• The Mathematical Education
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• v.57 no.2
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• pp.93-110
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• 2018

One of the biggest changes in the 2015 revised mathematics curriculum is shifting to the second year of middle school in Pythagorean theorem. In this study, the following subjects were studied. First, Pythagoras theorem analyzed the expected problems caused by the shift to the second year middle school. Secondly, we have researched the reconstruction method to solve these problems. The results of this study are as follows. First, there are many different ways to deal with Pythagorean theorem in many countries around the world. In most countries, it was dealt with in 7th grade, but Japan was dealing with 9th grade, and the United States was dealing with 7th, 8th and 9th grade. Second, we derived meaningful implications for the curriculum of Korea from various cases of various countries. The first implication is that the Pythagorean theorem is a content element that can be learned anywhere in the 7th, 8th, and 9th grade. Second, there is one prerequisite before learning Pythagorean theorem, which is learning about the square root. Third, the square roots must be learned before learning Pythagorean theorem. Optimal positions are to be placed in the eighth grade 'rational and cyclic minority' unit. Third, Pythagorean theorem itself is important, but its use is more important. The achievement criteria for the use of Pythagorean theorem should not be erased. In the 9th grade 'Numbers and Calculations' unit, after learning arithmetic calculations including square roots, we propose to reconstruct the square root and the utilization subfields of Pythagorean theorem.

• Communications of Mathematical Education
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• v.35 no.2
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• pp.193-212
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• 2021

This study is to support the school's mathematics exploration activities. Mathematics exploration is a very important mathematical activity not only for mathematics teachers, but also for students. Looking at the development of mathematics, it has been extended from one mathematical fact to a new mathematical fact. Mathematics exploration activities are not unique to mathematicians, and opportunities are equally given to all ordinary people who are learning mathematics and teaching mathematics. Therefore, the purpose of this study is to develop a method of mathematics exploration activities that teachers and students can perform in schools, based on mathematics exploration activities based on one mathematical fact. Specifically, the cosine law was selected as one mathematical fact, and mathematical exploration activities were performed based on the cosine law. By analyzing the results of these mathematics exploration activities, we developed a method to explore school mathematics. Through the results of this study, it is expected that mathematics exploration activities will be conducted equally by students and teachers in the mathematics classroom.

• The Mathematical Education
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• v.61 no.1
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• pp.47-62
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• 2022

This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

• Journal of the Korean School Mathematics Society
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• v.17 no.4
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• pp.507-539
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• 2014

The algebra is an important tool influencing on a mathematics in general. To make good use of the algebra, it is necessary to transfer from a given situation to a proper algebraic representation. But some research in related to algebraic word problems have reported the difficulty changing to a proper algebraic representation. Our study have focused on transformation and elaboration of algebraic representation. We investigated in detail the responses and perceptions of 29 Grade 7 students while transforming to algebraic representation, only concentrating on the literature expression form the problematic situations given. Most of students showed difficulties in transforming both descriptive and geometric problems to algebraic representation. 10% of them responded wrong answers except only a problem. Four of them were interviewed individually to show their thinking and find the factor influencing on a positive elaboration. As results, we could find some characteristics of their thinking including the misconception that regard the problem finding a functional formula because there are the variables x and y in the problematic situation. In addition, we could find the their fixation which student have to set up the equation. Furthermore we could check that making student explain own algebraic representation was able to become the factor influencing on a positive elaboration. From these, we also discussed about several didactical implications.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.499-524
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• 2015

In the present study, we propose four participating $8^{th}$ grade students' genetic decomposition of congruent transformation and investigate the role of their dragging activities while understanding the concept of congruent transformation in GSP(Geometer's Sketchpad). The students began to use two major schema, 'single-point movement' and 'identification of transformation' simultaneously in their transformation activities, but they were inclined to rely on the single-point movement schema when dealing with relatively difficult tasks. Through dragging activities, they could expand the domain and range of transformation to every point on a plane, not confined to relevant geometric figures. Dragging activities also helped the students recognize the role of a vector, a center of rotation, and an axis of symmetry.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.391-410
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• 2017

This study aims to analyze mathematically gifted students' characteristics of generalization and justification for a given mathematical task and induce didactical implications for individual teaching methods by students' learning styles. To do this, we identified the learning styles of three mathematically gifted 6th graders and observed their processes in solving a given problem. Paper-pencil environment as well as dynamic geometrical environment using Geogebra were provided for three students respectively. We collected and analyzed qualitatively the research data such as the students' activity sheets, the students' records in Geogebra, our observation reports about the processes of generalization and justification, and the records of interview. The results of analysis show that the types of the students' generalization are various while the level of their justifications is identical. Futhermore, their preference of learning environment is also distinguished. Based on the results of analysis, we induced some implications for individual teaching for mathematically gifted students by learning styles.

• The Mathematical Education
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• v.57 no.3
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• pp.311-328
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• 2018

In school mathematics, the concept of an average is not a concept that is limited to a unit of statistics. In particular, high school students will learn about arithmetic mean and geometric mean in the process of learning absolute inequality. In calculus learning, the concept of average is involved when learning the concept of average speed. The arithmetic mean is the same as the procedure used when students mean the test scores. However, the procedure for obtaining the geometric mean differs from the procedure for the arithmetic mean. In addition, if the arithmetic mean and the geometric mean are the discrete quantity, then the mean rate of change or the average speed is different in that it considers continuous quantities. The average concept that students learn in school mathematics differs in the quantitative nature of procedures and objects. Nevertheless, it is not uncommon to find out how students construct various mathematical concepts into mathematical knowledge. This study focuses on this point and conducted the interviews of the students(three) in the second grade of high school. And the expression of students in the process of average concept formation in arithmetic mean, geometric mean, average speed. This study can be meaningful because it suggests practical examples to students about the assertion that various scholars should experience various properties possessed by the average. It is also meaningful that students are able to think about how to construct the mean conceptual properties inherent in terms such as geometric mean and mean speed in arithmetic mean concept through interview data.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.731-744
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• 2010

Nowadays in school mathematics, the skill and method for solving problems are often emphasized in preference to the theoretical principles of mathematics. Students pay attention to how to make an equation mechanically before even understanding the meaning of the given problem. Furthermore they do not get to really know about the principle or theorem that were used to solve the problem, or the meaning of the answer that they have obtained. In contemporary textbooks the conic section such as circle, ellipse, parabola and hyperbola are introduced as the cross section of a cone. But they do not mention how conic section are connected with the quadratic equation or how these curves are related mutually. Students learn the quadratic equations of the conic sections introduced geometrically and are used to manipulating it algebraically through finding a focal point, vertex, and directrix of the cross section of a cone. But they are not familiar with relating these equations with the cross section of a cone. In this paper, we try to understand the quadratic curves better through the analysis of the discussion made in the process of the discovery and eventual development of the conic section and then seek for way to improve the teaching and learning methods of quadratic curves.

• Education of Primary School Mathematics
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• v.22 no.1
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• pp.1-12
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• 2019

This study examined the attention and attention shift of general students and mathematically gifted students about pattern by the types of mathematical patterns. For this purpose, we analyzed eye movements during the problem solving process of 5th general and mathematically gifted students using eye tracker. The results were as follows: first, there was no significant difference in attentional style between the two groups. Second, there was no significant difference in attention according to the generation method between the two groups. The diversion was more frequent in the incremental strain generation method in both groups. Third, general students focused more on the comparison between non-contiguous terms in both attributes. Unlike general students, mathematically gifted students showed more diversion from geometric attributes. In order to effectively guide the various types of mathematical patterns, we must consider the distinction between attention and attention shift between the two groups.

• Smart Media Journal
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• v.13 no.5
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• pp.45-51
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• 2024

Recently, realistic contents such as virtual reality(VR) and augmented reality (AR) are widely used for education to provide beneficial learning environments with thee-dimensional(3D) information and interactive technology. Specially, AR technology will be helpful to intuitively understand by adding virtual objects registered in the real learning environment with effective ways. In this paper, we developed an AR learning system using 3D spatial information in the 2D based textbook for studying math related to geometry. In order to increase spatial learning effect, we applied to solid shapes such as prisms and pyramids in mathematics education process. Also, it allows participants to use various shapes and expression methods (e.g., wireframe mode) with interaction. We conducted the experiment with our AR system, evaluated achievement and interest. Our experimental study showed positive results, our results are expected to provide effective learning methods in various classes through realistic visualization and interaction methods.