• 제목/요약/키워드: mathematical understanding

검색결과 1,034건 처리시간 0.021초

일반화 과정과 그 정당화에서 '이해'의 완전성에 대한 연구 - 산술, 기하, 조화평균을 중심으로 (A study on the completeness of 'the understanding' in the generalization process and justification - centered on the arithmetical, geometric and harmonic average -)

  • 김창수
    • 한국수학교육학회지시리즈A:수학교육
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    • 제51권4호
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    • pp.377-393
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    • 2012
  • The understanding demands the different degree of the understanding according to student's learning situation. In this paper, we investigate what is the foundation for the complete understanding for the generalization in the generalization-process and justification of some concepts or some theories, through a case. We discovered that the completeness of the understanding in the generalization-process and justification requires 'the meaningful-mental object' which can give the meaning about the concept or theory to students. Students can do the generalization-process through the construction of 'the meaningful-mental object' and confirm the validity of generalization through 'the meaningful-mental object' which is constructed by them. And we can judge the whether students construct the completeness of the understanding or not, by 'the meaningful-mental object' of the student. Hence 'the meaningful-mental object' are vital condition for the generalization-process and justification.

수학 교과에서의 주목하기(Noticing)에 관한 이해 (The Understanding on the Noticing in Mathematics Education)

  • 김슬비;황혜정
    • East Asian mathematical journal
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    • 제37권4호
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    • pp.461-480
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    • 2021
  • There have been gradually a few studies on Noticing in the domestic and international area. For the purpose of increasing the concern on teacher noticing and pursuing the affluent studies on the noticing, this study tried to explore and understand the background, the meaning, and the properties of the teacher noticing while summing up the views of the various researchers. As a result, the teacher noticing could be defined as a cognitive process which is focused on mathematical objects, students' mathematical thinking, students' emotions, teaching strategies, classroom environment and interprets them to determine how to react. From this, noticing might be cognitive process which is a combined form of the objects and cognitive behavior, while the objects whom teachers notice covers up the mathematical objects and the teaching objects. Eventually, this study expects to serve as a basis to foster the in-depth understanding of teacher noticing and to derive the follow-up studies.

Constructive Evaluation of Definitions in a Dynamic Geometry Context

  • Govender, Rajendran;de Villiers, Michael
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제7권1호
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    • pp.41-58
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    • 2003
  • This study firstly examined 18 prospective secondary mathematics teachers' understanding of the nature of definitions and the use of the dynamic geometry software Sketchpad to not only improve their understanding of definitions, but also their ability to define geometric concepts themselves. Results indicated that the evaluation of definitions by accurate construction and measurement enabled students to achieve a better understanding of necessary and sufficient conditions, as well as the ability to more readily find counter-examples, and to recognize uneconomical definitions, and improve them.

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Understanding Statistical Terms: A Study with Secondary School and University Students

  • Garcia Alonso, Israel;Garcia Cruz, Juan Antonio
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제14권2호
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    • pp.143-172
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    • 2010
  • In this paper, we present an analysis of how students understand some statistical terms, mainly from inferential statistics, which are taught at the high school level. We focus our analysis on those terms that present more difficulties and are persistent in spite of having been studied until the college level. This analysis leads us to a hierarchical classification of responses at different levels of understanding using the SOLO theoretical framework.

수리논술형 문제에 대한 초등학교 5학년 학생들의 문제해결력과 수학적 정당화 과정 분석 (An Analysis of Problem-solving Ability and Mathematical Justification of Mathematical Essay Problems of 5th Grade Students in Elementary School)

  • 김영숙;방정숙
    • 한국수학교육학회지시리즈A:수학교육
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    • 제48권2호
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    • pp.149-167
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    • 2009
  • This study was aimed to examine problem-solving ability of fifth graders on two types of mathematical essay problems, and to analyze the process of mathematical justification in solving the essay problems. For this purpose, a total of 14 mathematical essay problems were developed, in which half of the items were single tasks and the other half were data-provided tasks. Sixteen students with higher academic achievements in mathematics and the Korean language were chosen, and were given to solve the mathematical essay problems individually. They then were asked to justify their solution methods in groups of 4 and to reach a consensus through negotiation among group members. Students were good at understanding the given single tasks but they often revealed lack of logical thinking and representation. They also tended to use everyday language rather than mathematical language in explaining their solution processes. Some students experienced difficulty in understanding the meaning of data in the essay problems. With regard to mathematical justification, students employed more internal justification by experience or mathematical logic than external justification by authority. Given this, this paper includes implications for teachers on how they need to teach mathematics in order to foster students' logical thinking and communication.

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알고리즘, 어떻게 가르칠 것인가\ulcorner (How to Teach Algorithms\ulcorner)

  • 조완영
    • 한국수학교육학회지시리즈A:수학교육
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    • 제39권1호
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    • pp.49-58
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    • 2000
  • The purpose of this study is to investigate how to teach algorithms in mathematics class. Until recently, traditional school mathematics was primarily treated as drill and practice or memorizing of algorithmic skills. In an attempt to shift the focus and energies of mathematics teachers toward problem solving, conceptual understanding and the development of number sense, the recent reform recommendations do-emphasize algorithmic skills, in particular, paper-pencil algorithms. But the development of algorithmic thinking provides the foundation for student's mathematical power and confidence in their ability to do mathematics. Hence, for learning algorithms meaningfully, they should be taught with problem solving and conceptual understanding.

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Paying Attention to Students and Promoting Students' Mathematics Understanding

  • Li, Miao;Tang, Jian-Lan;Huang, Xiao-Xue
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제12권1호
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    • pp.67-83
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    • 2008
  • Promoting students' mathematics understanding is an important research theme in mathematics education. According to general theories of learning, mathematics understanding is close to active learning or significant learning. Thus, if a teacher wants to promote his/her students' mathematics understanding, he/she should pay attention to the students so that the students' thinking is in active situation. In the first part of this paper, some mathematics teachers' ideas about paying attention to their students in Chinese high school are given by questionnaire and interview. In the second part of this paper, we give some teaching episodes about how experienced mathematics teachers promote their students' mathematics understanding based on paying attention on them.

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초등학교 수학 교과서에 제시된 용어 사용과 표현의 적절성 고찰 (A Note on Appropriate Use and Representation of Terms in Elementary School Mathematics Textbooks)

  • 백대현
    • 대한수학교육학회지:학교수학
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    • 제12권1호
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    • pp.61-77
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    • 2010
  • 수학 학습에서 수학 용어의 의미를 이해하는 것은 그것과 관련된 학습 내용을 이해하고 활용하는데 중요한 역할을 한다. 수학 용어의 의미를 잘 이해하기 위해서는 용어를 학생의 이해 수준과 언어 능력에 맞도록 적절하게 제시하여 일관성 있게 사용하고 표현하는 것이 필요하다. 본 연구에서는 초등학교 수학 교과서에 나타난 용어의 의미를 서술하여 사용하는 방식과 표현이 부적절한 사례를 수학적 관점과 일관성 관점에서 고찰하여 용어 사용과 표현의 적절성에 대한 시사점을 얻고자 한다.

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수학 우수아의 통계적 개념 이해도 조사 (An Investigation of Mathematically High Achieving Students' Understanding of Statistical Concepts)

  • 이경화;유연주;홍진곤;박민선;박미미
    • 대한수학교육학회지:학교수학
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    • 제12권4호
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    • pp.547-561
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    • 2010
  • 통계학은 학교수학의 일부분으로 포함되어 있지만 전통적인 수학과는 본질적으로 다른 점을 많이 가지고 있다는 연구결과가 보고되어 왔다. 그러나 통계 고유의 특징에 대한 교육 연구, 특히 학교수학의 다른 영역과 차별되는 통계적 개념 이해에 대한 실증적인 자료와 논의가 매우 부족하다. 그러므로 수학적 사고 능력과 통계적 개념 이해 능력이나 통계적 사고 능력 사이의 관계에 대한 논의가 거의 이루어지지 않았다. 이 연구에서는 통계적 사고의 근간을 이루는 몇 가지 핵심 개념들을 추출한 후, 수학적으로 우수한 능력을 갖춘 학생들이 이 통계적 개념들을 이해하는 정도를 조사하였다. 조사 결과, 수학적으로 우수한 능력을 갖춘 학생들이 자연스럽게 발달시킨 개념과 발달시키지 못한 개념이 있었다. 수학적 능력과 통계적 개념 이해 수준 사이에는 낮은 상관관계가 나타났다.

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다양한 표상활동 중심 분수학습이 분수의 이해 및 수학적 태도에 미치는 효과 (The Effect of the Fraction Comprehension and Mathematical Attitude in Fraction Learning Centered on Various Representation Activities)

  • 안지선;김민경
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제29권2호
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    • pp.215-239
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    • 2015
  • 본 연구는 다양한 표상활동을 중심으로 한 분수학습이 분수의 이해 및 수학적 태도에 미치는 영향을 알아보기 위한 것으로서 서울 소재 B초등학교 4학년 33명 전체학생을 대상으로 실시하였다. 활동적, 영상적, 상징적 표상활동으로 이루어진 분수학습을 6주간 15차시에 걸쳐 진행한 결과 관계적 이해에 도달한 학생들의 비율이 증가하였으며, 분수 학업성취도 검사 I, II, III에서 평균 90점 가까이 또는 그 이상의 높은 성취도를 보였다. 수학적 태도 변화를 알아보기 위해서 두 종속표본 t검정을 실시한 결과, 유의수준 .01에서 통계적으로 유의미한 차이가 있는 것으로 나타났다. 결론적으로 다양한 표상활동 중심의 분수학습은 학생들의 관계적 이해도와 분수 이해력을 향상시키고, 학생들의 학습지향성, 자기통제, 흥미, 가치인식, 자신감을 높이며, 불안감을 감소시키는 등의 수학적 태도면에서도 긍정적 영향을 미쳤다고 할 수 있다.