• Title/Summary/Keyword: Mathematical Activity

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Case Analysis of Modeling Lessons

  • Noh, Jihwa
    • East Asian mathematical journal
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    • v.35 no.2
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    • pp.217-237
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    • 2019
  • This Modeling is a cyclical process of creating and modifying models of empirical situations to understand them better and improve decisions. The role of modeling and teaching mathematical modeling in school mathematics has received increasing attention as generating authentic learning and revealing the ways of thinking that produced it. In this paper and interactive lecture session, we will review a subset of the related literature, discuss benefits and challenges in teaching and learning mathematical modeling, and share our attempts to improve traditional textbook problems so that they can become more authentic modeling activities and implications for instruction and assessment as well as for research.

A Case Study on Activating of High School Student's Metacognitive Abilities in Mathematical Problem Solving Process using Visual Basic (비주얼 베이식을 이용한 수학 문제해결 과정에서 고등학생의 메타인지적 능력 활성화)

  • 이봉주;김원경
    • The Mathematical Education
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    • v.42 no.5
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    • pp.623-636
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    • 2003
  • Metacognition is defined to be 'thinking about thinking' and 'knowing what we know and what we don't know'. It was verified that the metacognitive abilities of high school students can be improved via instruction. The purpose of this article is to investigate a new method for activating the metacognitive abilities that play a key role in the Mathematical Problem Solving Process(MPSP). Hyunsung participated in the MPSP using Visual Basic Programming. He actively participated in the MPSP. There are sufficient evidences about activating the metacognitive abilities via the activity processes and interviews. In solving mathematical problems, he had basic metacognitive abilities in the stage of understanding mathematical problems; through the experiments, he further developed his metacognitive abilities and successfully transferred them to general mathematical problem solving.

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Analysis of problem posing activity of fifth grade students (초등학교 5학년 학생들의 문제 만들기 활동 분석)

  • Sung, Chang-Geun;Lee, Nam kyung;Lee, Dae Hyun
    • Education of Primary School Mathematics
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    • v.20 no.3
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    • pp.193-204
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    • 2017
  • The purpose of the study was to investigate and develop a practical approach to integrating student-driven mathematical problems posing in mathematics instruction. A problem posing activity was performed during regular mathematics instruction. A total of 540 mathematical problems generated by students were recorded and analysed using systemic procedures and criteria. Of the problems, 81% were mathematically solvable problem and 18% were classified as error type problems. The Mathematically solvable problem were analysed and categorized according to the complexity level; 13% were of a high-level, 30% mid-level and 57% low-level. The error-type problem were classified as such within three categories: non-mathematical problem, statement or mathematically unsolvable problem. The error-type problem category was distributed variously according to the leaning theme and accomplishment level. The study has important implications in that it used systemic procedures and criteria to analyse problem generated by students and provided the way for integrating mathematical instruction and problem posing activity.

A Study on the Development of Computer Assisted Instruction for the Middle School Mathematics Education - Focused on the graph of quadratic function - (중학교 수학과 CAI 프로그램 개발 연구 -이차함수의 그래프를 중심으로-)

  • 장세민
    • Journal of the Korean School Mathematics Society
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    • v.1 no.1
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    • pp.151-163
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    • 1998
  • In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

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Mathematical Modeling for the Transmission Dynamics of HIV infection and AIDS with Heterogeneity in Sexual Activity (성 활동 성분을 고려한 HIV 감염과 AIDS의 전염특성에 관한 수학적 모델화)

  • Chung, Hyeng-Hwan
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.50 no.12
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    • pp.597-603
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    • 2001
  • In the mathematical model for the transmission dynamics of HIV infection described in previous papers, the population under consideration is assumed to be homogeneous community of homosexual males for which the parameter x represents the constant rate at which individual members of the population acquire new sexual partners. This is a gross oversimplification since it is well known that individuals vary widely in their levels of sexual activity and in this papers the heterogeneous model is modified to allow for this variation. The pattern on the epidemic character of HIV, the causative agent of AIDS, was analysed by heterogeneous-mixing model. The computer simulation was performed using real date.

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Rigorous Model for Spherical Cell-support Aggregate

  • Moon, Seung-Hyeon;Lee, Ki-Beom;Satish J. Paruekar
    • Biotechnology and Bioprocess Engineering:BBE
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    • v.6 no.1
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    • pp.42-50
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    • 2001
  • The activity of immobilized cell-support particle aggregates is influenced by physical and biochemical elements, mass transfer, and physiology. Accordingly, the mathematical model discussed in this study is capable of predicting the steady state and transient concentration profiles of the cell mass and substrate, plus the effects of the substrate and product inhibition in an immobilized cell-support aggregate. The overall mathematical model is comprised of material balance equations for the cell mass, major carbon source, dissolved oxygen, and non-biomass products in a bulk suspension along with a single particle model. A smaller bead size and higher substrate concentration at the surface of the particle, resulted in a higher supply of the substrate into the aggregate and consequently a higher biocatalyst activity.

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Intuition and metacognition in Mathematical Problem Solving Process (수학 문제해결 과정에서의 직관과 메타인지)

  • 이대현;이봉주
    • Journal of Educational Research in Mathematics
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    • v.12 no.2
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    • pp.265-274
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    • 2002
  • The purpose of the paper is to provide the importance of matacognition as a factor to correct the errors generated by the intuition. For this, first of all, we examine not only the role of metacognition in mathematics education but also the errors generated by the intuition in the mathematical problem solving process. Next, we research the possibility of using metacognition as a factor to correct the errors in the mathematical problem solving process via both the related theories about the metacognition and an example. In particular, we are able to acknowledge the importance of the role of metacognition throughout the example in the process of the problem solving It is not difficult to conclude from the study that emphasis on problem solving will enhance the development of problem solving ability via not only the activity of metacognition but also intuitive thinking. For this, it is essential to provide an environment that the students can experience intuitive thinking and metacognitive activity in mathematics education .

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A Case Study of an Activity Based Mathematical Education: A Kernel Density Estimation to Solve a Dilemma for a Missile Simulation

  • Kim, G. Daniel
    • Communications of Mathematical Education
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    • v.16
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    • pp.139-147
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    • 2003
  • While the statistical concept 'order statistics' has a great number of applications in our society ranging from industry to military analysis, it is not necessarily an easy concept to understand for many people. Adding some interesting simulation activities of this concept to the probability or statistics curriculum, however, can enhance the learning curve greatly. A hands-on and a graphic calculator based activities of a missile simulation were introduced by Kim(2003) in the context of order statistics. This article revisits the two activities in his paper and point out a dilemma that occurs from the violation of an assumption on two deviation parameters associated with the missile simulation. A third activity is introduced to resolve the dilemma in the terms of a kernel density estimation which is a nonparametric approach.

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An Analysis of Metacognition on the Middleschool Students' Modeling Activity (중학생들의 모델링 활동에서 메타인지 분석에 관한 사례연구)

  • Shin Eun Ju;Lee Chong Hee
    • Journal of Educational Research in Mathematics
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    • v.14 no.4
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    • pp.403-419
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    • 2004
  • The perspective on this study assumes that the mathematical modeling activity provides students with the environment which promotes metacognitive thinking. The purposes of this paper are to investigate metacognitive thinking on the mathematical modeling with the result of case study. The study revealed that development of students' model was accompanied with the control and monitoring of modeling activities. Also students refined the model by self-assessment and peer-assessment in small group modeling activities and developed generalizable model.

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The Effect of Problem Posing Teaching on Mathematical Problem-Solving Ability and Creativity (문제제기 수업이 수학 문제해결력과 창의력에 미치는 효과)

  • Lee, Sang-Won
    • The Mathematical Education
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    • v.44 no.3 s.110
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    • pp.361-374
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    • 2005
  • I analyzed the effect of problem posing teaching and teacher-centered teaching on mathematical problem-solving ability and creativity in order to know the efffct of problem posing teaching on mathematics study. After we gave problem posing lessons to the 3rd grade middle school students far 28 weeks, the evaluation result of problem solving ability test and creativity test is as fellows. First, problem posing teaching proved to be more effective in developing problem-solving ability than existing teacher-centered teaching. Second, problem posing teaching proved to be more effective than teacher-centered teaching in developing mathematical creativity, especially fluency and flexibility among the subordinate factors of mathematical creativity. Thus, 1 suggest the introduction of problem posing teaching activity for the development of problem-solving ability and mathematical creativity.

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