• Title/Summary/Keyword: 컴퓨터 대수 체계

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컴퓨터 대수체계(CAS) Module이 포함된 graphing Calculator를 활용한 교실 수업모형 -연립 일차방정식과 이차함수를 중심으로, Casio fx2.0-

  • Heo, Man-Seong
    • Communications of Mathematical Education
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    • v.10
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    • pp.505-517
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    • 2000
  • 수학 학습에서 컴퓨터와 계산기의 활용은 시각화의 강화로부터 직관력과 사고력의 향상을 가져왔다. 컴퓨터 대수체계(Computer Algebra System)가 탑재된 수학 학습용 컴퓨터 프로그램과 계산기가 활발히 사용되고 있으며, 교수매체로서의 활용은 지식 정보전달 체계와 학습자의 지식 구성방법에 새로운 패러다임을 형성하였다. 특히 수학학습용 그래픽 계산기(Graphing Calculator)는 휴대형(Hand-held Technology)으로 학습공간의 이동(Mobil Education)이 가능하며, 수학학습 전용기라는데 의미를 둘 수 있다. Symbolic Graphing Calculator를 활용한 수업에서 학습자는 계산기를 가지고, 기호연산 실행 조작을 통해 자신의 사고과정을 표현하고, Symbolic Graphing Calculator는 실행 조작에 즉각적으로 과정과 결과를 제공하며, 다른 표상과 상호작용을 함으로써 학습자 스스로의 규제가 강화된 과정을 통해 지식을 구성하게 된다. 이때 교사는 지식 정보전달 체계인 대화형 실행매체(IMTs)를 작성하여 학습자의 지식 형성에 안내자의 역할을 하게 된다. 이번 워크샵에서는 CASIO fx 2.0을 활용한 교실 수업모형을 그래프 표상과 연계한 방정식의 풀이과정을 통해 알아본다.

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Learning Mathematics with CAS Calculators: Integration and Partnership Issues (CAS계산기를 활용한 수학학습)

  • Thomas Michael O. J.;Hong Ye Yoon
    • Journal of Educational Research in Mathematics
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    • v.15 no.2
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    • pp.215-232
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    • 2005
  • Computer algebra system (CAS) calculators are becoming increasingly common in schools and universities. While Hey offer quite sophisticated mathematical capability to teachers and students, it is not clear at present how they may best be employed. In particular their integration into students' learning and problem-solving remains an issue. In this paper we address this issue through the lens of a study that considered the introduction of the TI-89 CAS calculator to students about to enter university. We describe a number of different aspects of the partnership they formed with the calculator as they began the process of instrumentation of the CAS in their learning.

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How to Use CAS to Solve Certain Minmax Problems (어떤 최대최소문제들에 대한 컴퓨터대수체계(CAS)의 이용)

  • Kim, Seon-Hong
    • Journal of the Chosun Natural Science
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    • v.3 no.4
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    • pp.241-245
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    • 2010
  • In this paper, we study how to use CAS to solve certain minmax problems. More specifically, we reduce some to the problems about the packing of certain convex sets in the plane, and use Recognize algorithm to obtain good hypotheses for results. This method can be widely used to solve same types of mathematical problems.

Comparative Study in Algebra Education with CAS: Korea and US cases (컴퓨터 대수체계(CAS) 대비 중등대수교육 기초 연구)

  • Chang, Kyung-Yoon
    • School Mathematics
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    • v.10 no.2
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    • pp.297-317
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    • 2008
  • This study was designed to gain insight to adopt CAS into secondary level algebra education in Korea. Most inactive usage of calculators in math and most negative effects of calculators on their achievements of Korean students were shown in International studies such as TIMSS-R. A comparative study was carried out with consideration of mathematical backgrounds and technological environments. 8 Korean students and 26 US students in Grade 11 were participated in this study. Subjects' Problem solving process and their strategies of CAS usage in classical Box-problem with CAS were analyzed. CAS helped modeling by providing symbolic manipulation commands and graphs with students' mathematical knowledge. Results indicates that CAS requires shifts focus in algebraic contents: recognition of decimal & algebraic presentations of numbers; linking various presentations, etc. The extent of instrumentation effects on the selection of problem solving strategies among Korea and US students. Instrumentation

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A Note on the Relationship between IMTs and the Prototype Design of Computer Applications in the School Mathematics (수학 교수-학습을 위한 컴퓨터 응용 프로그램 모형설계에 따른 대화형 실행매체(IMTs)의 작성에 관한 소고)

  • 허만성;박용범;김부윤
    • Journal of Educational Research in Mathematics
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    • v.9 no.1
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    • pp.321-332
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    • 1999
  • This article made overtures of the relationship between interactive mathematics texts nd the prototype design of computer application with Computer Algebra System Math. Engine, linking together in the school mathematics. School teachers and researchers would try to construct mathematical materials with computers in educating students in the middle and high school grades. As the individual users come to manage hyper-media materials, so they meet with the problem of 'Who does control?'A mass user would be concerned with interactive mathematics materials directly or off-line at realtime and manipulate the process of problem-solving symbolically with MathView/sup 11)/ and ON-Math/sup 12)/. Discussion was made in developing the factor in the domestic situation and reaching out their hands for it. In conclusion, a user may reform the information of math-curriculum limitedly.

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The Case Study of High School Students' Understanding of the Concept of Parameter In A Computer Algebra Environment (컴퓨터 대수 환경에서 매개변수 개념에 대한 고등학생의 이해에 관한 사례 연구)

  • Cho, Yeong-Ju;Kim, Kyung-Mi
    • Communications of Mathematical Education
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    • v.24 no.4
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    • pp.949-974
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    • 2010
  • The purpose of the study was to investigate how students' understanding was formed for solving the algebra problems involving parameters in a computer algebra environment. The teaching experiment has been conducted with 6 high school students. As a result, students studied the parameter in different roles such as placeholder, changing quantity, unknown and generalizer. The results indicate that a computer algebra environment offers opportunities for algebra activities that may support the development of understanding of the concept of parameter.

A Qualitative analysis of students' factorization of xn-1 using a CAS application (CAS 어플리케이션을 이용한 xn-1의 인수분해 일반화 과정에 대한 질적 분석)

  • Cho, Yeong Ju;Kim, Kyung Mi;Whang, Woo Hyung
    • The Mathematical Education
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    • v.52 no.3
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    • pp.271-301
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    • 2013
  • The purpose of the study was to investigate how students generalize and prove the factoring of $x^n-1$ using a Computer Algebra System application and the role of CAS in this process. The theoretical framework consists of the anthropological and the instrumental approach. In particular, the basis of the Task-Technique-Theorization(T-T-T) frame adapted form Chevallard's anthropological approach of Didactics is utilized. We found that Technique-Theorization emerges in mutual interaction between paper-and-pencil techniques and computer algebra techniques. And this interaction led to the students' theoretical reflection and conceptual understanding. In this process, we could identify three epistemic role of CAS : the role of checking the result, the role of cognitive stimulation and the role of extending thinking. Therefore CAS plays on a epistemic role of checking the result of a task, stimulating the student' cognition and extending their thinking as well as pragmatic role of producing the result of a input.

The Influence of Instrumentalization of Computer Algebra System(CAS) on the Sequence of Mathematics Curriculum in the Optimization Problem Solving Activities of CAS (최적화 문제해결 활동에서 "CAS의 도구화"가 교육과정 내용제시 순서에 미치는 영향)

  • Han, Se-Ho
    • Journal of Educational Research in Mathematics
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    • v.20 no.2
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    • pp.185-202
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    • 2010
  • This study was designed to investigate the possibility that the optimization problem solving activities based on the instrumented CAS can have an influence on the sequence of mathematics curriculum in secondary mathematics education. Some optimization problem solving activities based on CAS were constructed and executed to eleventh grade(the penultimate year of Korean high school) 7 students for nine class hours. They have experienced using CAS in mathematics class for three months, but never learned calculus. The data which consists of classroom observations(audio and video taped) and post-unit interviews with students were analyzed. In the analysis, with CAS, students can highly deal with the applied optimization problems made up of calculus, cubic equation, solution of radical equation, and graph analysis which never learned. This result shows CAS may have an influence on the sequence of mathematics curriculum in secondary mathematics education.

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Instrumental Genesis of Computer Algebra System(CAS) in Mathematical Problem Solving among High School Students (고등학교 수학 문제해결에서 CAS의 도구발생)

  • Han, Se-Ho;Chang, Kyung-Yoon
    • School Mathematics
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    • v.11 no.3
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    • pp.527-546
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    • 2009
  • This study was designed to gain insights into instrumental genesis process of CAS in Korean high school students and to explore its practical potentials in secondary mathematics education. Two activities, such as Concept-Centered Mathematics Activity based on CAS and Problem Solving Activities, were constructed and executed to 10th Grade seven students for twelve class hours. The finding on the students' activities are as follows : it is meaningful in mathematics education, especially in algebra education, in that the CAS based concept centered mathematics activity offers great opportunities to deal with high-qualified application problems. The problem solving activities based on the instrumented CAS may have an influence on the sequence of mathematics curriculum, e.g. the optimization problems may precede the calculus problems such as derivatives in high school. The results of this study to investigate the instrumental genesis of CAS in mathematical activities will give insights into the secondary mathematics curriculum to prepare the CAS in Korea.

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