• Journal of Elementary Mathematics Education in Korea
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• v.11 no.2
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• pp.99-115
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• 2007

The purpose of this study was to look into whether this mathematising learning utilizing realistic context has an effect on the mathematical thinking. To solve the above problem, two 5th grade classes of D Elementary School in Seoul were selected for performing necessary experiments with one class designated as an experimental group and the other class as a comparative group. Throughout 17 times for six weeks, the comparative group was educated with general mathematics learning by mathematics and "mathematics practices," while the experimental group was taught mainly with mathematising learning using realistic context. As a result, to start with, in case of the experimental group that conducted the mathematising learning utilizing realistic coherence, in the analogical and developmental thoughts which are mathematical thoughts related to the methods of mathematics, in the thinking of expression and the one of basic character which are mathematical thoughts related to the contents of mathematics, and in the thinking of operation, the average points were improved more than the comparative group, also having statistically significant differences. The study suggested that it is necessary to conduct subsequent studies that can verify by expanding to each grade, sex and region, develop teaching methods suitably to the other content domains and purposes of figures, and demonstrate the effects. In addition to those, evaluation tools which can evaluate the mathematical thinking processes of children appropriately and in more diversified methods will have to be developed. Furthermore, in order to maximize mathematising for each group in each mathematising process, it would be necessary to make efforts for further developing realistic problem situations, works and work sheets, which are adequate to the characteristics of the upper and lower groups.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.57-76
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• 2006

In this paper, we generalized number partion problems in elementary situations to number partition models that provide some mathematical problem situations for experiencing mathematising of secondary pre-service teachers. We designed substantial teaching units entitled 'the inquiry intof number partition models' through 4 steps: (1) key problems, (2) integration from the view of partition, (3) defining partition (4) a real practice of inquiry into models. This teaching unit can contribute to secondary pre-service teacher education as follows: first, This teaching unit have pre-service teachers experience mathemtising. second, This teaching unit have pre-service teachers see the connection between school mathematics and academic mathematics. third, This teaching unit have pre-service teachers foster their mathematical creativity.

• School Mathematics
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• v.8 no.2
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• pp.161-176
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• 2006

Some adequate programs for mathematising are necessary to pre-service mathematics teachers, if they can guide their prospective students in secondary school to make a mathematising. They should be used to mathematising. In this paper, mathematising teaching units for the inquiry into number partition models with constant differences are designed for this purpose. They guide a series of process to make nooumenon for organizing phainomenon which is organized already through number partition model. Especially the new nooumenon and the process of obtaining it are discussed. But it is restricted when the numbers for partitioning are natural numbers, and elements and their differences are integers. Through these teaching units, pre-service mathematics teachers can experience and practice secondary mathematising, as they go through the procedures which are similar with those of mathematicians making theorems.

• School Mathematics
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• v.8 no.3
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• pp.327-339
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• 2006

In this study, a teaching units for teaching and learning of secondary preservice teachers' mathematising is designed, focusing on reinvention of Bretschneider's formula. preservice teachers can obtain the following through this teaching units. First, preservice teachers can experience mathematising which invent a noumenon which organize a phenomenon, They can make an experience to invent Bretscheider's formula as if they invent mathematics really. Second, preservice teachers can understand one of the mechanisms of mathematics knowledge invention. As they reinvent Brahmagupta's formula and Bretschneider's formula, they understand a mechanism that new knowledge is invented Iron already known knowledge by analogy. Third, preservice teachers can understand connection between school mathematics and academic mathematics. They can understand how the school mathematics can connect academic mathematics, through the relation between the school mathematics like formulas for calculating areas of rectangle, square, rhombus, parallelogram, trapezoid and Heron's formula, and academic mathematics like Brahmagupta's formula and Bretschneider's formula.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.297-312
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• 2009

We study the process of horizontal and vertical mathematization on the polyhedron problems through the history of mathematics, computer experiments, problem posing, and justifications. In particular, we explore the Hamilton cycle problem, coloring problem, and folding net construction on the Archimedean and Catalan polyhedrons. In this paper, we present our mathematical results on the polyhedron problems, and we also present some unsolved problems that we found. We found that the history of mathematics and mathematical experiments are very useful in such R&E exploration as polyhedron problem posing and solving project.

• Journal of the Korean School Mathematics Society
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• v.18 no.4
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• pp.353-370
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• 2015

This study was conducted as a qualitative case study that explored how gifted 3rd-grade elementary school children who had learned the primary concepts of division and fraction, when they studied contents about decimal, formed the transformed primary concept and transformed schema of decimal by the learning of accurate primary concepts and connecting the concepts. That is, this study investigated how the subjects attained relational understanding of decimal based on the primary concepts of division and fraction, and how they formed a transformed primary concept based on the primary concept of decimal and carried out vertical mathematizing. According to the findings of this study, transformed primary concepts formed through the learning of accurate primary concepts, and schemas and transformed schemas built through the connection of the concepts played as crucial factors for the children's relational understanding of decimal and their vertical mathematizing.

• The Mathematical Education
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• v.49 no.3
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• pp.353-373
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• 2010

This research was to help slow learners to be motivated and to make their outcome productive, using GSP based on the mathematization theory for learning mathematics, as a way of encouraging the learner-centered approach. With 2 of the second graders in a high school, who had not yet understood trigonometric functions in their first grade period, 7 units of lesson plans were designed for the research. The results showed that first, understanding real life contexts and analyzing properties by observation, and experiment using GSP, to build the concept of trigonometric functions could be a foothold on which learner's organization and outcome from a horizontal mathematization led to vertical mathematization. Despite the delay during the level-up-stage for a while, the learners could attain the vertical mathematization stage and moreover the applicative mathematization through effective use of GSP and the interaction between the learners or a teacher and the learners. Second, using GSP was a vertical tool of connecting horizontal mathematization with vertical mathematization in forming the concept of trigonometric functions and its meaning could be understood by their verbalizing and presenting the outcomes through their active performance. Using GSP is helpful for slow learners to overcome learning difficulties, based on the instructional materials designed by Realistic Mathematics Education.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• Journal of Educational Research in Mathematics
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• v.19 no.1
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• pp.143-161
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• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Proceedings of the Acoustical Society of Korea Conference
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• 1998.06d
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• pp.9-12
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• 1998

공기경계층을 갖는 유리평판에서 힘의 크기가 10N이고 상승시간이 약 280ns 인 경사 점하중이 인가된 경우에 대하여 진앙점에서 입자 변위와 입자 속도를 계산하였다. 이론적으로 계산된 수직성분이 입자속도가 PZT변환자에 입사한다고 가정하여 PZT 변환자의 과도 응답특성을 Mason 등가회로와 격자점을 이용하여 계산하였다. 유리모세관의 파과시에 방출괴는 과도탄성파를 이용하여 유리평판의 진앙점에서 PZT 변환기의 응답을 조사하였고, 이론과 비교한 결과 상당히 일치하였다. 이를 이용하여 음향방출 시스템인 발생원, 전파매질, 변환자 및 신호분석시스템을 수학적으로 모형화할 수 있는 기초를 마련하였다.