• Title/Summary/Keyword: Dienes의 수학학습이론

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Review of Six Stages Theory of Learning Mathematics Suggested by Zoltan Dienes (Zoltan Dienes의 수학학습 6단계 이론의 재음미)

  • Kim, Soo-Mi
    • School Mathematics
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    • v.10 no.3
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    • pp.339-355
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    • 2008
  • This article tried to review the meaning and implication of six stages theory of learning mathematics suggested by Zoltan Dienes in "Building up Mathematics" in 1971. It was not much concretely known to Korean mathematics education society. In particular, there is no mathematical example which could cover all the stages to know what the theory tells. So this article focused on the example which Dienes developed for learning integers in 2000 to dig the theory. As a result, some critical aspects and problems of six stages theory were found. And finally educational implication was described.

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An Analysis of Example Spaces Constructed by Students in Learning the Area of a Trapezoid based on Dienes' Theory of Learning Mathematics (Dienes의 수학학습이론에 따른 사다리꼴의 넓이 학습에서 학생들이 구성한 예 공간 분석)

  • Oh, Min Young;Kim, Nam Gyun
    • Education of Primary School Mathematics
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    • v.24 no.4
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    • pp.247-264
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    • 2021
  • The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

The life and scholastic career of a New Math campaigner, Zoltan P. Dienes (새수학 운동가 Zoltan P. Dienes의 생애 및 연구 업적)

  • Kim, Soo-Mi
    • Journal for History of Mathematics
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    • v.22 no.3
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    • pp.153-170
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    • 2009
  • Zoltan, P. Dienes is a famous researcher and practitioner who has tried to teach mathematical structures to children for about 50 years. Even though his ideas of teaching mathematics and materials including MAB have been well known in Korea, they are only a part of his achievement he has developed for his whole life. So this article is designed for taking an overview of his whole life and achievement and getting some implications for today's mathematics education. In this article, his life story could be divided by five periods in terms of a scholastic career and his research achievement could be reorganized with respect to five theses: psychology of learning mathematics, mathematical curriculum, teacher education, games and material for mathematical learning. As a result, it is found that there is a deep connection between his personal life and his scholastic career.

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Analysis of Students' Mathematical Thinking Characteristics Appeared in the Process of Searching for All type of Triangle that Can be Made with Sphinx Puzzle (스핑크스퍼즐로 모든 삼각형 해법 찾기 과제에서 나타나는 학생들의 수학적 사고 특성 분석)

  • Bang, Sin Young;Song, Sang Hun
    • Journal of Elementary Mathematics Education in Korea
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    • v.17 no.1
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    • pp.165-184
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    • 2013
  • In order to utilize Sphinx Puzzle in shape education or deductive reasoning, a lesson employing Dienes' six-stage theory of learning mathematics was structured to be applied to students of 6th grade of elementary school. 4 students of 6th grade of elementary school, the researcher's current workplace, were selected as subjects. The academic achievement level of 4 subjects range across top to medium, who are generally enthusiastic and hardworking in learning activities. During the 3 lessons, the researcher played role as the guide and observer, recorded observation, collected activity sheet written by subjects, presentation materials, essays on the experience, interview data, and analyzed them to the detail. A task of finding every possible triangle out of pieces of Sphinx Puzzle was given, and until 6 steps of formalization was set, students' attitude to find a better way of mathematical deduction, especially that of operational thinking and deductive thinking, was carefully observed and analyzed.

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