• School Mathematics
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• v.9 no.1
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• pp.13-28
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• 2007

Division of fractions can be categorized as measurement division, partitive or sharing division, the inverse of multiplication, and the inverse of Cartesian product. Division algorithm for fractions has been interpreted with manipulative aids or models mainly in the contexts of measurement division and partitive division. On the contrary, there are few interpretations for the context of the inverse of a Cartesian product. In this paper the significance and the limits of existing interpretations of division of fractions in the context of the inverse of a Cartesian product were discussed. And some new easier interpretations of division algorithm in the context of a Cartesian product are developed. The problem to determine the length of a rectangle where the area and the width of it are known can be solved by various approaches: making the width of a rectangle be equal to one, making the width of a rectangle be equal to some natural number, making the area of a rectangle be equal to 1. These approaches may help students to understand the meaning of division of fractions and the meaning of the inverse of the divisor. These approaches make the inverse of a Cartesian product have many merits as an introductory context of division algorithm for fractions.

• School Mathematics
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• v.19 no.4
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• pp.663-690
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• 2017

The aim of this study is to look into the meaning and sub-factors of spatial orientation, compare and analyze mathematics curriculums and textbooks of several countries with respect to spatial orientation and offer suggestions to improve teaching spatial orientation in elementary school mathematics in Korea. In order to attain these purposes, this study examined the meaning and sub-factors of spatial orientation through the theoretical consideration regarding various studies on spatial sense. Based on such examination, this study compared and analyzed mathematics curriculums and textbooks used in South Korea, Singapore, Japan, China, Hong Kong, Finland, United States of America, and Germany with respect to contents of mathematics curriculum and textbooks in grades, sub-factors of spatial orientation, and contexts for spatial orientation. In the light of such theoretical consideration and analytical results, this study provided suggestions for improving teaching spatial orientation in elementary schools in Korea as follows: extending content of spatial orientation in mathematics curriculum, emphasizing spatial orientation across the several grades, especially in the upper grades, providing opportunities to learn the sub-factors of location, direction, coordinates, route, and distance variously, and utilizing various familiar and realistic contexts in the world around students.

• Journal of Educational Research in Mathematics
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• v.26 no.1
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• pp.47-62
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• 2016

Cultivating mathematical creativity is one of the aims in the recently revised mathematics curricular. However, there have been lack of researches on how to nurture mathematical creativity for ordinary students. Perspective of Realistic Mathematics Education(RME), which pursues education of creative person as the ultimate goal of mathematics education, could be useful for developing principles and methods for cultivating mathematical creativity. This study reanalyzes RME from the points of view in mathematical creativity education. Major findings are followed. First, students should have opportunities for mathematical creation through mathematization, while seeking and creating certainty. Second, it is vital to begin with realistic contexts to guarantee mathematical creation by students, in which students can imagine or think. Third, students can create mathematics in realistic contexts by modelling. Fourth, students create the meaning of 'model of(MO)', which models the given context, the meaning of 'model for(MF)', which models formal mathematics. Then, students create MOs and MFs that are equivalent to the intial MO and MF given by textbook or teacher. Flexibility, fluency, and novelty could be employed to evaluate the MOs and the MFs created by students. Fifth, cultivation of mathematical creativity can be supported from development of local instructional theories by thought experiment, its application, and reflection. In conclusion, to employ the education model of cultivating mathematical creativity by RME drawn in this study could be reasonable when design mathematics lessons as well as mathematics curriculum to include mathematical creativity as one of goals.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.363-384
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• 2001

The purpose of this thesis is, through analysing the characteristics of the definitions in Korean school mathematics textbooks, to explore the levels of them and to make suggestions for definition - teaching as a mathematising activity, Definitions used in academic mathematics are rigorous. But they should be transformed into various types, which are presented in school mathematics textbooks, with didactical purposes. In this thesis we investigated such types of transformation. With the result of this investigation we tried to identify the levels of the definitions in school mathematics textbooks. And in school mathematics textbooks there are definitions which carry out special functions in mathematical contexts or situations. We can say that we understand those definitions, only if we also understand the functions of definitions in those contexts or situations. In this thesis we investigated the cases in school mathematics textbooks, when such functions of definition are accompanied. With the result of this investigation we tried to make suggestions for definition-teaching as an intellectual activity. To begin with we considered definition from two aspects, methods of definition and functions of definition. We tried to construct, with consideration about methods of definition, frame for analysing the types of the definitions in school mathematics and search for a method for definition-teaching through mathematization. Methods of definition are classified as connotative method, denotative method, and synonymous method. Especially we identified that connotative method contains logical definition, genetic definition, relational definition, operational definition, and axiomatic definition. Functions of definition are classified as, description-function, stipulation-function, discrimination-function, analysis-function, demonstration-function, improvement-function. With these analyses we made a frame for investigating the characteristics of the definitions in school mathematics textbooks. With this frame we identified concrete types of transformations of methods of definition. We tried to analyse this result with van Hieles' theory about levels of geometry learning and the mathematical language levels described by Freudenthal, and identify the levels of definitions in school mathematics. We showed the levels of definitions in the geometry area of the Korean school mathematics. And as a result of analysing functions of definition we found that functions of definition appear more often in geometry than in algebra or analysis and that improvement-function, demonstration-function appear regularly after demonstrative geometry while other functions appear before demonstrative geometry. Also, we found that generally speaking, the functions of definition are not explained adequately in school mathematics textbooks. So it is required that the textbook authors should be careful not to miss an opportunity for the functional understanding. And the mathematics teachers should be aware of the functions of definitions. As mentioned above, in this thesis we analysed definitions in school mathematics, identified various types of didactical transformations of definitions, and presented a basis for future researches on definition teaching in school mathematics.

• Journal of Educational Research in Mathematics
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• v.9 no.1
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• pp.81-109
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• 1999

This study aims to reflect the basic principles and teaching-teaming principles of Realistic Mathematics Education in order to suppose an way in which mathematics as an activity is carried out in primary school. The development of what is known as RME started almost thirty years ago. It is founded by Freudenthal and his colleagues at the former IOWO. Freudenthal stressed the idea of matheamatics as a human activity. According to him, the key principles of RME are as follows: guided reinvention and progressive mathematisation, level theory, and didactical phenomenology. This means that children have guided opportunities to reinvent mathematics by doing it and so the focal point should not be on mathematics as a closed system but on the process of mathematisation. There are different levels in learning process. One should let children make the transition from one level to the next level in the progress of mathematisation in realistic contexts. Here, contexts means that domain of reality, which in some particular learning process is disclosed to the learner in order to be mathematised. And the word of 'realistic' is related not just with the real world, but is related to the emphasis that RME puts on offering the students problem situations which they can imagine. Under the background of these principles, RME supposes the following five instruction principles: phenomenological exploration, bridging by vertical instruments, pupils' own constructions and productions, interactivity, and interwining of learning strands. In order to reflect how to realize these principles in practice, the teaming process of algorithms is illustrated. In this process, children follow a learning route that takes its inspiration from the history of mathematics or from their own informal knowledge and strategies. Considering long division, the first levee is associated with real-life activities such as sharing sweets among children. Here, children use their own strategies to solve context problems. The second level is entered when the same sweet problems is presented and a model of the situation is created. Then it is focused on finding shortcomings. Finally, the schema of division becomes a subject of investigation. Comparing realistic mathematics education with constructivistic mathematics education, there interaction, reflective thinking, conflict situation are many similarities but there are alsodifferences. They share the characteristics such as mathematics as a human activity, active learner, etc. But in RME, it is focused on the delicate balance between the spontaneity of children and the authority of teachers, and the development of long-term loaming process which is structured but flexible. In this respect two forms of mathematics education are different. Here, we learn how to develop mathematics curriculum that respects the theory of children on reality and at the same time the theory of mathematics experts. In order to connect the informal mathematics of children and formal mathematics, we need more teachers as researchers and more researchers as observers who try to find the mathematical informal notions of children and anticipate routes of children's learning through thought-experiment continuously.

• Journal of Educational Research in Mathematics
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• v.14 no.4
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• pp.367-385
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• 2004

This study intends to compare the way of introducing fractions in elementary mathematics textbooks of south and those of north Korea. After thorough investigations of the seven differences were identified. First, the mathematics textbooks of south Korea use concrete materials like apples when they introduce equal partition context, while those of north Korea do not use that kind of concrete materials. Second, in the textbooks of south Korea, equal partition of discrete quantities are considered after continuous ones are introduced. This is different from the approach of the north Korean text-books in which both quantities are regarded at the same time. Third, the quantitative fraction which refers to the rational number with unit of measure at the end of it, is hardly used in the textbooks of south. However, the textbooks of north Korea use it as the main representations of fractions. Fourth, in the textbooks of south Korea, vanous activities related to fractions are more emphasized, while in the textbooks of north Korea, various meanings of fractions textbooks from south and north Korea focused on the ways of introducing partition approach and equivalence relation as operational schemes of fractions, the following play an important role before defining fraction. Fifth, the textbooks of south Korea introduce equivalent fractions with number one using number bar, and do not consider the reason why that sort of fractions are regarded. On the contrary, the textbooks of north Korea introduce structural equivalence relation by using various contexts including length measure and volume measure situations. Sixth, whereas real-life contexts are provided for introducing equivalent fractions in the textbooks of south Korea, visual explanations and mathematical representations play an important role in the textbooks of north Korea. Seventh, the means of finding equivalent fractions are provided directly in the textbooks of south Korea, whereas the nature of equivalent fractions and the methods of making equivalent fractions are considered in the textbooks of north Korea.

• (The) Korean Journal of Educational Psychology
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• v.22 no.2
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• pp.461-478
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• 2008

This study attempted to test whether or not students' collaborative argumentation and explanation activity while using concept mapping did improve understanding on texts. Total of 52 college students participated in this study. They were randomly assigned to one of four experimental conditions. The experiment lasted for two or three weeks and students were tested on comprehension level of a text material that they have studied over the period. As a result, with two independent factors of explanation and collaboration, there was a significant interaction effect without main effects. That is, individual did better when they did have to explain what they were doing. However, this is not the case when students collaborate. Students in the paired condition, they did better when they do not have to explain what they were doing with concept maps. This study showed efficiency with using computerized software does not always guarantee higher understanding on text materials. Instructional contexts and variables, collaboration and explanation, needs to be considered. Collaborating with others and explaining their own learning processes should be carefully designed when they are combined with concept mapping contexts. How to minimize learning obstacles from discussing ideas with others are a critical issue for future research.

• Journal of Korean Elementary Science Education
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• v.41 no.2
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• pp.186-198
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• 2022

With the science curriculum about to be revised in 2022, this study aimed to guide curriculum revision by addressing suggested approaches to the electromagnetism education in elementary school science curriculum. The core concepts of electromagnetism are "electric field" and "magnetic field" as a medium of force, but the current curriculum does not properly describe the core concepts of electromagnetism. Mechanics and electromagnetism should be linked in elementary schools to form science curriculum based on core concepts to solve this problem. Additionally, the nine aspects of technology extracted in this study offer various educational contexts to match the development of engineering technology based on electromagnetism. However, the current curriculum does not comprise these various contexts and focuses on the limited content of electric circuits using light bulbs. Therefore, it is necessary to expand the scope of the curriculum to better mirror real-life technology. Through the use of more diverse materials and contexts, the scope and level of STS education as well as conceptual learning could be expanded. Finally, in the case of electric circuit learning, various issues such as difficulty in connecting electric circuits and electric field concepts, representativeness of electric circuit, students' learning difficulty, and phenomena-oriented learning should be considered.

• Journal of the Korean earth science society
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• v.22 no.5
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• pp.427-447
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• 2001

Science teachers need to understand what science is, how students learn, how to teach science effectively, and the rationale for their teaching methods. Along this line, this article discusses constructivist learning theory as an alternative to the traditional pedagogy and the origin of various versions of constructivism. Constructivism is defined and used in a variety of contexts including philosophical constructivism, constructivist research paradigm, sociological constructivism, and educational constructivism. Educational constructivism (or psychological constructivism) can be divided into three distinct versions (i.e., individual, radical, and social constructivism) depending on unique ontological and epistemological beliefs that underlie each version. Each version of educational constructivism supports different conceptions of science teaching and learning that are consistent with its specific ontological and epistemological beliefs. In this article, the main tenets of each version of educational constructivism are examined with regard to ontological beliefs, epistemological commitments, and pedagogical beliefs. In addition, two major criticisms on constructivist pedagogy as well as implications for research methods for each version are also discussed.

• Journal of Christian Education in Korea
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• v.65
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• pp.163-187
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• 2021

The purpose of this study is to find the implications of Christian education on the relationship between the formation of faith and digital literacy in the Korean society, which is rapidly changing within the fourth Industrial Revolution today through critical conversations on educational contexts. Over the past decade, Korean society has lived in an era of rapid and radical change more than any other time through a new way of life called the Fourth Industrial Revolution. The Korean church is also facing the reality that it must fulfill its urgent mission to deliver the unchanging truth in an ever-changing era. With this in mind, this study (1) identifies digital literacy as an essential competency requested in the era of the fourth industrial revolution by examining the relationship with congregation's life as well as its definition and contents, (2) discovers educational rationale for the relationship between faith formation and digital literacy by applying educational context of Christian education with attention to the educational efficiency of digital literacy, and (3) finds educational implications of digital literacy by re-conceptualizing the contents, context, role of teachers and students, and evaluation in the context of Christian education. I hope that this study will help Christian education serve for the spread of the Gospel of Christ and the realization of the kingdom of God on this earth through digital media in the future more time-responsively and mission-practically.