rewriting rules` and this representation is characterized by having nondeterministic rule applicationsand mathematical variables that is difficult to be implemented in general programming languages. In this paper, we show that the representation can be easily implemented by using nondeterministic control, logical variables and data structure `list` provided in Prolog. Our implementation has following advantages.First we have implemented the full features of the language. Second we have described the implementation detail in thisresearch. Third other used the commercial Prolog called SICStus, but we are using CIAO Prolog with GNU GPL(General Public License) and anyone can use it freely. Forth the software of our implementation is open source so anyone can use, modify, and distribute it freely.

• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.1-30
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• 2020

This study was carried out in order to identify the error types of statistical graphs for statistical literacy education. We analyze the meaning of using graphs in statistical problem solving, and identify categories, frequencies, and contexts as the components of statistical graphs. Error types of representing categories and frequencies make statistics consumers see incorrect distributions of data by subjective point of view of statistics producers and visual illusion. Error types of providing contexts hinder the interpretation of statistical information by concealing or twisting the contexts of data. Moreover, the findings show that tasks provide standardized frame already for drawing graphs in order to avoid errors and pay attention to the process of drawing the graph rather than statistical literacy for analyzing data. We suggest some implications about statistical literacy education, ethical problems, and knowledge for teaching to be considered when teaching the statistical graph in elementary mathematics classes.