• Title/Summary/Keyword: mathematical problem solving

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A Study on Solving Word Problems Related with Consistency Using the Lever Model (지렛대 모델을 이용한 농도 문제의 해결에 대한 연구)

  • Kim, Jae-Kyoung;Lee, Seong-Hyun;Han, In-Ki
    • Communications of Mathematical Education
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    • v.24 no.1
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    • pp.159-175
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    • 2010
  • In this paper we make a new problem solving model using the principle of the lever. Using the model we solved many word problems related with consistency. We suggest new problem solving method using the lever model and describe some characteristics of the method.

JACOBI DISCRETE APPROXIMATION FOR SOLVING OPTIMAL CONTROL PROBLEMS

  • El-Kady, Mamdouh
    • Journal of the Korean Mathematical Society
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    • v.49 no.1
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    • pp.99-112
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    • 2012
  • This paper attempts to present a numerical method for solving optimal control problems. The method is based upon constructing the n-th degree Jacobi polynomials to approximate the control vector and use differentiation matrix to approximate derivative term in the state system. The system dynamics are then converted into system of algebraic equations and hence the optimal control problem is reduced to constrained optimization problem. Numerical examples illustrate the robustness, accuracy and efficiency of the proposed method.

PRECONDITIONED SSOR METHODS FOR THE LINEAR COMPLEMENTARITY PROBLEM WITH M-MATRIX

  • Zhang, Dan
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.657-670
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    • 2019
  • In this paper, we consider the preconditioned iterative methods for solving linear complementarity problem associated with an M-matrix. Based on the generalized Gunawardena's preconditioner, two preconditioned SSOR methods for solving the linear complementarity problem are proposed. The convergence of the proposed methods are analyzed, and the comparison results are derived. The comparison results showed that preconditioned SSOR methods accelerate the convergent rate of the original SSOR method. Numerical examples are used to illustrate the theoretical results.

A Study on the 6th Graders' Use of Visual Representations in Mathematical Problem Solving (수학 문제 해결과정에서 초등학교 6학년 학생들의 시각적 표현에 관한 연구)

  • Hwang, Hyun-Mi;Pang, Jeong-Suk
    • Education of Primary School Mathematics
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    • v.12 no.2
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    • pp.81-97
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    • 2009
  • Visual representations play an important role for students to understand the meaning of a given problem, devise problem-solving approaches, and implement them successfully. The purpose of this study was to investigate how 6th graders would use visual representations in solving mathematical problems and in what ways such use might affect successful problem solving. The results showed that many students preferred numerical expressions to visual representations. However, students who used visual representations, specifically schematic representations, performed better than those who employed numerical representations. Given this, this paper includes instructional implications to nurture students' use of visual representations in a way to increase their problem solving ability.

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The Effects of Mathematical Games with Motion on Young Children's Development (운동요소가 포함된 수학게임이 유아발달에 미치는 효과)

  • Chang, Bo-Kyung
    • Korean Journal of Human Ecology
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    • v.19 no.2
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    • pp.271-283
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    • 2010
  • This study was planned to investigate the effects of mathematical games with motion on young children's development. The study was performed to compose mathematical games with motion and just mathematical games for young children. The games were set up to be executed 16 times for 8 weeks. The results of this study were as follows: Mathematical games with motion had a significant effect on young children's mathematical problem-solving ability. Mathematical games with motion had a significant effect in every category on young children's ability for motion competence and mathematical games with motion had a significant effect on young children's socio-emotional development. There were significant differences between the control group and the experimental group except for the independence from teachers and peer interaction. Mathematical games with motion had a significant effect on young children's language ability.

A Case study on the Effects of Mathematically Gifted Creative Problem Solving Model in Mathematics Learnings for Ordinary students (수학 영재의 창의적 문제해결 모델(MG-CPS)을 일반학생의 수학 학습에 적용한 사례연구)

  • Kim, Su Kyung;Kim, Eun Jin;Kwean, Hyuk Jin;Han, HyeSook
    • The Mathematical Education
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    • v.51 no.4
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    • pp.351-375
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    • 2012
  • This research is a case study of the changes of students's problem solving ability and affective characteristics when we apply to general students MG-CPS model which is creative problem solving model for gifted students. MG-CPS model which was developed by Kim and Lee(2008) is a problem solving model with 7-steps. For this study, we selected 7 first grade students from girl's high school in Seoul. They consisted of three high level students, two middle level students, and two low level students and then we applied MG-CPS model to these 7 students for 5 weeks. From the study results, we found that most students's describing ability in problem understanding and problem solving process were improved. Also we observed that high level students had improvements in overall problem solving ability, middle level students in problem understanding ability and guideline planning ability, and that low level students had improvements in the problem understanding ability. In affective characteristics, there were no significant changes in high and middle level classes but in low level class students showed some progress in all 6 factors of affective characteristics. In particular, we knew that the cause of such positive changes comes from the effects of information collection step and presenting step of MG-CPS model.

A Study on the Effect by Self-oriented Learning in Group for Improvement of Problem-solving Ability - Gentered to the 2nd Grade curriculum of Middle School - (수학과 그룹별 자기 주도 학습이 문제해결능력 신장에 미치는 영향 - 중학교 2학년 과정을 중심으로 -)

  • 오후진;김태흥
    • Journal of the Korean School Mathematics Society
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    • v.4 no.2
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    • pp.115-123
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    • 2001
  • In its seventh revision to start in 2001, mathematics will have a new emphasis in the middle school curriculum. Mathematics subject is now composed of practical things in the use of mathematics. Also, the future of new generation, which has been known as the information age, places much focus on problem-solving in order to collect, analyze, synthesize, and judge various kinds informations. This demand of problem-solving ability is not only related with mathematical education but, along the entire educational process, its related to actual life. With this change of social structure, the importance of school education is increasing rapidly. Therefore, in order to grow abilities and create new knowledge, adapted this new method of self-oriented learning in groups to middle school 2nd graders for one year, the results were as follows : 1. Students developed their ability of the use of mathematical terms and signs correctly. 2. Students' mathematical knowledge and problem-solving ability improved as they had increased interest in mathematics. 3. Students' peership was enhanced through their communication and cooperative activities in groups during the class. 4. Students themselves were more willing to volunteer and participate during the class.

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Development and Application of Real-life Problems for Uplifting Problem Solving Skills - Focused on Geometry of Middle School Mathematics Curriculum - (문제해결력 향상을 위한 실생활 문제의 개발과 적용 - 중학교 수학과 교육과정의 도형 영역을 중심으로 -)

  • Pyo, Yong-Soo;Lee, Ji-Won
    • Communications of Mathematical Education
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    • v.21 no.2 s.30
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    • pp.177-197
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    • 2007
  • This study analyzes the theoretical background concerning problem solving, mathematization and real-life problems. Further it examines how middle school mathematics teachers and high school students of first grade recognize the real-life problems provides in textbooks concerning the area of geometry. Following those results found from this analysis, this paper reveals the issues and problems that we noticed through the analysis of real-life problems from textbooks, level 8 and level 9, Also we suggest the application of them along with the development of real-life problems for students' uplifting problem solving skills.

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The Effects of Middle School Mathematical Statistics Area and Python Programming STEAM Instruction on Problem Solving Ability and Curriculum Interest (중학교 수학 통계 영역과 파이썬(Python) 프로그래밍 융합수업이 문제해결력과 교과 흥미도에 미치는 영향)

  • Lee, Do-Young;Chung, Jong-In
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.4
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    • pp.336-344
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    • 2019
  • The Ministry of Education (2015) announced the "2015 Revised Curriculum for Elementary and Secondary Schools" and announced that SW (Software) training for elementary and junior high school students to develop Computational Thinking will be gradually introduced from 2018. In addition, 'problem solving' and 'programming' have become important areas. Furthermore, the ability to analyze and utilize big data is becoming more emphasized. We developed and applied the statistical - Python programming convergence curriculum based on the idea that convergence education combining information and mathematics, programming and statistical literacy is needed according to current trends. Before and after the experiment, problem solving ability test and programming / mathematical interest test were conducted and compared with the corresponding sample t-test. According to the analysis results, there were significant differences in the pre- and post-test on problem solving ability, programming interest and mathematical interest at the significance level of 0.05.

An Analysis of the Pre-service Teachers' Conceptions on Mathematical Problems (수학문제에 대한 예비교사의 인식분석)

  • Park, Mangoo
    • Education of Primary School Mathematics
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    • v.25 no.1
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    • pp.125-141
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    • 2022
  • The purpose of this study is to analyze how pre-service teachers perceive mathematics problems by making good mathematics problems at the elementary school level and applying them to elementary school students. In this study, 86 pre-service teachers enrolled in the second and third grades of A University of Education presented good mathematics problems they thought of. In addition, these pre-service teachers predicted the solution strategies of elementary school students for the proposed mathematics problem and described the teacher's expertise while observing the problem-solving process of elementary school students. As a result of the study, pre-service teachers preferred mathematical problems needed for using mathematical concepts or algorithms, motivation, and open-ended problems as good mathematics problems, and thought that students' in-depth observation and analysis experiences could help improve teachers' problem-solving expertise. In order to enhance teachers' expertise in solving mathematics problems, the researcher proposed for pre-service teachers to observe students' mathematics problem-solving processes, to experience in developing high-quality mathematics problems, and also to distribute high-quality mathematics problems linked to textbook problems.