• Title, Summary, Keyword: 수학화

Search Result 1,230, Processing Time 0.096 seconds

Students' Learning of Geometry through Freudenthal's Mathematizaton (수학화에 의한 도형지도에서 학생의 학습발달 과정 연구)

  • Go, Sang-Suk;Jang, Deok-Im
    • Communications of Mathematical Education
    • /
    • v.18 no.2
    • /
    • pp.427-440
    • /
    • 2004
  • Freudenthal의 수학화 이론에 대한 지금까지의 대부분의 연구는 이론의 탐색에 집중하고 이에 따른 학습 지도 방안과 자료개발에만 역점을 두었던 것이 그 한계점으로 지적되어져 왔다. 이에 본 연구자는 실제 이 이론이 어떻게 학습 현장에 적용될 수 있는지에 대해 첫째, Freudenthal의 수학화에 의한 도형 지도에서 학생이 어떻게 수학화를 이루어 가는지를 조사하였고, 둘째, 학습의 주체자인 학생들의 능동적인 활동을 강조한 수학화 과정에서 교수의 주체자인 교사는 학생들의 수학화가 원만히 이루어지게 하기 위하여 어떤 역할을 수행하게 되는지를 중학교 1학년 학생을 대상으로 사례연구를 실시하여 조사하였다.

  • PDF

A Study of Byproduct Mathematization (Byproduct Mathematization에 관한 연구)

  • Kim, Boo-Yoon;Chung, Young-Woo
    • Journal of Educational Research in Mathematics
    • /
    • v.20 no.2
    • /
    • pp.145-161
    • /
    • 2010
  • Concepts in mathematics have been formulated for unifying and abstractizing materials in mathematics. In this procedure, usually some developments happen by necessity as well as for their own rights, so that various interesting materials can be produced as byproducts. These byproducts can also be established by themselves mathematically, which is called byproduct mathematization (sub-mathematization). As result, mathematization and its byproduct mathematization interrelated to be developed to obtain interesting results and concepts in mathematics. In this paper, we provide explicit examples:the mathematization is the continuity of trigonometric functions, while its byproduct mathematization is various trigonometric identities. This suggestion for explaining and showing mathematization as well as its byproduct mathematization enhance students to understand trigonometric functions and their related interesting materials.

  • PDF

Effects on Mathematical Thinking Ability of Mathematising Learning with RME -Based on measurement region for fifth grade in elementary school- (RME를 적용한 수학화 학습이 수학적 사고능력에 미치는 효과 -초등학교 5학년 측정 영역을 중심으로-)

  • Baek, In su;Choi, Chang Woo
    • Journal of Elementary Mathematics Education in Korea
    • /
    • v.19 no.3
    • /
    • pp.323-345
    • /
    • 2015
  • This study is intended to establish and apply a program created with RME for mathematising instruction and learning and identify how it influences on the mathematical thinking process in the field. In order to deal with this study inquiries, related theories have been analyzed establishing a program for mathematising instruction and learning method based on a model of them and RME theory principles and re-organizing education courses for instruction on the fields concerned. Study subjects were limited to two classes consisting of fifth graders in S elementary school located in the city of Daegu and divided them in an experiment group and a control group. An experiment group was given a mathematising learning method applied with RME, while a control group had a class with regular methods of learning and instruction during the period of experiment. As a summary of aforementioned results of the study, mathematising learning method applied with RME had an effect on improving mathematical thinking ability for students and also on promoting mathematising outcome through a repetitive experience in each procedure obtained on a regular basis.

Effect of Mathematising Learning Using Realistic Context on the Children's Mathematical Thinking (현실적 맥락을 활용한 수학화 학습이 아동의 수학적 사고에 미치는 효과 -초등학교 5학년 도형 영역을 중심으로-)

  • Kim, Yoo-Jin
    • Journal of Elementary Mathematics Education in Korea
    • /
    • v.11 no.2
    • /
    • pp.99-115
    • /
    • 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.

  • PDF

Cuboid가 형성하는 공간의 표상

  • Lee, Jae-Sun;Lee, Cheong-Ju;Kim, Ga-Yeon;Han, Jae-Yeong
    • Communications of Mathematical Education
    • /
    • v.9
    • /
    • pp.317-325
    • /
    • 1999
  • 수식에 의한 컴퓨터 그래픽의 입력과 출력에 관한 프로그램의 개발은 수학의 역동화, 인간화, 보편화에 기여하고 있다. 현실적으로 해결해야할 문제와 수식에 의한 해답이 전부인 현재의 수학을 소프트웨어를 활용하여 그래픽 기능을 첨부하면 움직이는 수학을 가시화 할 수 있다. 컴퓨터 프로그램에 의한 수학의 실현은 수학자들 모두의 염원으로 전세계적으로 활발한 연구가 진행되고 이는 것이다. 수학의 원리와 응용성을 가미한 수학적 그래픽의 발전은 새로운 천년을 장식할 새로운 학문분야로 등장하고 있다. 기초과학의 여러 자료를 분석, 검토하여 그래픽으로 조립하는 작업은 수학적 그래픽의 힘으로 가능하며, 실험과 실습의 양상을 바꾸어 놓고 있다. 건축이나 토목 또는 전기전자 학과의 응용수학은 새로운 소프트웨어의 출현으로 컴퓨터 강의로 전환되고 있으며 수학 그 자체로 전산기능을 강화하는 방향으로 개편되고 있다. 수학 교과 내용의 전산 프로그램화와 컴퓨터 활용 수학 학습은 거부할 수 없는 시대적 요구이다. 이 연구에서는 새로운 천년의 시작은 컴퓨터 프로그램에 의한 완성된 그래픽의 연출이라는 시각에서 수식에 의한 컴퓨터 그래픽의 기본 방향을 제시하고 있다. 2차원 평면이나 3차원 공간에 이와 같은 다변수함수의 역할을 구현함으로써 다양한 그래픽을 영상화할 수 있다. 다중화면의 연출, 다단계화면의 조합, 다단계다중화면의 영상화 등은 수학에 의한 애니메이션의 기초가 된다. 평면도형의 기본동작을 화면에 구체화시키는 Table 기능을 실제로 구현한다. 연습과 실행 그리고 재구성을 반복하여 조형미를 갖춘 수학적 그래픽을 실현한다. 수학의 학습에 적용할 가치가 있는 학습조형물을 개발하고, 프로그램의 단순화에 노력한다. 미분기하학의 여러 공식을 이용하여 숨어 있는 그림을 표출하며 미분방정식의 해가 갖는 그래픽의 묘미를 형상화한다. 수식에 의하여 출력된 그래픽의 여러 효과를 응용수학에 활용할 수 있도록 재조립하는 과정을 걸쳐 완성하는데 이 연구의 참된 의미가 있다.

  • PDF

An Analysis of Various Russian Studies in an Early Stage Related with Differentiated Mathematics Education (수학교육의 차등화에 관련된 러시아의 초창기 연구들의 분석)

  • Han, In-Ki
    • Communications of Mathematical Education
    • /
    • v.22 no.2
    • /
    • pp.187-209
    • /
    • 2008
  • In this paper we analyze various russian studies related with differentiated mathematics education. Especially we work on the studies published in 1980-1995 years. As a result, we find that many studies are carried out with various view points in different directions, draw out essential variables, embodiment methods of differentiated mathematics education in Russia.

  • PDF

Comparison and Analysis among Mathematical Modeling, Mathematization, and Problem Solving (수학적 모델링과 수학화 및 문제해결 비교 분석)

  • Kim, In-Kyung
    • Journal for History of Mathematics
    • /
    • v.25 no.2
    • /
    • pp.71-95
    • /
    • 2012
  • Nowadays, the big issues on mathematics education are mathematical modeling, mathematization, and problem solving. So, this paper looks about these issues. First, after 1990's, the researchers interested in mathematical model and mathematical modeling. So, this paper looks about mathematical model and mathematical modeling. Second, it looks about Freudenthal' mathematization after 1970's. And then, it compared with mathematical modeling. Also, it looks about that problem solving focused on mathematics education since 1980's. And it compared with mathematical modeling.

A Study on Designing Mathematising Teaching Units for the Inquiry into Number Partition Models with Constant Differences (일정한 차를 갖는 수 분할 모델의 탐구를 위한 예비중등교사용 수학화 교수단원의 설계)

  • Kim Jin-Hwan;Park Kyo-Sik;Lee Kwang-Ho
    • School Mathematics
    • /
    • v.8 no.2
    • /
    • pp.161-176
    • /
    • 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.

  • PDF

A Study on Mathematizing Teaching and Learning in Highschool Calculus (고등학교 미적분에서의 수학화 교수.학습에 관한 연구)

  • Cho, Wan-Young
    • School Mathematics
    • /
    • v.8 no.4
    • /
    • pp.417-439
    • /
    • 2006
  • Many studies indicate the emerging crisis of education of calculus even though the emphasis of calculus have been widely recognized. In our classrooms, the education of calculus also has been faced with its bounds. Most instructions of calculus is too much emphasis on the algebraic approach, thus students solve mathematical problems without truly understanding the underlying concept. The purpose of this study is to develop mathematization teaching and learning materials and methods in caculus based on the mathematization teaching and learning theories by Freudenthal and the variability principles of conceptual learning by Dienes, In order to this purpose, first, we analyzed the high school mathematics II textbook of 7th curriculum in Korea. Second, we developed mathematization teaching and learning materials and methods in highschool calculus. Consequently, the following conclusions have been drawn: we have reorganized and reconstructed the context problem in calculus based on concepts of tangent line and instantaneous rate of change.

  • PDF