• Title/Summary/Keyword: mathematical problem solving

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A Case Study of Procedural and Conceptual Knowledge Construction in the Computer Environments

  • Lee, Joong-Kwoen
    • Research in Mathematical Education
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    • v.8 no.2
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    • pp.81-93
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    • 2004
  • This study investigated three preservice teachers' mathematical problem solving among hand-in-write-ups and final projects for each subject. All participants' activities and computer explorations were observed and video taped. If it was possible, an open-ended individual interview was performed before, during, and after each exploration. The method of data collection was observation, interviewing, field notes, students' written assignments, computer works, and audio and videotapes of preservice teachers' mathematical problem solving activities. At the beginning of the mathematical problem solving activities, all participants did not have strong procedural and conceptual knowledge of the graph, making a model by using data, and general concept of a sine function, but they built strong procedural and conceptual knowledge and connected them appropriately through mathematical problem solving activities by using the computer technology.

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The Effect of Picture Book Based Mathematical Activities on Mathematical Problem-Solving Performance in children (그림책에 의한 수학활동이 유아의 수학적 문제해결력에 미치는 영향)

  • Park, Seok Youn;Choi, Kyoung Sook
    • Korean Journal of Child Studies
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    • v.21 no.4
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    • pp.227-241
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    • 2000
  • This study investigated the effectiveness of mathematical activities based on picture books for the development of children's problem-solving performance. Subjects were 72 children divided in two groups of 36 each; one group had mathematical activities based on picture books and the other group had of pencil-and-paper tasks. The problem-solving performance was measured in terms of the test by Ward(1993) with a few modification for pretest and posttest. Mathematical activities were performed 12 times over a 6 week period. The data was analyzed by Analysis of Covariance(ANCOVA). The group taught by picture books significantly improved mathematical problem-solving performance.

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Instructional Design in All (K-3) Students' Mathematical Achievement in Solving Word Problems

  • Lee Kwangho;Niess Margaret L.
    • Research in Mathematical Education
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    • v.9 no.1 s.21
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    • pp.1-9
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    • 2005
  • This paper investigates instructional strategies with potential for improving students' achievement in word problem solving. This review compares and analyzes the direct instruction (DI) and cognitively guided instruction (CGI) research on K-3 word problem solving mathematics students in a demonstration of my position that teachers need to understand student mathematical thinking to enhance students' achievement in word problem solving. CGI provides a more appropriate instructional model than DI for teaching word problem solving. For example, student-centered, conceptual understanding, and children's informal or invented problem solving strategies communicating with each other mathematically, etc. Korean teachers and teacher educators need to consider implementing CGI teaching strategies.

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Individual Strategies for Problem Solving

  • Revathy Parameswaran
    • Research in Mathematical Education
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    • v.9 no.1 s.21
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    • pp.11-24
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    • 2005
  • Problem solving is an important aspect of learning mathematics and has been extensively researched into by mathematics educators. In this paper we analyze the difficulties students encounter in various steps involved in solving problems involving physical and geometrical applications of mathematical concepts. Our research shows that, generally students, in spite of possessing adequate theoretical knowledge, have difficulties in identifying the hidden data present in the problems which are crucial links to their successful resolutions. Our research also shows that students have difficulties in solving problems involving constructions and use of symmetry.

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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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Case Study : An analysis on Problem Solving Processes of Gifted Math Students (수학영재아의 문제해결 과정에 따른 사례 연구 - 수학적 사고능력을 중심으로 -)

  • Jung, Chan-Sik;Roh, Eun-Hwan
    • The Mathematical Education
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    • v.48 no.4
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    • pp.455-467
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    • 2009
  • During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The test questions are formulated into several areas of questioning-types which can reveal rather different result. The lower level questions are to investigate individual ability to solve multiple mathematical problems while using "mathematical thought." During problem solving, "mathematical thought process" is a systematic sequence of thoughts triggered between logic and insight. The scope of this case study is to present a desirable model in solving mathematical problems and to improve teaching methods for math teachers.

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Teachers Solving Mathematics Problems: Lessons from their Learning Journeys

  • Tay, Eng Guan;Quek, Khiok Seng;Dindyal, Jaguthsing;Leong, Yew Hoong;Toh, Tin Lam
    • Research in Mathematical Education
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    • v.15 no.2
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    • pp.159-179
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    • 2011
  • This paper reports on the learning journeys in mathematical problem solving of 21 teachers enrolled on a Masters of Education course entitled Discrete Mathematics and Problem Solving. It draws from the reports written by these teachers on their personal journeys: the commonalities and differences among them in terms of how they look at their own problem solving experiences, what language they employ in talking about problem solving, and what impact the course has on their views about problem solving. One particular aspect of problem solving instruction, a pedagogical innovation called the Practical Worksheet, is addressed in some detail. These graduate students are full-time mathematics teachers with at least two years of classroom experience. They include primary and secondary teachers.

Notes on "Perpetual Question" of Problem Solving: How Can Learners Best Be Taught Problem-Solving Skills?

  • Oleksiy, Yevdokimov;Peter, Taylor
    • Research in Mathematical Education
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    • v.12 no.3
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    • pp.179-191
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    • 2008
  • Although problem solving was a major focus of mathematics education research in many countries throughout the 1990s, not enough is known about how people best acquire problem-solving skills. This paper is an attempt to advance further development of problem-solving skills of talented school students through combination of some methods accessible from curriculum knowledge and more special techniques that are beyond curriculum. Analysis of various problems is provided in detail. Educational aspects of challenging problems in mathematical contests up to IMO level are, also, taken into account and discussed in the paper.

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Effects of Project Based Material on Problem solving Ability and Attitude of Mathematically Gifted in Science High School - Focusing on Probability and Statistics - (주제탐구형 자료가 과학고 수학영재의 문제해결 및 태도에 미치는 효과 - 확률.통계 영역을 중심으로 -)

  • Lee, Jong-Hak
    • The Mathematical Education
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    • v.50 no.4
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    • pp.467-487
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    • 2011
  • The purpose of this study is to analyze of gifted students' improvement on mathematical attitude and problem-solving ability through project-based materials in science high school. For this study, research questions are established as follows. 1. Does the project-based materials-used instruction have a positive effect on improving problem-solving ability? 2. Does the project-based materials-used instruction have a positive effect on improving mathematical attitude? To solve these research questions, this study employed a survey and interview type investigation for gifted students' mathematical attitude and problem-solving ability. A subject of classes were randomly selected among the 11th grader in D science high school and designated one class as the experimental group and the other class as the control group. Twelve hours of the project-based materials-used instruction and the traditional textbook-oriented instruction had been carried out in each class. Findings on this study are as follows: First, the project-based material-used instruction is shown to be more effective in enhancing problem-solving ability than the traditional textbook-oriented instruction. Second, the project-based material-used instruction is shown to be more effective in improving mathematical attitude than the traditional textbook-oriented instruction.

Ability to Shift a Viewpoint and Insight into Invariance in Stage of Mathematical Problem Solving Process (수학 문제 해결 과정에서 사고(발상)의 전환과 불변성의 인식)

  • Do, Jong-Hoon
    • The Mathematical Education
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    • v.48 no.2
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    • pp.183-190
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    • 2009
  • This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

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